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Figure 24. The new Xh Yh coordinate system In order to study the Distanced Hexagon Coloring problem, we consider a new Xh Yh coordinate system based on hexagon centers in H. Axes of the Xh Yh coordinate system are inclined at 600 and its two unit vectors are i(^, 0) and ( 3), as shown in Figure 24. Each hexagon h e H in Xh Yh coordinate system can be identified by coordinates of its center as h(i,j). The Euclidean distance between two hexagon centers h(ii,ji) and h(i2,j) is given as v3 (i i2)2 + (i 2)l ) + i J,2)2. The Euclidean distance of a hexagon center h(i,j) from the origin h(0, 0) is given as v /2 +j + j2. As the first step to provide the solution for Distanced Hexagon coloring problem, we identify the closest hexagon h(i,j) to h(0, 0) in the first quadrant of Xh Yh plane, such that two closest points, pi in h(0, 0) and p2 in h(i,j) are at least at a distance deR+. We observe that closest points pi and P2 can appear in three ways as shown in Figure 25: * pi is the upper right corner of h(0, 0) and p2 is the lower left corner of h(i,j), in Figure 25 (i = 3,j = 5). p is the mid point of upper right side of h(0, 0) and p2 is the mid point of lower left side of h(i,j), in Figure 25 (i = 0,j = 7). 1.2 Efficient InNetwork Detection and Tracking of Dynamic Phenomena Contemporary wireless sensor network (WSN) research done in the area of detection and tracking has primarily concentrated on observing motion of objects whose shape and size are invariant [4143]. However, many reallife events such as oil spills, gas clouds, or random walking motion of people, henceforth called Phenomena Clouds, are characterized by nondeterministic, dynamic temporal variations of cloud shape, size and direction of motion along multiple axes. These events cannot be modeled in welldefined terms. Thus, it is difficult to apply existing mechanisms in such situations. Furthermore, the utility of phenomena cloud detection and tracking is not restricted only to application domains involving gas clouds or oil spills. In fact, they can also be utilized in situations where the quality of data originating from individual sensors cannot be trusted in isolation. In such cases, the raw sensor data originating from the system is typically extremely noisy which makes it very difficult to distinguish actual events from random stimuli. Hence, a quorum of multiple sensors, which are located in close proximity to each other, is required to reduce the probability of false positives. Through our collective research and systems experience over the years in building Smart Spaces at University of Florida's Mobile and Pervasive Computing Laboratory, we have found a significant utility in applying the phenomena cloud concept for efficiently and accurately monitoring various events in the space, such as detection of barefoot walking, which is a critical application for diabetes patients. With a new application and broader concept of phenomena clouds, early studies on boundary detection and tracking of welldefined shapes are no longer sufficient [12, 13, 19, 44, 45]. Only one work recently studied on similar applications, called NilePDT (a streambased mechanism) may be applicable [46]. However, this centralized approach does not take into account the cost of acquiring and transmitting sensor readings and typically requires participation from all sensors in the network. Unfortunately, sensor sampling costs and networking and processing overheads can have a critical effect 4. Providing a novel localized algorithm, called Optimized Density Algorithm (ODA) which can further enhance the resource utilization based on a new technique, called hexagon tiling. This new algorithm locally allows sensor nodes to be in active or sleeping modes without compromising on the quality of detection and tracking. 5. Presenting a practical application which has been deployed in a realworld smart space and utilizes the phenomena detection and tracking mechanism described in this paper, to solve critical challenges faced during its deployment. 6. Validating our approaches using both realworld applications and simulations to analyze their performances as compared to streambased approaches [46]. The remainder of this paper is structured as follows. Section 5.2 describes the phenomena clouds, their characteristics along with the critical challenges and analyzes their structures using the set of proposed parameters. Our first innetwork detection and tracking algorithm, including its fault tolerance mechanism, is proposed in Section 5.3. In Section 5.4, we optimize the power consumption and resource utilization, on which we formulate an integer program for detection and tracking of a phenomena cloud and propose a localized protocol based on the hexagon tiling technique. Section 5.5 presents an interesting practical realworld application of our phenomena detection and tracking algorithm in the smart space. Section 5.6 provides evaluation and analysis of the performance of our approaches through reallife experiments and simulations. Section 5.7 provides the overview of the existing literature. Finally, Section ?? concludes the paper with some future work. 5.2 Phenomena Cloud: Challenges and Representation A phenomenon cloud can be defined as a manifestation of a number of simultaneous events reaching critical mass and spanning a contiguous space. As such a phenomenon expands, shrinks, or translates randomly in a nondeterministic fashion over the time, its shape, size and direction of movement either cannot be anticipated accurately or have models which are usually too complex for realtime computing 6 LOCALIZED ENERGY EFFICIENT DETECTION AND TRACKING OF DYNAMIC PHENOMENA BOUNDARY ............................. 126 6.1 Introduction ................................... 126 6.2 System Model ................... .............. 128 6.3 Detecting and Tracking of Dynamic Phenomena Boundary . . . ... 128 6.4 Localized Clustering and Data Aggregation . . . . . . .... 134 6.5 Performance Evaluation ............................ 136 6.6 C conclusion . . . . . . . . . . . . . . . . . 14 1 7 CONCLUSION ... ............. .. .............. ... 142 REFERENCES ................ ................... ..145 BIOGRAPHICAL SKETCH ............. ..... .............. 151 delay constraint distributed protocols in WSNs such as route discovery, service discovery, broadcasting updates etc, which require data promulgation. In contrast, data aggregation is performed to efficiently collect the sensed information from all sensor nodes at a sink node or a base station for further processing or forwarding. A WSN can be closely modeled using a graph G = (V, E), where the vertices in set V represent network nodes and edges in set E represent the communication links. The data broadcast in wireless network has been studied using different kinds of graph models with an objective to minimize the broadcast latency. The theoretical lower bound on minimum latency is the radius R of the network with respect to the source node vs E V. In [24], Chlamtac et. al. proved that the minimum latency broadcast schedule problem is NPhard for general graphs. There are several additive [25],[26], and multiplicative [27], [28], [24],[29] approximation algorithms proposed for this problem in general graphs. In [30] Elkin et. al. proved that the minimum latency broadcast scheduling problem cannot have an Q(logn) multiplicative approximation unless NP c BPTIME(n'(loglogn)). In [31], they also proved that it is impossible to have an opt(G) + log2(n) additive approximation algorithm unless NP c BPTIME(no(loglogn)). However, for wireless networks, restrictive graph models such as Unit Disk Graphs (UDG) and Disk Graphs (DG) in 2D and Unit Ball Graphs (UBG) and Ball Graphs (BG) in 3D, are more suitable. The UDG and UBG models a wireless network whose nodes have the same transmission range, the DG and BG models the wireless networks where the nodes have different transmission ranges. In [15], Gandhi et. al. studied the broadcast scheduling problem in Disk Graph (DG) and proved that the minimum latency broadcast scheduling problem is NPhard. In [32], Scott et. al. presented a solution for UDG, using the geometric property of UDG they prove a lower bound of 16R 15. Further, they extend the pipelined broadcasting algorithm in [33] for general graph to UDG and get a lower bound of R + O(log(R)). The pipelined broadcast algorithm in [33] is based on standard ranking algorithm [34] the same transmission range or their transmission ranges are equal to their interference ranges. These assumptions are not practical. Furthermore, they entirely ignore the existence of WSNs in 3D. Most of the existing research on phenomena detection and tracking using WSNs assume the phenomena are invariant in shape, size and motion. However, in real life there exist dynamic phenomena such as oil spills, mud flow, diffusion or leakage of gases, which are characterized by nondeterministic variations in shape, size and direction of motion. These dynamic phenomena are termed as phenomena cloud. Due to the absence of any well defined model for phenomena clouds, their detection and tracking through WSNs is extremely challenging. Since sensor nodes have limited energy and processing power, the efficient detection and tracking of phenomena cloud with an objective to maximize network life time is a challenging optimization problem. The focus of this dissertation is mainly on following two imperative optimization problems: 1. Efficient data broadcasting and aggregation. 2. Efficient detection and tracking of dynamic phenomena. The main contributions of this dissertation are: 1. A constant approximation algorithm for broadcast scheduling in WSNs, which has the state of the art approximation ratio. 2. The first constant localized approximation algorithm for broadcast scheduling in WSNs. 3. The first constant distributed approximation algorithm for alltoone data aggregation. 4. The first constant distributed approximation algorithm for alltoall broadcast scheduling. 5. A localized innetwork algorithm for detection and tracking of phenomena cloud. Algorithm 8 Supplier Identification Algorithm: Runs locally on all v e V. INPUT: A set L = {(v, C,) Iv, e HN(v)}, where C, is the set of colors in the neighborhood of node v, E HN(v). OUTPUT: Set of ordered pairs of Supplier nodes for v's hexagon and the respective neighboring colors they cover to receive broadcast message. Ch UviHN(v) Ci Supplier = while Ch d o do Select a node v, e L covering maximum colors in Ch (break the ties on the basis of smaller id). C, = Set of colors in Ch that are covered by vi. Supplier Supplier U v,, C,' Ch Ch\ C: end while Return Supplier Epoch, Epoch, Trrice .,_ Select time Receive time Figure 34. An Epoch some Epoch assigned to its hexagon, the source node vs e V initiates the broadcast by transmitting the message m to all nodes in its hexagon. As shown in Figure 34, each Epoch is divided into two parts EpochR and EpochT. EpochR is primarily used by a Supplier node in a hexagon for receiving the broadcast message from one of its Provider nodes. Further, it uses EpochT for broadcasting the received message to all other nodes in its hexagon. EpochR is further divided into two parts; Select time and Receive time. Select time for a hexagon is divided into smaller time slots called Trices, equal to the number of Supplier nodes in it. These Trices are allocated to Supplier nodes in increasing order of their ids. During its corresponding Trice, a Supplier node broadcasts a Request Message to all its Providers neighbors and if any of them have earlier received the broadcast message m, they respond with Response Messages. As Response Messages are by sensor networks, which largely consist of lowend nodes with limited processing capabilities. Examples of phenomena clouds include gas clouds, floods, oil spills, wild forest fires or even movement of tourists in a museum. 5.2.1 Major Challenges The major challenges that are faced during detection and tracking of phenomena clouds are as follows: 1. Initial detection of phenomenon. Initial occurrences of the phenomenon might be scattered throughout the space. Detection therefore must be attempted at multiple locations. 2. Avoiding false positives. The probability of a single sensor outputting accurate readings at a specific point in time is very low. It is quite possible for a sensor to temporarily malfunction or be subject to environmental conditions which might cause it to output values which incorrectly indicate the occurrence of a phenomenon. Thus detection must require inputs from multiple sensors located closely to each other. 3. Tracking a phenomenon in realtime. A phenomenon can suddenly grow or shrink in size and also move in multiple directions simultaneously. Therefore, tracking it in realtime can become a massively complex task. To enable costeffective realtime tracking, the rate of status updates from the sensor network to the user needs to be kept at a minimum to reduce network cost and processing overhead. 4. Operating under harsh conditions resulting in disconnected operation: Hostile phenomena like fires can lead to disruption of communications between the sensor network and the base station. Therefore, the detection and tracking process should be able to operate in an autonomous manner without requiring remote supervision. 5.2.2 Representation In this section, we propose a set of parameters to formally describe the structure of phenomena clouds. We represent a phenomenon cloud as a 5tuple, P = (a, b, PT, m, n). The lower and upper bounds of the range of sensor values which 6. Validating our approaches using both realworld applications and simulations to analyze its performance and resource requirements as well as comparing it with that of streambased approaches. Furthermore, in Chapter 6, we provide an energy efficient localized in network detection and tracking protocol for tracking the boundary of the phenomena cloud. This protocol is more relevant for scenarios such as oil spills, gas leakage, etc, where it is more sensible to detect and track only the phenomena boundary engulfing the affected area instead of tracking the entire phenomena. Simulation results are provided to show that the proposed protocol is more efficient than the existing works.Finally, in Chapter 7, we provide a brief summary of this dissertation and conclude it. Case 2: Assume that the transmissions of two Supplier nodes, Vsup, and Vsup2 are interfering (which occurs if they are transmitting at the same time during the EpochT of an Epoch). This is possible only if vsup, and v,,p2 belong to the same color hexagons. This give rise to two possibilities: 1) Both v,,up and V,,p2 are in the same hexagon, in this case v,,~p and s,,p2 cannot be scheduled to transmit at the same time, hence, this is a contradiction. 2) v,,up and Vsup2 are in different hexagons of same color. In this case the distance between v,,up and Vsup2 is at least (a 1)rTax and according to Lemma 1 they cannot interfere each other. O Theorem 3.1. The approximation ratio for localized broadcasting algorithm for the IABS problem in 2D WSN is 2 a/ + ] 2. Proof. The theoretical lower bound of lABS problem is R, i.e. the radius of the network with respect to the source node. For comparing the latency of localized algorithm with the theoretical lower bound, we consider the BFS tree of the graph G = (V, E) rooted at vs, which divides the network into layers L1, L2 ..., LR. According to our localized algorithm, within (3l/ + 1]2 Epochs, all nodes in hexagons in which nodes in layer L2 are located will receive the message m from the hexagon in which the source node v, c L, is located. And within next (a 312 + 1 Epochs, nodes in all hexagons in which nodes in Ls are located will receive the broadcast message m from hexagons in which nodes in L2 are located, and so on. After (R 1) L(a1)/3 +12 Epochs nodes in hexagons in which nodes in LR are located will receive the message m. As each Epoch has two time slots EpochR and EpochT during which the broadcast message is transmitted, hence, the broadcast latency of the localized algorithm is 2(R 1) ()+ 1 2. Thus, the approximation ratio is 2 l/3 + 1]2. 3.2.4 Localized Broadcast Scheduling Algorithm in 3Dimension The localized broadcast scheduling algorithm can be applied to 3D WSNs, if we consider the 3Dspace is partitioned into truncated octahedrons of sides r forming a 10i 6. R6: Potential Candidate > Idle: A potential candidate transitions into an idle sensor if all of its neighbors are either potential candidates or idle, that is, none of its neighbors is in the candidate category or tracking category. 5.3.4 Initial Selection of Potential Candidate Sensors The main goal of this stage is to detect initial occurrences of phenomena clouds. A phenomenon cloud can manifest itself in multiple locations simultaneously, hence, monitoring one particular location is not adequate. However, in the interest of conserving network resources and power for the entire sensor grid, we cannot require each and every node to monitor its readings. A compromise between the two approaches can be followed where specific sensors are directly chosen to be potential candidates by the centralized query processor. The criterion for such a selection can be based on the location of nodes or past history of their readings. For example, if we are planning to detect gas leaks in a pipeline, it might be useful to choose the sensors located at the valves and joints to be the initial set of potential candidate sensors since the probability of a leak getting started at those locations is higher. We used this criterion in the Smart Floor application described in Section 5.5, where sensors located near doorways are selected as initial potential candidates so that whenever a person enters the room, the system is immediately able to pick up their presence and commence the detection and tracking process to monitor their movement. Another criterion can be the offline use of an available mathematical model of the phenomenon cloud to determine locations where the probability of occurrence is the highest. In case such a criterion is hard to formulate, alternatively the system can randomly select sensors as initial potential candidates such that they are uniformly distributed over the sensor space. These sensors and their respective neighborhoods can be viewed as autonomous clusters of early warning systems for detecting the sudden manifestation of possibly multiple phenomena clouds. Since sensor deployment patterns tend to be highly application and phenomenonspecific, we do not go into details of their deployment. For purposes of Lemma 14. The distributed alltoall broadcast is interference free. Proof. The proof is similar to Lemma 11. D Lemma 15. The latency to disseminate the aggregated data from sink vs to all the other nodes is 2 V L(+l + +2 2R 1(+l3 12 Proof. In 2k = 2 2(/3 + 1 time slots at least one message is received by all nodes in 52 from the sink node in 51. So, in at most 2 VI ( 3 + 2 time slots, all the  V messages will be received by all the nodes in 52 from the sink node in S1. During this time at least I VI 1 messages must be received by all nodes in 5s from the nodes in 52, similarly nodes in 54 must have received I V 2 messages from the nodes in S3 and so on. Finally the last message will take at most 2(R 1) (l + 1 time slots to reach to all the nodes in 5R. Hence, the total latency for disseminating the data of all the nodes from sink to all the nodes is 2  VI (+i) + 1]2 (2R 1 + ]2. /V3/2  R 3/2  Lemma 16. [51] The lower bound of all to all broadcast is I V + R 1. Theorem 4.2. The approximation ratio of the distributed protocol for all to all broadcast is 4[(+)3/ + l]2 Proof. From Lemma 13 and 15, we have the latency of alltoall broadcast scheduling is 4 V (al3 + 12 + 2R (al/ + 1 2, and compared to the lower bound, we have the approximation ratio 4 13/ + l 2. O 4.5 Experimental Evaluation In this section, we present the experimental evaluation of our proposed algorithms through simulations. We ran our algorithms on randomly generated network topologies and evaluated them in terms of experimental approximation ratio (which is the ratio of the experimental latency to the theoretical lower bound). We studied the behavior of our 80 / r rT T r T  T r 'A GHA ' ApproxAlgo S40 v LocalizedAlgo 20. 20 ____. _, .__ _ _ __ 1 1.5 2 2.5 Alpha Figure 311. Effect of a on Average Latency 1.0 to 3.0 with an increment of 0.1 to closely monitor its effect. For every value of a we generate 100 network instances and average respective latencies produced by our algorithms. Figure 311 shows that a has an effect similar to 3 on Localized Algorithm. This can be explained as the number of colors needed to color the hexagon tiling is directly proportional to a, so a has a direct impact on the latency of Localized Algorithm. Further, in Figure 311 we see that there are not much variations in the latency of Approximation Algorithm on changing a. This is because a does not have any effect on the BFS height of the network, it only increases the interference range of a node. As we know that in case of Approximation Algorithm, in a given time slot the transmissions are considered within two consecutive BFS layers but not in the entire network, therefore, the effect of a on broadcast latency is not noticeable. In case of GHA, we see a gradual increase in latency with respect to a. This is the direct effect of increase in interfering transmissions with increase in a. Figure 312 compares the performance of various heuristic algorithms, based on different criteria used for scheduling various interfering transmissions. For each criterion, the average optimality ratio over all the 11, 000 sample graphs is listed. It is interesting to see that many of chosen optimization criteria actually degrade the performance of the algorithm. This is because the criteria which are based on the topology of the 250 DistAilToAII Experimental Ratio S 200 LocAIIToAll Experimental Ratio  e Theoretical Ratio . 150  oo 501 0o   50 100 150 200 250 300 350 400 450 # of Sensor Naod in WSN Figure 41. Effect of No. of Nodes on Average Experimental Approximation Ratio of AlltoAll data broadcasting Algorithms. algorithms based on three important parameters: 1) number of sensor nodes in the WSN, 2) 3 and 3) a. 4.5.1 Results for Varying the Number of Sensor Nodes In this set of experiments, we placed the sensor nodes in a square area of sides 500m. We considered a = 2, rn = 100m and rnMax = 200m (i.e. /3 = 2). We varied the number of sensor nodes I VI from 10 to 500, with an increment of 10. For every value of I VI we ran all algorithms on 100 randomly generated network topologies and averaged their results. Figure 41 shows the effect of number of sensor nodes in the WSN on alltoall data broadcasting. We observe that the performance of the localized alltoall broadcast algorithm is always better than the distributed one. The main reason for this is that in case of distributed alltoall broadcast algorithm all the messages are first aggregated at the sink node vs. And then from there they are further disseminated to all other sensor nodes. This may result in bottlenecks on the paths from various sensor nodes to vs, causing higher latency. We observe that as the number of nodes in WSN increases, the curves for both the algorithm tends to become constant. This can be explained as, after increasing number of nodes to a certain extent, the diameter of the WSN starts decreasing and becomes almost constant after certain number of nodes. This results in almost same number of hops a message needs to travel the distance between the most distant node. 534 Active Sensors during Epoch t10, for ODA. . . . . . . . ... . 118 535 Active Sensors during Epoch t15, for DistPDT. . . . . . . . . .. 118 536 Active Sensors during Epoch t15, for FDA. . . . . . . . ... . 118 537 Active Sensors during Epoch t15, for ODA. . . . . . . . . . .. 118 538 Active Sensors during Epoch t20, for DistPDT. . . . . . . . . .. 118 539 Active Sensors during Epoch t20, for FDA. . . . . . . ... . . 119 540 Active Sensors during Epoch t20, for ODA. . . . . . . . . . .. 119 541 Percentage of holes generated wrt percentage of update messages lost . . 120 542 Detection and Tracking with 5% update message lost for FDA. . . . ... 125 543 Detection and Tracking with 5% update message lost for ODA. . . . ... 125 544 Detection and Tracking with 10% update message lost for FDA. . . . ... 125 545 Detection and Tracking with 10% update message lost for ODA. . . . ... 125 546 Detection and Tracking with 15% update message lost for FDA. . . . ... 125 547 Detection and Tracking with 15% update message lost for ODA. . . . ... 125 61 Classification of Sensor Nodes in the WSN . . . . . . ... . . 129 62 Types of Nodes in the WSN ........... .. .............. 129 63 Types of messages in the WSN ......................... 130 64 The Transition Rules .. . .. . .. . .. . .. . .. . .. . .. . 130 65 State Transition Diagram for a Sensor node . . . . . . . .... 131 66 Expansion of the phenomena cloud . . . . . . . ..... ...... 131 67 Shrinking of the phenomena cloud . . . . . . . ..... ........ 133 68 Xh Yh coordinate System for Hexagon tiling H . . . . . . . . 134 69 Data aggregation based on clustering generated by the hexagonal tiling . . 136 610 Power consumption specifications for a sensor node . . . . . . . 136 611 Comparison based on number of boundary nodes. . . . . . . . . 137 612 Comparison based on number of update messages. . . . . . .. . 137 613 Comparison based on energy consumption. . . . . . . ... . . 137 some set Si and receives messages from some Transmitter node in set Si,+, or 2) when v acts a Transmitter node and collects messages from other nodes in its hexagon. The Forward queue shrinks: 1) when v forwards messages to its respective Transmitter node or 2) when v acts as a Transmitter node and forwards message to its Collector. During the EpochR of the allocated Epochs, nodes in all hexagons attempt to transfer one message from their Forward queue to the Forward queue of their Transmitter node using RoundRobin scheduling based on increasing order of their ids. The Transmitter node then during the EpochT forwards a message from its Forward queue to its Collector, which is one hop closer to vs. In this manner the data messages are aggregated from all nodes to the sink node vs on multihop paths without interference. Lemma 10. Two Transmitter nodes in two different hexagons with the same color cannot have the same Collector. Proof. Assume that two Transmitter nodes vtj and vt2 in two different hexagons of same color have same Collector node v,. For this vc has to be in transmission range of vti and vt2. According to the triangular inequality, the Euclidean distance d(vtj, vt2) between vt~ and vt2 will be less than or equal to d(vl, v,) + d(vt2, Vc) < 2rTx, this is a contradiction, as the d(vtl, Vt2) > (a 1)rmax, where a > 1. D Lemma 11. The data aggregation from all the nodes to the sink is interference free. Proof. The Transmitter node in different hexagons are scheduled to receive and forward messages based on hexagon coloring. As a result of which they satisfy the sufficient conditions for interferenceawareness. Therefore, interhexagon interference cannot exist. Further, only a single node can transmit to its Transmitter node during the EpochR of the Epoch allocated to its hexagon. Hence, there cannot be intrahexagon interfere. Consequently, there is no interference while aggregating data from all the nodes to the sink node vs. O Lemma 12. Messages from all nodes are eventually aggregated at the sink vs. Proof. Every MIS(Lj) node is assigned the color of the truncated octahedron in which it is located. Consequently, the maximum number of colors assigned to MIS(Lj) nodes are bounded by the number of colors needed to color the truncated octahedron tiling. As described in section 2.4, when truncated octahedrons tiling the 3D space have side length for a distance d = (m 1) = (n 1) the m2ncoloring algorithm uses [m]2 [n] colors. Therefore, when truncated octahedrons of side length tile the 3D space, [m]2 [n] colors can be used for d = (m 1)rn = (n 1)r,Tn 5. Base on Lemma 1, d is (a + )rlx. Consequently, we have m = (a + 1)/3 1 and n = (a 1)/3 1. Hence, the number of colors needed are bounded by F j(a+ 1)+l] 2 !(a+ 1)3+l D Theorem 2.4. The BSA algorithm provides an approximation ratio 2 [L ( 1)/ + 1) 2 1J (oL) 1)+ for IABS problem in 3D WSNs. Proof. In the first phase, the ISA takes (a + 1)3 I+ 2 (a + 1) + 1 time slots to schedule all nodes in MIS(Lj) to receive the broadcast message m from their parents in Li without interference. Similarly, in the second phase, it takes another [( (a 1)3 + 1]2 !(a 1) + 1] time slots to schedule all nodes in MIS(Lj) to transmit the broadcast message m to nodes in Lj \ MIS. Hence, it take total 2 /(a 1)/ 1]2 l [/(a 1)/ 1] time slots to transfer the broadcast message m from Li to Lj. BSA runs R 2 iterations of ISA, so, the total number of time slots needed or the broadcast latency of BSA is given as: 1 +(R 2)2 !(a 1)3 1 j(a 1)3 1] Furthermore, the theoretical lower bound of the broadcast scheduling problem is R. Hence, the approximation ratio is: 2 j,(oa 1)/3+ 11 2[(a 1)/ + I]. 500 , DistAIIIITAll Epeirneial Rato  LDCEIITa.:i II EaFrimenial R DaO * ** 400 TI* m I,cal I Rallo ...4 . S I g 300 . S2 ..2.0 0 , , .. , 0 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Figure 47. Effect of a on Average Experimental Approximation Ratio of AlltoAll data broadcasting Algorithms. 4.5.3 Results for Varying a In this set of experiments, we placed 300 nodes in a square area of sides 500m. We considered, rT, = 100, rTax = 200 (i.e. = 2) and varied a from 1.0 to 3.0 with increment of 0.1 to closely monitor its effect. For each value of a we ran all algorithms on 100 randomly generated network topologies and averaged their results. Figure 47 shows the plots of localized alltoall data broadcast and distributed alltoall data broadcast. We observe that both the plots do not show much variation on increasing a. This can be explained by the fact that increasing a does not affects the diameter of the graph, which remains constant for same number of nodes. Hence, the experimental approximation ratio remains the same. Figure 48 and 49 shows the plots of alltoone data aggregation and onetoall data broadcasting on varying a. The plots are similar to the plots of localized and distributed alltoall broadcast and can be explained in the similar manner. In our experimental evaluation, we observed that the factors such as number of nodes in the network and /, that directly affects the diameter of the network, have reasonable impact on the latency of data broadcasting and aggregation in WSNs. Further, we observed that our algorithm shows a much better performance in comparison to their proposed theoretical bounds. 2.6693 2.2665 2.7656 3.5419 6.015( 217 187 227 291 50( 101 71 111 195 50( Figure 530. Comparison based on overall 5 TTO E 'u i: : 0 ;. : . .... . .. ", . 1,0 :.: .: :. : .: : : : *. .. 100 200 300 400 500 meters Figure 531. Snapshots of expanding phenomena cloud during Epochs t1o, t15, t20. Epochs 500 400 E2 300 E 200 100 n  * Pot. Candidate * Candidate * Tracking 100 200 300 400 500 meters Figure 532. Active Sensors during Epoch to1, for DistPDT. 526529 provide an epochwise comparison whereas Figure 530 summarizes the results overall the 5 epochs. As can be seen, StreamPDT uses 62.5% more active nodes in comparison to the IP solution. DistPDT improves the result by using 35.74% more active sensors compared to the IP solution. FDA further improves the solution by using only 17.62% more active nodes compared to the IP solution. And as expected, ODA shows the best performance and only uses 13.82% more active nodes in comparison to the optimal solution. In terms of the number of update messages sent to the CQP, StreamPDT shows the worst performance by generating 88.2% more update messages than the IP solution. DistPDT shows considerable improvement by generating 40% more update messages 117 =2(IS1 2+ + SRI) (a3l + 1i =2 V1 +l/a 3 12 time slots. Theorem 4.1. Distributed alltoone data aggregation scheduling algorithm has an ap proximation guarantee of 2 L(3 + 1 2 Proof. The trivial theoretical lower bound for alltoone data aggregation is IV 1. And, according to Lemma 13, the latency of all to one data aggregation of the distributed protocol is 2  V 1 \I(+ 1)3 hence, the approximation ratio is 2 L(a+31 + 2. D 4.4 Distributed AllToAll Broadcast Scheduling Algorithm The distributed protocol for alltoall broadcast scheduling works in two phases. In the first phase, the date messages from all the nodes are aggregated at the sink node vs. In the second phase, vs distributes all the messages it received in the first phase to all the nodes in WSN. For the first phase the distributed scheduling protocol for alltoone data aggregation can be used. After all the messages are collected in the first phase, in the second phase the scheduling of distribution of the data messages received from all nodes at the sink nodes vs is performed as follows: When the sink node vs e S receives all the IV 11 messages, the Forward queues of all the Transmitter nodes are empty in all the hexagons and are ready to receive messages from their respective collectors to broadcast them to nodes in their hexagon during the allocated Epochs. Now the sink node in S starts broadcasting one message in every Epoch allocated to its hexagon. As a result of this in every k2 Epochs one message is received by all nodes in 52. The Transmitter nodes in S3 after k2 Epochs will start scheduling themselves to receive a new broadcast message from their Collector in 52 during the EpochR and broadcast it to all the nodes in their hexagon during the EpochT of the allocated Epoch. Similarly, the Transmitter nodes in S3 receive and broadcast the messages from their Collectors in 52 and so on. This pipelining is followed till all the nodes in the network receive all the IV 1 messages. 511 512 513 514 515 516 517 518 519 Clustering on the basis of hexagon lattice . . . . . . . Gator Tech Smart House ....................... Smart Floor Tile with force sensors and Atlas Platform Node . . Ripple Effect of a Foot Step on the Smart Floor . . . . . . Walking motion as a Phenomena ................... Effect of varying n with pT = 0.4 and m = 150 . . . . . . Effect of varying pT with n = 3 and m = 150 . . . . . . . Effect of varying m with n = 3 and PT = 0.4 . . . . . . . Power Consumption Specifications for Atlas . . . . . . . 520 Epochwise comparison based on number and tracking process. ........... 521 Epochwise comparison based on number Centralized Query Processor (CQP) . . f active nodes involved in f update messages send . . . . . . . . 522 Epochwise comparison based on number of messages exchanged between onehop neighbors to implement the algorithms . . . . . . . . . 523 Epochwise comparison based on the Energy Consumption . . . . . 524 Comparison based on overall 50 Epochs . . . . . . . ... . . . 525 Comparison based on different grid size . . . . . . . . . . 526 Epochwise comparison based on number of active nodes involved in detection and tracking process . . .. . .. . .. . .. . .. . .. . .. .. 527 Epochwise comparison based on number of update messages send to the Centralized Query Processor (CQP) . . . . . . . . . . . . 528 Epochwise comparison based on number of messages exchanged between onehop neighbors to implement the algorithms . . . . . . . . . 529 Epochwise comparison based on the Energy Consumption . . . . . 530 Comparison based on overall 5 Epochs . . . . . . . . . . . 531 Snapshots of expanding phenomena cloud during Epochs t10, t15, t20. ..... 532 Active Sensors during Epoch t10, for DistPDT. . . . . . . . . . 533 Active Sensors during Epoch t10, for FDA. . . . . . . . ... ... . . . . 102 . . . . 102 . . . 103 . . . 103 . . . 104 . . . 104 . . . 107 . . . 108 . . . 109 . . . 110 detection to the 112 112 112 112 113 115 116 116 116 116 117 117 117 118 5.3.9 RealTime Monitoring by Applications The centralized query processor continuously maintains the Phenomenon Set at any given time. The query processor is able to track phenomenon clouds in realtime, with minimum processing and networking overhead of receiving updates from the sensor nodes. The Phenomenon Set is only updated whenever a sensor transitions to or from the tracking category. Hence, the query processor only requires minimal updates to continuously track phenomena clouds. We evaluate the network and processing costs for this update scheme in Section 5.6.2. Since the location of each sensor node is known beforehand, an application such as a GUIbased phenomenon cloud visualization tool can easily reconstruct a view of the various phenomenon clouds in realtime using information from the Phenomenon Set in conjunction with sensor location information. By looking at which sensors enter or leave the Phenomenon Set, the motion of multiple phenomenon clouds can also be tracked over time and more sophisticated analysis and prediction performed at a centralized level. This is extremely useful for applications such as [59] which can determine safe passages for rescue workers through multiple occurrences of phenomenon clouds such as gas leaks and wild fires. In addition, the cardinality of the Phenomenon Set together with sensor location can give applications some information about the size of various phenomena clouds. The size of a phenomenon cloud can have different impacts depending on the application context. For example, if an application is concerned with detection of phosphate dust clouds, a Phenomenon Set of low cardinality may not have much significance. However, if an application is tasked with the detection of hydrogen cyanide (HCN) leakage, then the detection of even a small cloud indicates serious consequences. 5.4 Optimizing Energy Consumption and Resource Utilization We now turn our attention to optimizing the energy consumption and resource utilization of our proposed mechanism. In order to minimize the number of active path (vi, vi,+ ..., vi+(kl), Vj) connects vi to vj, it is certain that vj will receive the message within finite number of Epochs, which is a contradiction. O 4.3 Distributed AllToOne Data Aggregation Scheduling Algorithm Alltoone data aggregation is an important operation in WSN. Periodically it is required that the sensed information from all the sensor nodes be aggregated at the sink node vs for further processing and forwarding. In this section, we introduce a distributed protocol to generate an interferenceaware schedule for data aggregation from all the nodes v E (V \ vs) at the sink node vs. We assume that, using the distributed BFS algorithm [56] or the distance vector algorithm, every node knows its closest distance in terms of hop counts to vs and its one hop neighbor on the closest path to vs, such a neighbor is termed as the Collector. Let the radius of the graph G = (V, E) with respect to vs is R and nodes in V are divided into subsets S1, 52 ...., SR, such that 5, is the subset of nodes which are i hops away from the vs. We observe that all nodes in 5, will have their Collector nodes in Si,. We assume the 2D plane covered by the WSN nodes is partitioned into regular hexagons with diameter rT, and is colored using Algorithm 7, considering distance d = (a+ 1)rax. All the nodes in a hexagon elects a Transmitter node among themselves, which has minimum hop distance to the sink (ties are broken on the basis of smaller id). The time is divided into Epochs and any hexagon with color c, is assigned the Tth Epochs, such that c, T mod Ik2 An Epoch is divided into two parts EpochR and Epochr. In all to one data aggregation protocol, the EpochR is used by a node in a hexagon to transmit a message to its respective Transmitter node and during EpochR the Transmitter node forwards that message to its Collector node. Hence, in a single Epoch, a message from a node in a hexagon is forwarded at least one hop closer to the sink without any interference. Each node v E V maintains a Forward queue which is initialized by inserting the message generated by v. The Forward queue expands when: 1) v acts as a Collector in Let (0, 0) be the coordinate of the base station in the new coordinate system. Node v can compute its new coordinates (xiv, yvh) as follows: (yh yb) rV, x = ( Xb) Yb)/ r3 (513) tan 600 2 13 y = (y yb) sin 600/ 3 (514) The coordinates of the hexagon h(i,j) in which node v is located is given as: h(y yb) r x (v b) (Yv Y) r (515) tan 600 2 13 y = (y yb) sin 600/ 3 (516) All the sensor nodes after computing the coordinates of their respective hexagons exchange this information with their neighbors and identify all the other nodes in their cluster. All the nodes having the same h(i,j) will belongs to the same cluster. Note that this communication is only 1hop as the hexagon has the length (hexagon diameter) of 2 and the clustering partition can be done only one time during the deployment and setup of a WSN. 5.4.2.2 Localized protocol We are now ready to introduce our localized protocol for optimizing energy consumption and resource utilization of the detection and tracking process described in Section 5.3. Notice that the partition allows all nodes in one hexagon and that of six adjacent hexagons be neighbors of each other. As shown in Figure 511, nodes in cluster C1 will have all nodes in clusters C2, C3, C4, C5, C6, C7 in their neighborhood. Now as the phenomena cloud will expand and the core tracking region will enlarge, there will be a large number of core tracking nodes in the network. The core tracking nodes will run the following protocol in online manner to schedule themselves into active and sleep mode: 2.5 Broadcast Scheduling Algorithm (BSA) We now present our centralized Broadcast Scheduling Algorithm (BSA) for lABS problem. BSA is applicable to 2D as well as 3D WSNs. In this section, we first describe BSA followed by its theoretical analysis for 0(1)approximation ratios in 2D and 3D WSNs respectively. 2.5.1 Algorithm Description BSA takes the graph G = (V, E), representing the WSN and the source node vs c V as inputs. It generates as output, the interferenceaware broadcast schedule for broadcasting the message m from vs to all the other nodes. BSA, in case of 2D WSNs, considers a tiling of 2D plane with regular hexagon of sides r and colors it using the method described in Section 2.3, assuming d = (a + 1)rT. In case of 3D WSNs, it considers a tiling of 3D space with truncated octahedrons of sides r Further, assuming d = (a + )r, x, it colors the tiling using m2n coloring algorithm described in Section 2.4. All nodes are assigned the color of their hexagons or truncated octahedrons in which they are located, in case of 2D or 3D WSNs respectively. Considering v, as root, BSA generates a BFS tree of G = (V, E) to partition it into a set of layers {L1, L,,..., LR} (where R is the height of the BFS tree). After this, BSA starts the broadcast by sequentiality transferring the broadcast message m between consecutive layers starting from layer L1 = {s}. Consequently, all nodes in the network receive the broadcast message. During the first time slot ti, the source node v, e L1 transmits the broadcast message to all nodes in layer L2. After this, BSA runs R 2 iterations of the Interlayer Scheduling Algorithm (ISA). In each iteration, ISA generates an interferenceaware schedule for transmissions between two consecutive layers. The ISA is illustrated in Algorithm 4. We also observed that when a person steps on a tile not only does this result in that tile's sensor registering a strong reading but some of its neighboring tiles also output significantly large readings. Hence, the stepping action of a foot on a floor tile causes a ripple effect in the immediate neighborhood of the tile. Figure 514 shows an actual screen shot of this phenomenon occurring in the Smart Floor where red dots indicate tiles registering readings of higher magnitude and green indicates tiles with lower yet significant magnitude. We used this observation to describe walking as a phenomenon by defining a step in terms of a phenomenon cloud (as shown in Figure 515), in order to reduce the number of false positives and provide accurate location information about the home's resident. Moreover, since our approach to phenomenon detection and tracking does not rely on mathematical modeling to track the direction of movement of a phenomenon, hence, this makes it extremely suitable for observing phenomena such as walking where it is extremely difficult to accurately model the path that a person will follow at any given time. A step can be described as a phenomenon cloud S = (a, b, PT, m, n), where a and b denote the lower and upper bounds of a force sensor reading indicating that a foot has stepped on a tile or in its immediate vicinity. This value depends on the particular sensor being used. For example, based on empirical study, we found that for the Interlink force sensors used in the Smart Floor (having an output range of [0, 1023], a = 150 and b = 600 for an individual weighing between 110 to 240 pounds. The optimal values of the other parameters were determined via experimentation and are described in the following section. More details about utilizing phenomenon detection and tracking to monitor resident location and observe walking characteristics such as gait velocity and stride length in the Gator Tech Smart House can be found in [65]. 5.6 Performance Evaluation In this section, we evaluate various aspects of the distributed phenomenon detection and tracking approaches described in this paper. The first set of experiments 105 of phenomena clouds in the sensor space. We next provide a mathematical model to optimize the energy consumption, on which we further propose a localized algorithm to minimize the resource utilization. Our proposed approaches not only ensure low processing and networking overhead at the centralized query processor but also minimize the number of sensors which are actively involved in the detection and tracking processes at any given time. We validate our approach using both reallife smart home applications as well as simulation experiments, which analyze the effectiveness and efficiency of our proposed algorithms. We also show that our algorithms result in significant reduction in resource usage and power consumption as compared to the contemporary streambased approaches. As part of our future work, we are looking for a modelassisted detection and tracking, where distribution of detection tasks will be streamlined based on predictions regarding the direction of movement of the phenomena cloud. We are also searching for reallife data sets from different application domains for further validating and fine tuning our approaches. need to communicate their status to their neighbors, which results in an increase in the exchanged message overhead. D. Effect of message losses on estimation of phenomena boundary at CQP: Our protocol works for detecting and tracking phenomena of any irregular shape, but for ease of implementation we consider the phenomena shape to be a circular disk. Figure 618 shows a snapshot of a dynamically spreading phenomena. Figure 619, 620, 621 and 622 show the estimated phenomena boundary at CQP for the snapshot in Figure 618, when the message losses in the WSN are 0%, 15%, 30% and 45% respectively. It can be observed that our proposed protocol is robust against the network message losses and produce a reasonably good estimation of the phenomena boundary at the CQP even if 45% of the network messages are lost. 6.6 Conclusion In this paper, we proposed a novel protocol for detection and tracking of dynamic phenomena of any irregular shape through WSN, with an objective of minimizing the resource usage and energy consumption. We also proposed a robust localized clustering and data aggregation method, which helps in reducing the network traffic generated by the information packet destined to the CQP. The experimental results shows that our proposed protocol consumed 90% lesser energy and generates 65% lesser network traffic destined to the CQP, in comparison to the existing work. Furthermore, our proposed protocol is robust against the network message losses and produce reasonably good boundary estimation at the CQP even if 45% of the network messages are lost. CHAPTER 1 INTRODUCTION A Wireless Sensor Network (WSN) is a collection of sensor nodes deployed to sense some phenomena, collect information and send it to the base station for further processing on multihop paths. WSNs have lots of applications in various fields where continuous monitoring is extremely critical and cannot be performed by humans due to issues like risk, reachability, accuracy and cost. Due to recent advancements in microelectronics and wireless technologies, various types of cost effective sensor nodes are modeled and realized for different applications such as environment and habitat monitoring [28], health monitoring [911], critical military operations like surveillance and reconnaissance to keep track of enemy. Recently, the use of WSNs is studied for applications involving dynamic phenomena such as oil spills, mud flow, etc [12, 13]. Mostly all network applications designed on top of WSNs involve detection and tracking of some physical phenomena. Additionally, they utilize some primitive services like broadcasting and aggregation for disseminating and collecting information. Broadcasting is an operation to promulgate some information from a source node to all other nodes in the network. In contrast, aggregation is an operation to collect the sensed information from all nodes at a specific node. Sensor nodes in WSNs communicate via radio transmissions. The broadcast nature of radio transmissions, called Wireless Broadcast Advantage (WBA) [14], enables a transmitting sensor to broadcast a message to all receiving sensors within its transmission range in a single transmission. However, more than one sensor transmitting simultaneously may result in interference at receivers. Consequently, performing efficient data broadcasting or data aggregation with minimum latency is nontrivial in WSNs and proved to be NPhard [15]. However, one straightforward approach to perform data broadcasting or aggregation is flooding [16, 17]. Unfortunately, it generates redundant transmissions, contentions and collisions in the network, which aggravates the network throughput and results in Corollary 2. If ratios a and / are bounded, the approximation ratio of the BSA algorithm for lABS problem in 3D WSNs is 0(1) . 2.6 Centralized Greedy Heuristic for broadcast scheduling In this section, we introduce a centralized Greedy Heuristic Algorithm (GHA) for broadcast scheduling in WSNs. GHA does not follow a layer by layer approach used in Algorithm 2.5, in which all nodes in a BFS layer must be informed before the broadcast proceeds to subsequent layers. Instead, GHA considers the set of all informed nodes at any point in time as potential transmitters. consequently, GHA schedules simultaneous transmissions in multiple layers. Thus, it avails the advantage of spatial distribution of transmitters by scheduling more nonconflicting transmissions in each time slot. Furthermore, GHA uses a manual interference avoidance technique based on checking individual transmitters whether they are violating sufficient conditions for interferenceawareness described in Lemma 1. This helps in increasing the number of simultaneous interferenceaware transmissions in each time slot. In order to select one out of possible interfering transmissions, most of existing heuristics and approximation algorithms [15, 32, 35] use variety of criteria to give higher priority to particular transmissions in a set of interfering transmissions. Usually, higher priority is given to transmitters with more neighbors in the network, or transmitters with more children in the BFS tree. On the other hand, since the ultimate goal of the broadcast scheduling is to inform all nodes in the network, we tried to follow a greedy rule for locally optimizing the progress rate of the broadcast by informing as many nodes possible with each new transmission. This greedy rule gives priority to transmitters which have the highest number of uninformed neighbors at that point in time. The pseudo code for GHA, which employs this greedy optimization, is given in Algorithm 5. 2.7 Conclusion In this chapter, we study the broadcast scheduling in 2D and 3D WSNs. We consider that sensor nodes may have different transmission ranges and their In order to study the tiling and coloring of 2D plane using identical regular hexagons, we consider a hexagon tiling H of the 2D plane. We color all hexagons in H, such that the distance between any two hexagons hi and h2 having the same color is at least d E R+. This distance is measured between two closest points pi and p2 on 2D plane, where p, is in h, and p2 is in h2. We provide an optimal solution to this problem for any arbitrary distance d R+. Furthermore, to study the tiling and coloring of 3D space using truncated octahedrons, we consider a tiling TOC of 3D space using identical truncated octahedrons. All truncated octahedrons in TOC are colored, such that the distance between any two truncated octahedrons to1 and to2 having the same color is at least d e R+. Similar to 2D, this distance is measured between two closest points pi and p2 in 3D space, where pi is in tol and P2 is in to2. We also propose an efficient centralized greedy heuristic algorithm for broadcast scheduling problem. Our heuristic algorithm considers all sensors that have received the broadcast message as potential transmitters. Further, to select among the interfering transmissions, it provides higher priority to the transmission which covers more uninformed nodes. In our simulations in Chapter 3, we perform a comparative analysis of performances of the heuristic algorithm under different priority metrics for greedily scheduling the interfering transmissions. The rest of the chapter is organized as follows: In Section 2.2, we describe the network and the interference model along with the formal definition of the interferenceaware broadcast scheduling problem. We introduce the tiling and coloring of 2D plane using regular hexagons in Section 2.3. Section 2.4 describes the tiling and coloring of 3D space using identical truncated octahedrons. The 0(1)centralized approximation algorithms for broadcast scheduling in 2D and 3D WSNs, along with theoretical analysis are described in Section 2.5. In Section 2.6, we introduce an To my parents, Mrs Shashi Tiwari and Mr Vasudev Tiwari some drawbacks of TOCOB. Firstly, it needs all the sensor nodes to participate in the detection and tracking process, which is not energy efficient. Secondly, it provides very sparse boundary information to the CQP, which limits the quality of phenomena boundary estimation. Thirdly, the method for identifying the RNs is not efficient and could suppress a large amount of boundary information from sending to the CQP, further degrading the detection and tracking of phenomena boundary. In this chapter, we propose an energy efficient localized protocol for detection and tracking of dynamic phenomena boundary of any irregular shape. In our proposed protocol, the detection and tracking process is localized to the nodes in the immediate neighborhood of the phenomena boundary. This results in only necessary nodes actively participating in sensing the phenomena boundary, while rest of the nodes remain inactive until they are required. In order to reduce the traffic generated by update messages, we propose an efficient, robust localized clustering algorithm based on hexagon tiling of the 2D plane covered by the WSN. The proposed clustering algorithm does not require reclustering when the phenomena boundary dynamically varies. Furthermore, we propose a data aggregation technique to aggregate the boundary information at the cluster heads. Our data aggregation technique considerably reduces the size of update messages sent to the centralized query processor without compromising on the amount of information to be reported. The simulation results show that our protocol performs remarkably better than TOCOB [13] in terms of energy consumption and resource usage. The rest of the chapter is organized as follows: In Section 6.2, we present the network model along with some preliminary definitions. We provide detailed description of the detection and tracking protocol for dynamic phenomena boundary in Section 6.3. The localized clustering method and data aggregation scheme is described in Section 6.4. In Section 6.5, we evaluate the proposed protocol through extensive simulations. Finally, Section 6.6 concludes the paper. 127 The plot for Localized Algorithm, in Figure 310, shows that when the value of 3 varies from 1.0 to 1.8, the latency increases rapidly from 54 to 80. This is mainly because, increasing / increases the number of colors used to color the hexagon tiling. Hence, the number of time slots a node has to wait to get a chance to transmit or receive the broadcast message also increases. This increases the broadcast latency. At the same time, increasing / increases the size of the neighborhood of a sensor node and so with a single transmission a node can cover more uninformed node in its neighborhood. This balances out the adverse effect of increase in hexagon colors on the latency and hence, with further increase in 3 there is no increase in the broadcast latency. Interestingly, we see that with increase in / the latency of the Approximation Algorithm decreases, this is because when / increases the size of the neighborhoods of sensor nodes also increase, which results in decreasing of the radius of the network. And as our approximation algorithm follows a layer by layer approach, hence, its latency directly depends upon the height of the BFS tree, i.e. the radius of the graph. It can be noticed that increasing / also increases the number of interfering transmissions, but as we know that in case of Approximation Algorithm, in a given time slot transmissions take place only within two consecutive BFS layer but not in the entire network. Therefore, the effect of increasing / on broadcast latency is not significant. Increasing / does not have much effect on the latency of GHA, this may be because GHA does not follow the layer by layer approach, hence, it is not affected by the radius of the network. Although, increasing / increases the size of the neighborhood of a node but it also increases the number of interfering transmission, which nullifies the good effect. 3.3.3 Effect of a on Broadcast Latency Figure 311 shows the effect of varying a on latencies of all three algorithms. We deploy 300 sensor nodes on a square area of side 500m. The parameter a varies from partitioning the plane into regular identical partitions, such that all nodes located within the same partition forms a cluster. The size of each partition will be defined by the transmission range r of a sensor node, and we consider all the sensor nodes have the same transmission range. Once the clustering is performed, the nodes within a partition elects the cluster heads. At any point in time, the cluster heads will remain active and the rest of core tracking nodes will sleep as long as each cluster head has at least n active neighbors. Let us consider how to perform such partition based on the tiling technique. What is the optimal shape of the regular unit partition so that we can partition the plane into the minimum number of clusters such that all nodes in adjacent clusters are neighbors of each other? Such a partition will minimize the total number of active core tracking nodes. There are four possible plane tiling polygons: 1) square, 2) rhombus, 3) equilateral triangle, and 4) regular hexagon. As we need the nodes in two adjacent partitions must be neighbors of each other, consequently, the maximum distance between two points located in two adjacent partitions must be r. Figure 56,57,58 and 59, shows the four possible partitioning using different plane tiling polygons. It is easy to see that tiling a plane using the regular hexagons covers the maximum area, thus lesser number of clusters for a given area. Therefore, we use regular hexagon as a partition shape for our tiling technique and next present how to locally perform this tiling. 5.4.2.1 Clustering method We partition the 2D plane covered by the WSN into regular hexagons of side length to form a hexagonal tiling as show in Figure 510. All the sensors located within the same hexagon form a cluster. Notice that their exists a coordinate system in which the axis are inclined at 600, such that all the hexagon centers lie on the integral coordinates of this new coordinate system. two neighbors B and C where B is a potential candidate and C is a tracking sensor. In this case, B will alert A whenever its readings satisfy the Probability Condition. And whenever A's reading is no longer satisfied the Probability Condition, A will only alert C but not B. Therefore, a single sensor node plays different roles with respect to different categories of its neighbors. Figure 54 lists the actions a sensor node required to perform with respect to the categories of its neighbors. The cells marked "Not Applicable" imply that such combinations are not possible according to transition rules given in next subsection. 5.3.3 Transition Rules We now ready to present a set of rules that govern the transition of a sensor from one category to another. These rules are executed innetwork and control the entire detection and tracking process. 1. R1: Candidate > Tracking: If a sensor satisfies the Phenomenon Condition then it transitions into the tracking category. Once a sensor is in the tracking category, it becomes a member of the Phenomenon Set. 2. R2: Potential Candidate > Candidate: A potential candidate sensor will transition to a candidate sensor if it satisfies the Probability Condition. This rule corresponds to the fact that whenever a phenomenon cloud moves or expands, a new set of sensors senses the phenomena and satisfies the Probability Condition, resulting in the movement or expansion of the phenomenon front. 3. R3: Idle > Potential Candidate: An idle sensor transitions into a potential candidate if any of its neighbors becomes a candidate sensor. 4. R4: Tracking > Candidate: A tracking sensor will transition down to the candidate category if it is unable to satisfy the Phenomenon Condition. In such a case, the sensor will cease to be a member of the Phenomenon Set. 5. R5: Candidate > Potential Candidate: A candidate sensor will transition to a potential candidate sensor if it does not satisfy the Probability Condition anymore. smaller time slots caller Trices, equal to the number of designated Provider nodes for the hexagon. During the Select time, the Supplier nodes are allocated the Trices on the basis of their designated Provider nodes in the increasing order of the ids of the Provider nodes. During their allocated Trice, a Supplier nodes negotiates with its respective Providers for that Trice to receive a new message. In order to negotiate with its Provider, a Supplier node during its allocated Trice sends a Request Message. Along with the Request Message, it sends its Message List. Based on the received Message List, the Provider node checks for any new message it can provide. If it has any, it sends the id of that message in the Response Message to the corresponding Supplier node. On receiving the Response Message, the Supplier node updates its Message List and broadcasts it in the Receiving Message. The purpose of the Receiving Message is three fold. Firstly, it acknowledges the respective Provider to send the message. Secondly, it broadcast its updated Message List to all the nodes in the hexagon. Thirdly, it notifies the other Supplier nodes not to attempt to receive from their Providers in the current Epoch. After this negotiation, the Provider transmits the message to the Supplier during the Receive time of the EpochR. During EpochT any node in the hexagon willing to broadcast its own message will broadcast. If there is no such node in the hexagon, then any Supplier node will broadcast a message which it has received from its Provider in a different hexagon. Lemma 9. Eventually every node receives message generated by all the other nodes. Proof. As we assume that the graph generated by the bidirectional links in the WSN is connected, therefore, there is at least a single path between any two nodes. Let's assume that the message generated by a node vi is not received by node vj at khop distance on path (vi, vi,+ ..., i+(k1), Vj). Now, the way the protocol works, the message mi generated by vi will be broadcasted in its hexagon during an Epoch assigned to its hexagon. If node vi,+ is in the same hexagon it will receive mi in the same Epoch, else it will receive mi in some later Epoch. Similarly, the message mi will be transferred from vi,+ to vi+2. As the CHAPTER 7 CONCLUSION This dissertation mainly focuses on following two imperative optimization problems in WSNs: 1. Efficient data broadcasting and aggregation. 2. Efficient detection and tracking of dynamic phenomena (phenomena cloud). In Chapter 2, we formulate data broadcasting in WSNs as Interferenceaware broadcast scheduling (lABS) problem with an objective to minimize the broadcast latency. We model WSN in 2D as a disk graph and in 3D as a Ball Graph. We consider a more realistic network model where the nodes may have different transmission ranges, while their interference range is a times of their transmission range, where a > 1. We propose 0(1)centralized approximation algorithms for lABS problem in 2D and 3D WSNs respectively. These approximation algorithms have the state of the art approximation ratio for the network model we considered. Further, in Chapter 3, based on the network and interference model introduced in Chapter 2, we study localized data broadcasting and propose a localized approximation algorithm for data broadcast. Our algorithm has a constant approximation guarantee of 2 +)3 1 2. This is the first localized approximation ratio for data broadcasting in WSNs. We also extended our localized algorithm for 3D WSNs. Furthermore, in Chapter 4, we study the alltoall data broadcasting and alltoone data aggregation and propose: 1. A O(1)distributed approximation algorithm for alltoone data aggregation. 2. A O(1)distributed approximation algorithm for alltoall data broadcast. 3. A Localized algorithm for alltoall data broadcast. Alltoone data aggregation is a fundamental operation in WSNs, in which the data from all the nodes is aggregated in a sink node for further processing and forwarding. Our distributed algorithm for alltoone data aggregation is the first in literature and has 142 [39] X. Xu, S. Wang, X. Mao, S. Tang, and X. Li, "An improved approximation algorithm for data aggregation in multihop wireless sensor networks," in In ACM Mobihoc 2009, 2009. [40] P.J. Wan, S.H. Huang, L. Wang, Z. Wan, and X. Jia, "Minimum latency aggregation schedulingin mulyihop wireless sensor networks," in In ACM Mo bihoc 2009, 2009. [41] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. Peh, and D. Rubenstein, "Energyefficient computing for wildlife tracking: design tradeoffs and early experiences with zebranet," SIGARCH Comput. Archit. News, vol. 30, no. 5, pp. 96107, 2002. [42] D. McErlean and S. Narayanan, "Distributed detection and tracking in sensor networks," in Proc. 36th Asilomar Conference on Signals, Systems and Computers, 2002. [43] Palm, "The 29 palms experiment: Tracking vehicles with a uavdelivered sensor network:http://tinyos.millennium.berkeley.edu/29palms.htm.," 2000. [44] S. Duttagupta, K. Ramamritham, and P. Kulkarni, "Tracking dynamic boundary fronts using range sensors," in The fifth European Conference on Wireless Sensor Networks, January 2008. [45] C. Zhong and M. Worboys, "Energyefficient continuous boundary monitoring insensor networks," in Technical Report, http://www.spatial.maine.edu/czhong /boundary_monitoring.pdf, 2007. [46] M. Ali, M. Mokbel, W. Aref, and I. Kamel, "Detection and tracking of discrete phenomena in sensornetwork databases," in SSDBM'2005: Proceedings of the 17th international conference on Scientific and statistical database management, Berkeley, CA, US, 2005, pp. 163172, Lawrence Berkeley Laboratory. [47] R. Kremens, J. Faulring, A. Gallagher, A. Seema, and A. Vodacek, "Autonomous fielddeployable wild land fire sensors," in International Journal of Wild land Fire, 2003, vol. 12, pp. 237244. [48] J. Heidemann, Y. Li, A. Syed, J. Wills, and W. Ye, "Underwater sensor networking: Research challenges and potential applications," in USC/ISI Technical Report ISI TR2005603, 2005. [49] J. Cassels, "An introduction to the geometry of numbers," in Berlin: Springer Verlag, 1971. [50] W. MathWorld, "Spacefilling polyhedron," http://mathworld. wolfram. corn/ SpaceFillingPolyhedron.html. [51] S.H. Huang, H. Du, and E. K. Park, "Minimum latency gossiping in multihop wireless network," in In Proceedings of Mobihoc 2008, 2008, pp. 733739. 148 [11] S. Rost and H. Balakrishnan, "Memento: A Health Monitoring System for Wireless Sensor Networks," in IEEE SECON, Reston, VA, September 2006. [12] X. ji, H. Zha, M. J.J., and K. G., "Dynamic cluster structure for object detection and tracking in wireless adhoc sensor networks," IEEE ICCC '04, 2004. [13] J.H. Kim, K.B. Kim, C. S. Hussain, M.W. Cui, M.S. Park, M.W. Cui, and M.S. Park, "Energyefficient tracking of continuous objects in wireless sensor networks," UIC '08, 2008. [14] N. Kurata, B.F.Spencer, and M. Sandoval, "Efficient broadcasting in multiradio multichannel, and multihop wireless network based on self pruning," in HPCC'07, 2007. [15] R. Gandhi, S. Parthasarthy, and A. Mishra, "Minimizing broadcast latency and redundancy in ad hoc networks," in Mobihoc '03, 2003, pp. 222232. [16] C. Ho, O. Katia, T. Gene, and V. Kumar, "Flooding for reliable multicast in multihop ad hoc networks," in DIALM '99: Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications, New York, NY, USA, 1999, pp. 6471, ACM. [17] K. Obraczka, K. Viswanath, and G. Tsudik, "Flooding for reliable multicast in multihop ad hoc networks," Wirel. Netw., vol. 7, no. 6, pp. 627634, 2001. [18] S.Y Ni, YC. Tseng, YS. Chen, and J.P. Sheu, "The broadcast storm problem in wireless ad hoc network," in MobiCom '99, 1999, pp. 151162. [19] S. Duttagupta, K. Ramamritham, and P. Ramanathan, "Distributed boundary tracking using sensor networks," in The 3rd IEEE Intl. Conference on Mobile Adhoc and Sensor Systems, Vancouver, Canada, October 2006. [20] K. Ren, K. Zeng, and W. Lou, "Secure and faulttolerant event boundary detection in wireless sensor networks," Wireless Communications, IEEE Transactions on, January 2008. [21] C. Zhang, Y Zhang, and Y Fang, "Distributed edge detection with composite hypothesis test in wireless sensor networks," Wireless Networks, January 2009. [22] P.K. Liao, M.K. Chang, and C.C. Kuo, "Distributed edge detection with composite hypothesis test in wireless sensor networks," GLOBECOM '04, 2004. [23] M. T. Thai, F Wang, D. H. Du, and X. Jia, "Coverage problems in wireless sensor networks: designs and analysis," IJSNET, 2008. [24] I. Chlamtac and S. Kutten, "On broadcasting in radio networksproblems analysis and protocol design," IEEE Transactions on Communications, vol. 33, pp. 12401246, 1985. 146 The ISA takes two consecutive layers Li and Lj as inputs and generates an interferenceaware transmission schedule from Li to Lj. In order to do this, ISA first generates a maximal independent set MIS(Lj) of the subgraph G[Lj] induced by nodes in Lj, such that MIS(Lj) is the dominating set of G[Lj]. ISA generates the schedule in two phases. In the first phase, based on their colors, nodes in MIS(Lj) are schedule to receive the broadcast message m from their parents in Li. In the second phase, based on their colors, nodes in MIS(Lj) are scheduled to transmit, so that all nodes in Lj \ MIS(Lj) receive the broadcast message m. Algorithm 3 BSA(G(V, E), s) In case of 2D (3D) WSNs, generate hexagon (truncated octahedron) tiling and color it. To all nodes in 2D (3D) WSN, assign the color of their respective hexagon (truncated octahedron) in which they are located . Run BFS rooted at vs to partition graph G = (V, E) into distinct layers {L1, L2, ... LR}. In time slot 1, L1 = {s} transmits to all nodes in L,. Time 1; i  2 while i fR 1 do Time Time + ILTS(L,, Li+,) iil end while 2.5.2 O(1)Approximation Ratio for InterferenceAware Broadcast Scheduling Problem in 2Dimension Lemma 3. The transmission schedule produced by ISA for 2D WSNs is interference aware. Proof. When ISA is applied to a 2D WSN, each hexagon can have only one MIS(Lj) node and hexagons having the same color are at least at a distance d = (a + 1)rmax. As MIS(Lj) nodes of the same colors transmits or receive simultaneously, they satisfy sufficient conditions for interferenceawareness described in Lemma 1, which results in interferenceaware transmission schedule. O 6.2 System Model Network Model: A set of insitu sensor nodes V deployed on a 2D plane along with a set of communication links E form the WSN. Each sensor node v e V is equipped with a radio transceiver with communication range r. The set of nodes within the communication range of v forms its neighborhood N(v). Furthermore, there exists a Centralized Query Processor (CQP), where the sensed information from the WSN is collected for further processing. A sensor node is active if its sensing functionality is on, otherwise it is inactive. An active sensor node is referred as detectpositive if it detects the phenomenon is existing, whereas if it detects the phenomena is not existing it is referred as detectnegative. Dynamic Phenomena: A dynamic phenomena represents the occurrence of any event that shows dynamic variations in shape, size and direction of motion. The most suitable examples of dynamic phenomena are oil spills, mud flow, diffusion or leakage of gases, etc. Phenomena Boundary: The phenomena boundary is defined as a curve that inscribes the area affected by the phenomena. It delineates the area under consideration into the region where the phenomena exists and the region where the phenomena has not yet reached. Based on the phenomena boundary, we present the classification of the sensor nodes described in Figures 61 & 62. 6.3 Detecting and Tracking of Dynamic Phenomena Boundary In this section, we present our protocol for detection and tracking the dynamic phenomena boundary. Figure 65 shows the state transition diagram for a sensor node. The states represent possible sensor classes and the edges represent conditions for the respective transitions. Figure 63 shows various types of messages that sensor nodes may generate and exchange to implement the detection and tracking protocol. Figure 64 shows the set of transition rules governing the transition of a sensor node from one state 128 4 ALLTOALL DATA BROADCASTING AND ALLTOONE DATA AGGREGATION 67 4.1 Introduction .................... ............... 67 4.2 Localized AllToAll Data Broadcast Scheduling Algorithm ......... 68 4.3 Distributed AllToOne Data Aggregation Scheduling Algorithm . . . 70 4.4 Distributed AllToAll Broadcast Scheduling Algorithm . . . .... 73 4.5 Experimental Evaluation ............................ 74 4.5.1 Results for Varying the Number of Sensor Nodes . . . ... 75 4.5.2 Results for Varying / .......................... 77 4.5.3 Results for Varying a .......................... 79 4.6 C conclusion . . . . . . . . . . . . . . . .. . 80 5 DETECTION AND TRACKING OF PHENOMENA CLOUD: NEW LOCALIZED APPROACHES AND APPLICATIONS ....................... 81 5.1 Introduction . . . . . . . . . . . . . . . .. . 8 1 5.2 Phenomena Cloud: Challenges and Representation . . . . ... 83 5.2.1 M ajor Challenges .. . .. . .. . .. . .. . .. . .. . 84 5.2.2 Representation . . . . . . . . . . . . . . 84 5.3 Proposed Solution for Detection and Tracking . . . . . ..... 86 5.3.1 Classification of Sensors . . . . . . . ..... .. .. .. 86 5.3.2 Keeping Tabs on the Neighborhood . . . . . . . ... 89 5.3.3 Transition Rules . . . . . . . . . . . . .. . 90 5.3.4 Initial Selection of Potential Candidate Sensors . . . . ... 91 5.3.5 Monitoring for Initial Occurrences . . . . . . . . ... 92 5.3.6 Notification of Initial Occurrence . . . . . . . ..... 92 5.3.7 Growth of Phenomenon Cloud . . . . . . . ..... 93 5.3.8 Shrinking of Phenomenon Cloud . . . . . . . . ... 94 5.3.9 RealTime Monitoring by Applications . . . . . . ... 95 5.4 Optimizing Energy Consumption and Resource Utilization . . . ... 95 5.4.1 The Integer Program Formulation . . . . . . . . ... 96 5.4.2 Optimized Density Algorithm. . . . . . . . .... . 98 5.4.2.1 Clustering method ...................... 99 5.4.2.2 Localized protocol . . . . . . . . . ... 101 5.5 A Practical Application of Phenomena Detection and Tracking ...... .103 5.6 Performance Evaluation ............................ 105 5.6.1 Effectiveness of Detection Strategy . . . . . . . ... 106 5.6.1.1 Experimental setup . . . . . . . . . ... 106 5.6.1.2 Results and analysis . . . . . . . ... . 106 5.6.2 Resource and Power Consumption . . . . . . . ... 109 5.6.2.1 Experimental setup . . . . . . . . . ... 110 5.6.2.2 Results and analysis . . . . . . . ... . 112 5.7 Related W ork . . . . . . . . . . . . . . . . . 121 5.8 C conclusion . . . . . . . . . . . . . . . . . 123 directly depends upon the number of active tracking nodes in the core region, the number of update messages is equal for both DistPDT and FDA. Due to the localized optimization protocol, ODA generates the minimum number of update messages without degrading the performance of detection and tracking. As in case of StreamPDT, all sensors need to report to the CQP through update messages; hence, it generates the maximum number of update messages. In details, as can be seen in Figure 524, ODA generates 86% and 39% lesser network traffic in terms of update messages comparing to StreamPDT and DistPDT (FDA) respectively. Figure 522 illustrates the epochwise comparison based on the number of protocol messages collectively exchanged by all the active nodes with their onehop neighbors. StreamPDT is a straightforward algorithm in which all sensor nodes perform onehop broadcast of their sensed information. Consequently, the number of protocol messages exchanged in an epoch is equal to the number of nodes in the network. However, for the other three algorithms, only active sensor nodes broadcast the exchanged message based on their respective categories. ODA performs the best and generates minimum number of exchanged messages, whereas FDA comparatively performs better than DistPDT. Figure 524 shows that FDA generates 77% and 6.41% lesser exchanged messages in comparison to StreamPDT and DistPDT repsectively. Furthermore, it shows that ODA generates 86% and 42.5% lesser exchanged messages in comparison to StreamPDT and DistPDT respectively. ODA improves FDA by generating 38.54% less exchanged messages and it has a huge significant improvement over StreamPDT. The epochwise comparison of the four algorithms based on the energy consumption is shown in Figure 523. As expected, StreamPDT requires all sensor nodes to always actively sense, thus it consumes energy the most. ODA performs the best, whereas FDA is better than DistPDT. Figure 524 shows that FDA consumes 74.52% lesser energy in comparison to StreamPDT and 5.86% in comparison to DistPDT. Similarly, ODA consumes 83.15% lesser energy in comparison to StreamPDT 500 500 400 400 I HHl tf:i.*,:::*:.!!!!! lU i.i:'n .tt r i 300 300 ii il'ltl iiliir :it.tl:rlsttili I *HlU il l .i:, ll iI, ll II E 200 Ih hE 200 i: il: ila li'H:l*I :Hli:.*lill 100 100 it :llltlU'l:ll )!: !! *II l n'llnj. llh'ioii bl l" ,il' 0 100 200 300 400 500 100 200 300 400 500 meters meters Figure 539. Active Sensors Figure 540. Active Sensors during Epoch t20, for during Epoch t20, for FDA. ODA. more than the IP solution. DistPDT and FDA respectively generates 63.59% and 36.04% more protocol messages compared to the IP solution. ODA generates 29.70% more protocol messages than the IP solution. Note that ODA uses only 13.82% more active nodes than that of the IP, however, the implementation of the optimization step adds an extra message overhead, thus it does not save much of exchanged messages as expected. The energy consumption is mainly contributed by actively sensing sensors. Again, as the StreamPDT needs updates from all sensors, it has the worst performance in terms of energy consumption. It consumes 62.32% more energy than the IP solution over the period of 5 epochs. DistPDT, FDA, and ODA consumes 36%, 18.05%, and 15.09% more energy than the IP solution, respectively. In order to have a better view of how the proposed algorithms function during the movement of the phenomena cloud, we performed the fourth set of simulations to pictorially illustrate the functioning and performance of DistPDT, FDA, and ODA. Figure 61 shows snapshots of the expanding phenomena cloud at epochs t1o, t15, and t20. Figures 532, 533, and 534 are the respective snapshots showing the active nodes for DistPDT, FDA, and ODA during epoch to1. Likewise, the result of epoch t15 is shown in Figures 535, 536, and 537 and that of epoch t20 is presented in Figures 538, 539, and 540. As can be seen, when the phenomenon expands, the number of active nodes 119 subject to xfP x + xf < 1 Vi e V (54) (xf + x,) (P, PT) > 0 Vi e V (55) S(x +x) N(i) (x+ x +x xf) < 0 Vi c V (56) jCN(i) S(xc x+) N(i)xf < n Vi E V (57) jCN(i) x, x, xix e {0,1} Vi E V (58) The above IP identifies the potential candidate, candidate and tracking sensors in the WSN based on the Probability and Phenomena conditions. Constraint 54 ensures that a node is either a potential candidate, or a candidate, or a tracking sensor, or none of them. (In this case, that sensor node should be idle.) In constraint 55, Pi and PT are the probability of sensing the phenomena for a sensor node i and the threshold probability for sensing the phenomena, respectively. This constraint ensures that if a node satisfies the probability condition, then it must be either a tracking sensor or a candidate sensor. Constraint 56 ensures that if there is a candidate or a tracking sensor in the neighborhood of any node i, then it must not be an idle sensor. Finally, constraint 57 ensures that a node must satisfy the phenomena condition to become a tracking sensor. Obtaining the solution of the above IP will classify sensors into their corresponding status. Let us define a core tracking node as a tracking node iff all of its neighbors are also tracking nodes. Let T denote a set of such core tracking sensor nodes. For each core tracking node i e T, define a variable xi as follows: 1 if i E T is an active node x, = (59) 0 otherwise Algorithm 1 Cocolor hexagon algorithm (H, d, h(i',j'),c) Input: The hexagonal lattice H, distance d, hexagon h(i',j') and a color number c assigned to h(i',j'). Output: A set S of cocolor hexagons of h(i',j') Compute i,j S  4; Queue  h(i'j'); while (Queue is not empty) do h(a, b)  Queue.Remove() S S U h(a, b); Color(h(a, b))  c Insert each of the following hexagons in the Queue if they are not inserted in the queue: h(a+ i, b +j) h(a+ (i +j),b i) h(a +j, b (i +j)j) h(a i, b j) h(a (i +j),b + i) h(a j,b (i +j)) end while return S; cocolor hexagons in S is proportional to the number of equilateral triangles of sides ' / (/2 +j2 + j) in the triangular lattice. Lets consider another method which provides a better solution than Algorithm 1. This method identifies a set of cocolor hexagon centers forming a regular or irregular triangular tiling of the area in which at least one triangle is nonequilateral. However, it is simple to observe that for the same smallest side length, the area of an equilateral triangle is always smaller than the area of any nonequilateral triangle. Hence, the number of nonoverlapping triangles in the tiling structure generated with the new method will be bounded by the number of equilateral triangle of sides (/'2 +2 U) in the triangular lattice generated by Algorithm 1. This results in the new method identifying lesser number of cocolor hexagons, in comparison to Algorithm 1. Hence, a contradiction. O based on which region they fall in at a particular time and how they are utilized to perform localized innetwork detection and tracking. 5.3 Proposed Solution for Detection and Tracking In this section, we present our proposed approach for the phenomenon cloud detection and tracking, called Full Density Algorithm (FDA). We begin with classifying sensors into different categories as discussed above according to their roles in the detection and tracking process. We then describe various responsibilities of any sensor node with respect to categories of its neighbors and list a set of rules which govern the transition of sensors from one category to another which form the main part of our detection and tracking strategy. The rest of this section covers the different stages of detection and tracking process in chronological order. It also describes mechanisms for handling node failures and how applications can utilize the realtime tracking data produced by the sensor network. Figure 53 pictorially depicts an example for detection and tracking process of a single phenomenon cloud. CI ore rei on 0 00 0 0 r I hkig 0 o 0 o Candidate Potential Candidate 0 Idle Sensors Figure 52. Classification of the Participating Sensors 5.3.1 Classification of Sensors Figure 62 shows the phenomenon cloud depicted in Figure 51 superimposed over a group of sensors. Sensors are classified according to the region where they are located, which determines their role in detection and tracking of phenomena cloud. The different categories are as follows: 15000 . ODA z 10000 FDA "*DistPDT vStreamPDT ; 5000 E z 10 20 30 40 50 Epoch Figure 520. Epochwise comparison based on number of active nodes involved in detection and tracking process. S1500 S,AODA S10000 .FDA * DlstPDT StreamPDT S5000 10 20 30 40 50 Epoch I VVUUrP S10000 5o o5 5000 E z Figure 521. 200 0 1150 0 100 0 O ULI LODA  FDA DistPDT StreamPDT 10 20 30 Epoch 40 50 Epochwise comparison based on number of update messages send to the Centralized Query Processor (CQP) AODA FDA *DistPDT jStreamPD 10 20 30 40 50 Epoch Epochwise comparison based on number of messages exchanged between onehop neighbors to implement the algorithms. Figure 523. Epochwise comparison based on the Energy Consumption. in receiving and transmitting data over the radio), which are based on the Atlas ZigBee node hardware specifications listed in Figure 610. 5.6.2.2 Results and analysis Simulation results for the first set of experiments are presented in Figures 520524 which compare performances of StreamPDT, DistPDT, FDA and ODA. Of which, Figures 520, 521, 522, and 523 provide epochwise comparison, whereas Figure 524 provides comparison based on an overall 50 epochs. 112 Figure 522. "  TVTVy TVTTV V TTV TTTTVTTTVTT TVVVY yVy TVTTV V REFERENCES [1] S.H. Huang, P.J. Wan, J. Deng, and Y Han, "Broadcast scheduling in interference environment," in IEEE Transaction on Mobile Computing, 2008, vol. 7. [2] E. Biagioni and K. Bridges, "The application of remote sensor technology to assist the recovery of rare and endangered species," In Special issue on Distributed Sensor Networks for the International Journal of High Performance Computing Applications, August 2002. [3] E. Biagioni and G. Sasaki, "Wireless sensor placement for reliable and efficient data collection," in In Proceedings of the Hawaiii International Conference on Systems Sciences, January 2003. [4] A. Cerpa, J. Elson, D. Estrin, L. Girod, M. Hamilton, and J. Zhao, "Habitat monitoring: Application driver for wireless communications technology," in In Proceedings of the 2001 ACM SIGCOMM Workshop on Data Communications in Latin America and the Caribbean, April 2001. [5] A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson, "Wireless sensor networks for habitat monitoring," in In ACM International Workshop on Wireless Sensor Networks and Applications (WSNA'02), Atlanta, GA, September 2002. [6] D. C. Steere, A. Baptista, D. McNamee, C. Pu, and J. Walpole, "Research challenges in environmental observation and forecasting systems," in In Pro ceedings of the sixth annual international conference on Mobile computing and networking. 2000, ACM Press. [7] H. Wang, J. Elson, L. Girod, D. Estrin, and K. Yao, "Target classification and localization in habitat monitoring," in In Proceedings of the IEEE ICASSP 2003, Hong Kong, April 2003. [8] R. Szewczyk, E. Osterweil, J. Polastre, M. Hamilton, A. Mainwaring, and D. Estrin, "Habitat monitoring with sensor networks," Commun. ACM, vol. 47, no. 6, pp. 3440, 2004. [9] S. Kim, S. Pakzad, D. Culler, J. Demmel, G. Fenves, S. Glaser, and M. Turon, "Wireless sensor networks for structural health monitoring," in SenSys '06: Proceedings of the 4th international conference on Embedded networked sensor systems, New York, NY, USA, 2006, pp. 427428, ACM. [10] S. Kim, P. S., C. D., D. J., F G., G. S., and M. Turon, "Health monitoring of civil infrastructures using wireless sensor networks," in Information Processing in Sensor Networks, 2007. IPSN 2007. 6th International Symposium on, April 2007, pp. 254263. 145 CHAPTER 5 DETECTION AND TRACKING OF PHENOMENA CLOUD: NEW LOCALIZED APPROACHES AND APPLICATIONS 5.1 Introduction Contemporary wireless sensor network research done in the area of detection and tracking has primarily concentrated on observing motion of objects whose shape and size are invariant [4143]. However, many reallife events such as oil spills, gas clouds, random walking motion of people, or movement of a group of people, henceforth called Phenomena Clouds, are characterized by nondeterministic, dynamic temporal variations of cloud shape, size and direction of motion along multiple axes. These events cannot be modeled in welldefined terms. Thus, it is difficult to apply existing mechanisms in such situation due to the fact that current cloudbased tracking techniques are oriented towards monitoring the motion of welldefined objects along a single axis at a particular time. They are not equipped for monitoring the shape, size and motion of phenomena clouds whose behavior cannot be readily modeled using classical theory. Moreover, the utility of phenomena cloud detection and tracking is not restricted only to application domains involving gas clouds or oil spills. In fact, they can also be utilized in situations where the quality of data originating from individual sensors cannot be trusted in isolation. In such cases, the raw sensor data originating from the system is typically extremely noisy which makes it very difficult to distinguish actual events from random stimuli. Hence, a quorum of multiple sensors which are located in close proximity to each other is required to reduce the probability of false positives. Through our collective research and systems experience over the years in a completely different deployment domain (Smart Spaces, also known as Ambient Intelligence), we have discovered a great utility in applying the phenomena cloud concept for efficiently and accurately monitoring various events in the space, such as detection of barefoot walking, which is an important application for diabetes patients. DislAIIToAll IVr'rim nial Ralio ' LnC..lToA.II ~prnmenT~l Ralio + 500 r,on Avee al i Raoto of A l 400 / S00  200  1 1i 14 =I 1 2 22 2.4 2, 28 p Figure 44. Effect of on Average Experimental Approximation Ratio of AlltoAll data broadcasting Algorithms. the broadcast is driven by the radius of the graph. Which tends to become constant after certain number of nodes in the network. 4.5.2 Results for Varying /3 In this set of experiments we placed 300 nodes in a square area of sides 500m. We fixed a = 2 and rin = 100m. We varied /3 from 1.0 to 3.0 with an increment of 0.1 to closely monitor its effect. For each value of / we ran all algorithms on 100 randomly generated network topologies and averaged their results. Figure 44 shows the plots of localized alltoall data broadcasting and distributed alltoall data broadcasting on varying /w. We observe there is a little rise in the experimental approximation ratios for both the plots when / changes from 1 to 1.2 after which the experimental approximation ratios tends to be constant. This can be explained by the fact that when /3 increases, the number of colors used to color the WSN also increases. With this the number of time slots a node need to wait to transmit the message also increases. This directly affects the latency, resulting in increase in the experimental approximation ratio. But, when /3 is further increased the size of the neighborhood of a node also increases and its transmission informs more number of nodes. Apart from this the diameter of the network also decreases with increase in /3. Hence, further increasing / does not effects the experimental approximation ratio. CHAPTER 6 LOCALIZED ENERGY EFFICIENT DETECTION AND TRACKING OF DYNAMIC PHENOMENA BOUNDARY 6.1 Introduction Most of the existing research in phenomena detection and tracking using Wireless Sensor Networks (WSNs) assumes the phenomena is invariant in shape, size and motion [1923]. However, in real life there exist dynamic phenomena such as oil spills, mud flow, diffusion or leakage of gases that are characterized by nondeterministic variations in shape, size and direction of motion. Due to the absence of any well defined model to represent dynamic phenomena, their detection and tracking through WSNs is very challenging. Since sensor nodes have limited energy and processing power, the detection and tracking of dynamic phenomena becomes even more challenging. In applications involving dynamic phenomena such as oil spills, gas leakage, etc, it is desirable to identify and track the area affected by the phenomena. Therefore, it is more sensible to detect and track only the phenomena boundary engulfing the affected area instead of tracking the entire phenomena. Existing works on detection and tracking o f phenomena boundary mostly consider static phenomena [1923] only few study dynamic phenomena [12, 13]. Due to the nature of their solutions, the works for static phenomena boundary cannot be extended to dynamic phenomena. Recently, Kim et. al[13] have proposed a protocol named TOCOB, which has the best performance in the literature. TOCOB needs all the sensor nodes to periodically sense phenomena and compare their current detection status with the previous one. If the detection status of a sensor node is changed, it is called a Changed Value Node(CVN). A CVN broadcasts a CompareOneZero(COZ) message to its neighbors. A node receiving at least one COZ message of different status than its own is called a Boundary Node (BN). Further, some Representative Nodes (RNs) are selected among the BNs which report the detection status of a single CVN in their neighborhood to the COP. There are 126 In [1], Scott et. al. proposed a 3k2hexagon coloring scheme for Distanced hexagon coloring problem. Figure 27, shows the comparison between their solution and the optimal solution generated by our proposed scheme. It can be seen that mostly our coloring scheme performs far better than Scott et. al. Only when i =j, the number of colors used by Scott et. al is equal to the number of colors used by our scheme. 2.4 Tiling and Coloring of 3Dimensional Space In this section, we study the tiling and coloring of 3D space using truncated octahedrons, which forms the kernel part of our solution for lABS problem in 3D WSNs. A regular tiling of the 3D space results in partitioning of 3D space into identical cells. Based on our requirements, the diameter of a unit cell should be 1 and its volume should be as large as possible. Therefore, to identify the shape of the unit partition cell, we compare volumes of the four possible space tiling primary polyhedra [50]: 1) Truncated Octahedron, 2) Rhombic Dodecahedron, 3) Cube and 4) Hexagonal Prism, considering their diameters are equal to 1 as shown in Figure 28. We observe that the truncated octahedron of sides 1 has the maximum volume. Hence, we selected truncated octahedron as the partition shape. Figure 29 shows the tiling of 3D space using truncated octahedrons. Similar to 2D, we formally define the tiling and coloring of 3D space using truncated octahedrons as Distanced truncated octahedron coloring problem: Distanced truncated octahedron coloring problem: Given a tiling TOC of 3D space using truncated octahedrons of sides 1 and a distance d e IR, find the minimum number of colors needed to color TOC, such that two truncated octahedrons to, and to2 having the same color must have the distance distance(tol, to2) > d. The distance distance(tol, to2) is the Euclidean distance between two closest points pi and p2 in 3D space, such that pi lies within tol and p2 lies within to2. In order to study the Distanced truncated octahedron coloring problem, we introduce a new Xt Yt Zt coordinate system in 3D space, in which, Xt, Yt, and sensors required for detection and tracking, first we propose a mathematical model based on Integer Program (IP) which uses a minimum number of active sensors (candidate, potential candidate, and tracking sensors) for detection and tracking. This model can be used as an excellent benchmark to evaluate our proposed mechanism. Next, we propose a localized algorithm, called Optimized Density Algorithm to further reduce the resource utilization based on our novel technique, called Hexagon tiling. 5.4.1 The Integer Program Formulation The IP is divided into two parts. In the first part, all the sensor nodes are categorized into Potential Candidates, Candidates, Tracking, and Idle sensors. In the second part, an optimization is performed to minimize the number of active tracking sensor nodes. Let V denote a set of all sensor nodes where I VI = N and N(i) denote a set of neighbors of sensor node i. For each i e V, we associate three variables defined as follows: 1 = if sensor / is a potential candidate x  (51) 0 otherwise 1 if sensor / is a candidate xf = (52) 0 otherwise S= if sensor / is a tracking (53) 0 otherwise We now formulate the first IP of which solutions determine the status of each sensor node i: min N 1(x + x + xf) Proof. In the first phase, the ISA takes at most [(o 1)2/2 + (a1 + time slots to schedule all nodes in MIS(Lj) to receive the broadcast message m form their parents in Li without interference. It takes another [(a + 1)2/2 + 8(+1) + 4] time slots, in the second phase, to schedules all nodes in MIS(Lj) to transmit the broadcast message m to nodes in Lj \ MIS(Lj). Hence, it takes total 2 [4( + 1)2/2 + 8(+1) + time slots to transfer the broadcast message m from layer Li to layer Lj. BSA runs R 2 iterations of ISA, hence, the total number of time slots or the broadcast latency of BSA is given as: 1+(R 2)2 [(a + )2/2 + 83 + 4 The theoretical lower bound of the lABS problem is R. Hence, the approximation ratio is: 2 (a + 1)2/2 + 83(al)+ 4 Corollary 1. If ratios a and 3 are bounded, the approximation ratio of the BSA algorithm for lABS problem in 2D WSNs is 0(1) . 2.5.3 0(1)Approximation Ratio for InterferenceAware Broadcast Scheduling Problem in 3Dimension Lemma 5. The transmission schedule produced by ISA in 3D WSNs is interference aware. Proof. This can be proved similar to Lemma 3. When ISA is applied in a 3D WSN, each truncated octahedron can have only one MIS(Lj) node and truncated octahedrons having the same color are at least at a distance d = (a + 1)rx,. As MIS(Lj) nodes of the same color, transmit or receive simultaneously, they satisfy sufficient conditions for interferenceawareness described in Lemma 1, which results in interferenceaware transmission schedule. O Lemma 6. MIS(Lj) nodes in ISA are colored using at most (a +1)3 + (a + 1)/ + 1I colors in 3D WSNs. them here. Chintalapudi and Govindan in [68] described algorithms for detecting sensors lying closest to the edges of a phenomenon cloud. However, their approach not only requires assumptions regarding the shape of the edges (such as whether it is a line or an ellipse), but can also lead to a high number of false positives, since the extreme fringes of a phenomenon are more susceptible to sensor errors and rapid fluctuations. From their description, it appears that their edge sensors correspond to the Outer region of the phenomenon cloud (defined in Section 5.3.1). Our mechanisms, on the other hand, avoid false positives by only reporting those sensors which lie in the Core region namely, tracking sensors. Moreover, our approach does not make any simplifying assumptions regarding the shape of the cloud edges. In [1921], the authors proposed a distributed method to statistically estimate the boundary of the phenomena, but they consider only static phenomena. In [6971], algorithms considering mobile sensor nodes are proposed to approximate the boundary of a phenomena cloud. In [45], Cheng et. al. proposed a method for continuously monitoring the boundary of the phenomena cloud, but they require all the sensors in WSNs actively sense all the time and they only concentrated on reducing the communication overhead. In [12], a dynamic cluster structure for object detection and tracking which requires all sensor nodes to be active is proposed. Their proposed cluster formation has high communication overhead, thus it is difficult to handle fast changes of phenomena cloud state. In [13], Kim et. al. proposed another algorithm for tracking the phenomena boundary but it requires all the sensor nodes to be active periodically. 5.8 Conclusion In this paper, we propose several distributed algorithms to detect and track several types of phenomena clouds, regardless of their shapes and movement direction. The phenomena clouds can have variant shapes, size and direction of motion along multiple axes. We first propose a distributed algorithm for insitu detection and tracking 123 C d Figure 28. Comparison of different spacing filling polyhedra. Figures a, b, c and d respectively show a truncated octahedron, a rhombic dodecahedron, a cube and a hexagonal prism, having maximum distance within them equal to 1. j . Figure 29. The tiling of space using truncated octahedrons Zt axes are inclined as shown in Figure 210. The angle between Xt and Yt axes is 01 = cosl( ), whereas, angles between Xt and Zt axes and Yt and Zt axes are equal to 02 = cos1( ). The angle between the Ztaxis and the Xt Yt plane is 03 = 450. The side length of the truncated octahedron is , the distance between its two parallel [25] M. Elkin and G. Kortsarz, "An improved algorithm for radio networks," Symposium On Discrete Algorithms (SODA), 2005. [26] I. Gaber and Y. Mansour, "Centralized broadcast on multihop radio networks," Journal of Algorithms, vol. 46, no. 1, pp. 120, 2003. [27] E. Kushilevitz and Y. Mansour, "An w(dlog(n/d)) lower bound for broadcast in radio networks," in SIAM journal on Computing, 1998, vol. 27, pp. 702712. [28] D. R. Kowalski and A. Pelc, "Centralized deterministic broadcasting in undirected multihop radio network," in APPROXRANDOM '04, 2004. [29] I.Chlamtac and 0. Weinstein, "The wave expansion approach to broadcasting problem in multihop radio network," IEEE Transactions on Communications, vol. 39, pp. 426433, 1991. [30] M. Elkin and G. Kortsarz, "Logarithmic inapproximability of the radio broadcast problem," Journal of Algorithms, vol. 52, pp. 825, 2004. [31] M. Elkin and G. Kortsarz, "Polylogarithmic additive inapproximability of the radio broadcast problem," In APPROXRANDOM '04: Proc. of 7th International workshop on Approximation Algorithms for Combinatorial Optimization Problems, 2004. [32] S.H. Huang, P.J. Wan, X. Jia, H. Du, and W.Shang, "Minimumlatency broadcast scheduling in wireless ad hoc networks," in INFOCOM '07, 2007, pp. 733739. [33] L. Gasieniec, D. Peleg, and Q. Xin., "Faster communication in known topology radio network," in PODC '05: Proceeding of 24th annual symposium on Principles of distributed computing, 2005, pp. 129137. [34] X. G. Viennot, "A strahler bijection between dyck paths and planar trees," in Discrete Math, 2002. [35] Z. Chen, C. Qiao, J. Xu, and T. Lee, "A constant approximation algorithm for interference aware broadcast in wireless networks," in INFOCOM '07, 2007, pp. 740748. [36] R. Mahjourian, F.Chen, R. Tiwari, M.T.Thai, H. Zhai, and Y. Fang, "An approximation algorithm for conflictaware broadcast scheduling in wireless ad hoc networks," in MobiHoc'08, 2008, pp. 331340. [37] X. Chen, X. Hu, and J. Zhu, "Minimum data aggregation time problem in wireless sensor networks," in In MSN 2005, 2005, pp. 133142. [38] S.H. Huang, P.J. Wan, T. Chinh, Y. S. li, and F. Yao, "Nearly constant approximation for data aggregation time problem in wireless sensor networks," in In IEEE INFOCOM 2007, 2007. 147 1. Candidate Sensor: A sensor which satisfies the Probability Condition is called a candidate sensor. It has the responsibility of actively sensing and notifying its neighbors about its state. It also receives notifications from its neighbors in order to identify whether it satisfies the Phenomena Condition to become a part of the Phenomenon Set. A sensor becomes a candidate sensor when it transitions from the potential candidate stage during the expansion of the phenomena, or when it transitions from the tracking stage during the shrinking of the phenomena. 2. Potential Candidate Sensor: A sensor which is actively sensing the phenomenon but does not satisfy the Probability Condition is called a potential candidate sensor. These sensors keep monitoring their reading to enable a neighbor candidate sensors to check the validity of their observations. A sensor becomes a potential candidate if either 1) it has been selected by the centralized query processor as part of the initial detection phase (described in Section 5.3.4), or 2) one of its neighbors becomes a candidate sensor during the expansion of the phenomena, or 3) when a candidate sensor transitions from candidate stage to potential candidate stage during the shrinking of the phenomena. The responsibility of the potential candidate is to notify its neighboring candidate sensors whenever its reading satisfies the Probabil ity Condition. Potential candidate sensors form the fringes of detection and make up the outer region of the phenomenon cloud. Essentially, the set of potential candidate sensors forms a phenomenon front which grows and shrinks dynamically. 3. Tracking Sensor: A sensor which has already detected a phenomenon event and is now actively engaged in the tracking process is called a tracking sensor. A candidate sensor becomes a tracking sensor after it satisfies the Phenomenon Condition (defined in Section 5.2.2). Tracking sensors covers the core region of the phenomena cloud. The Phenomenon Set is the collection of all tracking sensors, hence, each cloud consists of subsets of tracking sensors from the Phenomenon Set. neighbors ag, a17 and a20 in h(1, 0), (2, 1) and h(1, 1). During EpochT the Supplier nodes a30, a28 and a29 broadcast the broadcast message to all the other nodes in h(1, 1), (2, 2) and h(1, 2), respectively. Epoch 9 : During EpochR the Supplier node a33, a32, a31 and a34 in h(1, 1), (1, 2), h(2, 2) and (2, 1), respectively, receive the broadcast message from their respective Provider neighbors a40, a24, a22 and a8 in h(1, 0), (1, 1), h(2, 1) and h(1, 0). During EpochT the Supplier nodes a33, a32, a31 and a34 broadcast the broadcast message to all the other nodes in h(1, 1), (1, 2), h(2, 2) and (2, 1), respectively. Epoch 10 : During EpochR the Supplier node a39 in h(3, 0) receives the broadcast message from its Provider neighbor a12 in h(2, 0). During EpochT the Supplier nodes a39 broadcasts the broadcast message to all the other nodes in h(3, 0). As in all the Epochs, while receiving and transmitting the broadcast message, all the Supplier nodes follow the sufficient conditions for interferenceawareness introduced in Lemma 1, hence, there will be no interference during the broadcasting of the broadcast message. Lemma 8. There is no interference when: 1) any Supplier node receives broadcast message m from its Provider, 2) any Supplier node transmits the broadcast message m to other nodes in its hexagon. Proof. Case 1: Assume that a Supplier node s,,p receiving broadcast message from its respective Provider Vpro is interfered by a node vi. This would mean that vi and Vpro must be transmitting at the same time during the EpochR of an Epoch. Therefore, the receiver of vi, say vj (which should be a Supplier node) and Vsup, must be in hexagons with the same color. This gives rise to two possibilities: 1) Both vj and v,,p are in the same hexagon. In this case, only one of them can be scheduled to receive, hence a contradiction. 2) vj and v,,p are in different hexagons of same color. But in this case the distance between vj and v, will be greater than or equal to (a + 1)rax. Therefore, according to Lemma 1, vi cannot interfere v,, hence a contradiction. @ 2010 Ravi Tiwari Epoch 2 : During the EpochR the Supplier node a5 in h(1, 0) receives the broadcast message from the Provider node a, in h(0, 0). During EpochT the Supplier node a5 broadcasts the broadcast message to all the other nodes in h(1, 0). Epoch 3 : The Supplier nodes a10 in h(2, 0) and a13 in h(1, 0) receives the broadcast message during the EpochR from their respective Provider nodes a7 and a3. Further, during EpochT, the Supplier nodes a10 and a13 broadcast the broadcast message to all the other nodes in h(2, 0) and h(1, 0), respectively. Epoch 4 : During EpochR a Supplier node a15 in h(0, 1) receives the broadcast message from its Provider neighbor a6 in h(1, 0). During EpochT the Supplier node a15 broadcasts the broadcast message to all the other nodes in h(0, 1). Epoch 5 : During EpochR the Supplier nodes a18 and a16 in h(1, 2) and h(1, 2), respectively, receives the broadcast message from their respective Provider neighbors a7 and 14 in h(1, 0) and h(1, 0). During EpochT the Supplier nodes a18 and a16 broadcasts the broadcast message to all the other nodes in h(1, 2) and h(1, 2), respectively. Epoch 6 : During EpochR the Supplier nodes a23 and a21 in h(1, 1) and h(2, 1), respectively, receives the broadcast message from their respective Provider neighbors a4 and a19 in h(0, 0) and h(1, 1). During EpochT the Supplier nodes a23 and a21 broadcasts the broadcast message to all the other nodes in h(1, 1) and h(2, 1), respectively. Epoch 7 : During EpochR the Supplier nodes a27, a26 and a25 in h(0, 1), (3, 1) and h(0, 2), respectively, receive the broadcast message from their respective Provider neighbors a2, all and a15 in h(0, 0), (2, 0) and h(0, 1). During EpochT the Supplier nodes a27, a26 and a25 broadcast the broadcast message to all the other nodes in h(0, 1), (3, 1) and h(0, 2), respectively. Epoch 8 : During EpochR the Supplier nodes a30, a28 and a29 in h(1, 1), (2, 2) and h(1, 2), respectively, receive the broadcast message from their respective Provider 300 D,~riIIToOr,e Expenmental Ralio  250 Theoretcal Ralio * / 250 *.a*. Figure 45. Effect of on Average Experimental Approximation Ratio of AlltoOne data broadcasting Algorithms. 300 DisLOneToAll Experimental Ratio  250 Theoretical Ratio ., 200 S 150  1 00 50 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Figure 46. Effect of/3 on Average Experimental Approximation Ratio of OnetoAll data broadcasting Algorithms. In Figure 45 and Figure 46, the plots for distributed alltoone data aggregation and onetoall data broadcasting on varying / are given. We observe that the experimental approximation ration in both the plots minutely fluctuate around a certain point and does not show much increase. This can again be explained by the fact that increasing /3 decreases the radius of the graph, as nodes possibly have larger neighborhood when /3 is large. at our algorithm shows a much better performance, in comparison to their proposed theoretical approximation guarantees. theoretical approximation guarantees. We now introduce the second IP as follows: min yITi xi subject to x,n + x n > 0 Vi T (510) jcN(i) x,n xj < 0 V/i T (511) jcN(i) x, {0,1} ViE T (512) The second IP minimizes the number of active core tracking nodes in order to optimize the power consumption for detecting and tracking the phenomena cloud. Constraint 510 and 511 ensure that a core tracking node can go to the sleep mode if it satisfies the minimum quorum condition along with all of its neighbors. 5.4.2 Optimized Density Algorithm In light of the above IP, we now present a localized protocol, called Optimized Density Algorithm (ODA) to further enhance the resource utilization of our proposed FDA discussed in Section 5.3. As shown in the IP, we propose to identify a set of core tracking nodes, and then switch these nodes back and forth between the sleep and active modes following some certain rules. Remember that a core tracking node can go to the sleep mode if it satisfies the minimum quorum condition along with all of its neighbors. Before describing our protocol, we first discuss some preliminaries which lead to the formation of the protocol. The main idea of locally deciding a sleep/active mode of a core tracking node is based on an efficient clustering of the sensor nodes in the network. We partition the network into clusters in such a way that the nodes in adjacent clusters are neighbors of each other. Thus we first propose an idea to locally perform in network clustering with message complexity 0(1). Our idea is based on a geographically but locally Proof. For any node v belonging to the set 5,, during the Epoch allocated to its hexagon its message mv is forwarded to a node in 5i_,, from where it is further forwarded to a node in 5i_2 in some later Epoch and so on till the message reaches the sink. This applies to all the nodes in the network. Hence, the messages from all nodes in the network are aggregated at the sink node vs. D Lemma 13. The latency of data aggregation from all the nodes to the sink is bounded by 2 V 1 L( 2 + 12. Proof. Due to the property of hexagon coloring, the Transmitter nodes located in different hexagons of the same color in consecutive sets S, and S,+i satisfy the sufficient conditions for interferenceawareness mentioned in Lemma 1. Thus, they can be scheduled to receive or transmit during the same Epoch. Hence, during L(1/3 + 12 Epochs all the sets S, 52,..., SR can be scheduled based on the color of the hexagon their nodes belongs to. The number of Epochs required by the nodes in SR to forward their messages to nodes in 5R1 is bounded by SR 2 /3 1 During these Epochs all the sets S, 52,... 5R1 must have individually forwarded at most SRI 2(l 1 messages to one set closer to the sink node vs. Now in at most next 5R11 2/3 +1 Epochs, the set 5R1 will be able to completely forward all its remaining messages along with the messages it received from SR. And by this time S1, 52,..., SR2 must have individually forwarded at most (SR SR) (SR + 11 messages to one set closer to the sink node vs. Eventually after at most SRI / 12 + l + + ... + 152 2+ 1 Epochs, the sink node v, will receive the messages of all the nodes in different set. And as each Epoch has two time slots, hence, the latency is bounded by: 2SR L3/2 + 12 2 ISR1l I 3 +1 2 ... 21S21 (+l)3 2 "'" v'3/ 2 LIST OF FIGURES Figure page 21 Sufficient conditions for interferenceawareness based on transmitters .... 27 22 Sufficient conditions for interferenceawareness based on receivers. . . . 27 23 Comparison of different plane tiling polygon. Figures a, b, c and d respectively show a square, a rhombus, a triangle and a hexagon, having maximum distance within them equal to 1 . . . . . . . .. . . . . . .... 29 24 The new Xh Yh coordinate system ....................... 30 25 Closest points pi and p2 in two hexagons . . . . . . . ..... . 31 26 CoColor Hexagons of h(0, 0) for / = 2 andj = 3. The index of sublattice Rh in H i.e. Idet(A, B) = i2 +j2 + Y = 19 ...................... . 34 27 Comparison of number of colors used to color the hexagon tiling using our scheme and Scott et. al [1].................... .......... 35 28 Comparison of different spacing filling polyhedra. Figures a, b, c and d respectively show a truncated octahedron, a rhombic dodecahedron, a cube and a hexagonal prism, having maximum distance within them equal to 1 . . . . . .. . 37 29 The tiling of space using truncated octahedrons . . . . . . ..... 37 210 The Xt Yt Z Coordinate System ....................... 38 211 Coloring pattern for d = 1, [m] = 3 and [nl = 3, Colors assigned to the truncated octahedrons are represented by numbers. . . . . . .... 39 31 Elements of the Broadcasting Structure. . . . . . . . .. . . 49 32 Hexagon coloring generated by Algorithm 7 for k = 4, colors assigned to the hexagons are represented by numbers. . . . . . . . .... . 50 33 An Example showing the functioning of a part of the broadcast structure. .. 51 34 A n Epoch . . . . . . . . . . . . . . . . . .. . 53 35 A broadcast structure ................... ............ 55 36 Data broadcasting on top of a broadcast structure . . . . . . ... 55 37 Effect of number of nodes on Average Latency . . . . . . . ... 61 38 Average BFS height .. . .. . .. . .. . .. .. . .. . ... . 61 39 Average optimality ratio ............................... 61 .... ""f *,"y.. .' "h". ,' Figure 618. Snapshot of phenomena in WSN. e qF 'p s. Figure 619. Estimated boundary with 0% message loss. ...%. 1b',*  * > * Figure 620. Estimated boundary with 15% message loss. Figure 621. Estimated boundary with 30% message loss. .' . % I.O" Figure 622. Estimated boundary with 45% message loss. A. Boundary Nodes and update messages: Figure 611 & 612 show the comparison of two protocols based on number of boundary nodes and update messages respectively. The two figures together reflect the efficiency of our proposed localized clustering and data aggregation protocol in reducing the number of update messages destined to CQP without leaving behind the information generated by any boundary node. Our protocol generates 22% lesser boundary nodes and 65% lesser update messages in 139 0 80 60 Z < 40 E =2 =20 4 S80 .g, 2 60" 40 E 20 z 1 2 3 4 5 Epoch Figure 526. Epochwise comparison based on number of active nodes involved in detection and tracking process. 10C T 0 T S80 ODA g IPSol 60 FDA *DistPDT 40 SteamPDT 4 20 E z 1 2 3 4 5 Epoch Figure 528. Epochwise comparison based on number of messages exchanged between onehop neighbors to implement the algorithms. AODA *IPSol  FDA *DistPDT TStreamPDT F^ 1 2 3 4 5 Epoch Figure 527. Epochwise comparison based on number of update messages send to the Centralized Query Processor (CQP) I8 ODA 0 1 IPSol +FDA . 0.8 ADistPDT 0.6 StreamPDT 8 4 r^ ^ 0.! 0. LJJ 0 2 3 4 5 Figure 529. Epoch Epochwise comparison based on the Energy Consumption. and ODA performs the best in terms of all the comparison parameters. The performance of StreamPDT is the worst and not scalable. Figures 526530 present simulation results for the third set of experiments, of which we compare the solutions of the four algorithms with the optimal solution generated by the IP described in Section 5.4.1. Note that since solving IP is actually NPhard, we only simulated this set of experiments on the small size grid of 10 x 10 during 5 epochs of random movement and expansion of phenomena clouds. Figures 116 IPSol FDA DistPDT vStreamPDT 6. An energy efficient localized algorithm for detection and tracking of phenomena cloud boundary. Algorithm 4 ISA(L,, Lj) Generate graph G(Lj) induced by the nodes in Lj. MIS + GenMIS(G(Lj)) c  Number of colors used to color hexagon (truncated octahedron) tiling in case of 2D (3D) WSNs. Time + Initialize S1, 2, ... Sc to ( for all u e MIS do Select a node w c N(u) n Li Scolor(u) + Scolor(u) U {w} end for for i/ 1 to c do Si transmits end for Time  Time + c. Initialize S1, S2, ..., S to for all u e MIS do Scolor(u) + Scolor(u) U {u} end for for i/ 1 to c do Si transmits end for Time  Time + c. return Time Lemma 4. MIS(L/ ) nodes in ISA are colored using at most (a + 1)22 + 13 + colors in 2D WSN. Proof. Every MIS(Lj) node acquires the color of the hexagon in which it is located. When sides of the hexagon are 1, according to Theorem 2.2 for any distance d e R the number of colors needed to color the hexagon tiling is bounded by d 2 + d + Thus, when sides of the hexagon are r the number of colors used are bounded by + 8d + 4. Based on sufficient conditions for interferenceawareness in Lemma 1, d is (a+ 1)rax. Hence, the number of colors needed will be: [ (a 1)2/2 + 8(a 1) 4 Theorem 2.3. The BSA algorithm provides an approximation ratio 2 (a 1)2/2 + 3 + for lABS problem in 2D WSNs. 3r 3 3 140 120 O' DistAIIToOne Erperiernial Rato l S 100 Thec s.eri al Raio ....* 60 Ca 40 0 50 100 150 200 250 300 350 400 450 500 # of Sensor Nodes in WSN Figure 42. Effect of No. of Nodes on Average Experimental Approximation Ratio of AlltoOne data broadcasting Algorithms. 140 120 # of 3er,nor Nc,.es In WSN Figure 43. Effect of No. of Nodes on Average Experimental Approximation Ratio of OnetoAll data broadcasting Algo Erithms. R Thus, the latency increases only because of the increase in number of nodes and not because of increase in the diameter of graph. Therefore, the experimental approximation rratio is maintained. Figure 42 shows the effect of number of nodes for alltoone data aggregation algorithm. The plot is similar to that of alltoall data broadcast and can be explained in the same manner. The experimental approximation ratio becomes almost constant, after certain number of nodes because of nonvarying network diameter. Figure 43 shows the effect of number of nodes for onetoall data broadcasting. The plot is similar to the alltoall and alltoone. This is because, apparently the latency of 40 50 100 150 200 250 300 350 400 450 500 #of Bersbr Naaes In WSN Figure 43. Effect of No. of Nodes on Average Experimental Approximation Ratio of OnetoAll data broadcasting Algorithms. Thus, the latency increases only because of the increase in number of nodes and not because of increase in the diameter of graph. Therefore, the experimental approximation ratio is maintained. Figure 42 shows the effect of number of nodes for alltoone data aggregation algorithm. The plot is similar to that of alltoall data broadcast and can be explained in the same manner. The experimental approximation ratio becomes almost constant, after certain number of nodes because of nonvarying network diameter. Figure 43 shows the effect of number of nodes for onetoall data broadcasting. The plot is similar to the alltoall and alltoone. This is because, apparently the latency of are detectpositive, they will broadcast an INVK message to their immediate inactive 0 neighbors and transition into B nodes, based on rule R2. After receiving the INVK, the inactive 0 neighbors will transition into OB nodes and become active, based on rule R1. If an active node in an Epoch is detectpositive, it broadcasts a +ive PHST message to its neighbors, otherwise, it broadcasts a ive PHST message. C. Growth of phenomena: When the phenomena grows some of the OB nodes become detectpositive. These OB nodes broadcast INVK messages to their inactive 0 neighbors and transition into B nodes, based on rule R1. The inactive 0 nodes on receiving the INVK messages, transition into OB nodes, based on rule R2. Further, during the growth of phenomena, some B nodes, on receiving +ive PHST messages, may notice that all their neighbors are detectpositive. Additionally, if they have at least one B node in their neighborhood, they transition into IB nodes, based on rule R3, else they transition into I nodes, based on rule R4 and become inactive. Eventually, the phenomena is always covered by the set of currently active nodes and the information about the location of the phenomena boundary can be collected from the set of B nodes. D. Shrinking of phenomena: When the phenomena shrinks, some of the current B nodes become detectnegative. If any of these B nodes have at least one detectpositive B node in their neighborhood, they transition into OB nodes, based on rule R7. Otherwise, they transition into 0 nodes and become inactive, based on rule Rs. Further, during the shrinking phase, if an IB node on receiving a ive PHST notices that it has an OB node in its neighborhood, it transitions into a B node, based on rule R6 and broadcasts an IVNK message to invoke its inactive I neighbors. These I nodes, on receiving the INVK messages, activate and transition into IB nodes, based on rule Rs. This way the information about the location of the phenomena boundary is always contained in the current set of B nodes. E. Aggregation and Reporting Update messages to CQP: When there is any variation in the phenomena boundary, it should be reported to the CQP through 132 Theorem 2.2. The number of colors for Distanced Hexagon coloring problem for an arbitrary d is bounded by d2 + d+ Proof. Consider the hexagon h(0, 0) and one of its closest cocolor neighbors in the first quadrant of Xh Yh coordinate system is h(i,j). Without loss of generality, we consider (/ > i), we exclude the case when i = 0,j = 1, thus we have two cases: 1) = 0,j > 1 and 2) i > 0,j > 0. Case 1: We usej2 colors to obtain the distance d < (j 1) Therefore, the number of color is equal to d 2 + 4d +1 < d2 +d + Case 2: As shown in the proof of Theorem 2.1, the number of colors used is i2 + i +j2 and the guaranteed minimum distance between closest points of two cocolor hexagons is as follows: 3 2 2 2 2 d < )2 (i )j ) )2 4 3 3 3 = (/2 + +2 + 2(i )) 4 3 It is easy to prove that 2 + +2 < d2 8d + 4 for i,j > 0. The equality happens iff i =j. 120 S"o A Propoded Coloring Scheme S100 *Scott et. al E" 80 O o 60 0 0) 40 0 S20' 00 2 4 6 8 Distance d Figure 27. Comparison of number of colors used to color the hexagon tiling using our scheme and Scott et. al [1]. If we have d(vt1, vt2) > (a + 1)rTax as shown in Figure 21, according to triangular inequality d(vt, vr) > arTax and d(vt, vri) > arax. This will ensure that transmissions vt,  vri and vt2 vr will be interferenceaware. If we have d(vr, vr) > (a 1)rmax as shown in Figure 22, according to triangular inequality d(vt, vr) > arTx and d(vt, vr) > arTx. This will ensure that transmissions vt,  vr and vt2 vr will be interferenceaware. Hence, to ensure simultaneous transmissions vt,  v and vt  vr do not interfere each other, it is sufficient to have d(vt,, vt2) > (a 1)rmTax or d(vr, vr2) > (a 1)rmT.x . 2.2.2 Problem Definition InterferenceAware Broadcast Scheduling (IABS) problem: Given a multihop WSN G = (V, E) and a sensor node vs V having a message m. The lABS problem is to generate an interferenceaware broadcast schedule for broadcasting the message m from vs to all other sensor nodes. The interferenceaware broadcast schedule must satisfy following conditions: * The source node v, is scheduled to transmit during the first time slot ti. * A node u, if scheduled to transmit in time slot tj, must have received the message m in some earlier time slot ti, where / < j. Two nodes u and v are scheduled to transmit simultaneously, iff their transmissions are interferenceaware. The number of time slots required by the interferenceaware broadcast schedule to complete the broadcast, known as the broadcast latency, should be minimized. 2.3 Tiling and Coloring of 2Dimensional Plane Using Regular Hexagons In this section, we study the tiling and coloring of 2D plane using regular hexagons, which is the kernel part of our solution for lABS problem in 2D WSNs. A regular tiling partitions the 2D plane into identical partitions. We need that the maximum distance within a unit partition should be 1 and its area should be as large as possible. Therefore, to decide its shape, we consider each of the four possible plane Selection Criteria Avg, Optimality Ratio Larger number of uninformed neighbors 1.52 (GHA) Larger number of BFS descendants 2,32 Larger Euclidean hops to source 2.43 Larger BFS depth 2.47 Larger node ID (Random) 2.59 Larger BFS height 2.52 Larger number of neighbors 2.79 Larger distance to source 2.83 Larger number of neighbors 2.65 Smaller Euclidean hops to source 3.69 Smaller BFS depth 3.43 Smaller distance to source 6.02 Figure 312. Comparison of various heuristics algorithms network, are likely to provide higher priority to physically adjacent nodes in the network to transmit. This can aggravate the the spreading of broadcast message in the network. Figure 312 shows that it is better to prioritize nodes which are farther from the source rather than nodes which are closer to the source. This is in line with the observation that farther nodes are more effective in rapidly spreading the broadcast message in the network. 3.4 Conclusion In this chapter, we studied localized broadcast scheduling in the interference environment modeled by protocol interference model. We studied minimum latency broadcast scheduling and proposed the first localized approximation algorithms. Our localized algorithm has an approximation guarantee of r2(/3 + 1 2 Furthermore, in Chapter 6, we provide an energy efficient localized in network detection and tracking protocol for tracking the boundary of the phenomena cloud. This protocol is more relevant for scenarios such as oil spills, gas leakage, etc, where it is more sensible to detect and track only the phenomena boundary engulfing the affected area instead of tracking the entire phenomena. Simulation results are provided to show that the proposed protocol is more efficient than the existing works. 2. We present a distributed algorithms for alltoone data aggregation scheduling and alltoall data broadcast scheduling. Our distributed algorithm for alltoone data aggregation scheduling is the first in literature and has a constant approximation guarantee of 2 2(3 +1 2. 3. We also present a distributed algorithm for alltoall broadcast scheduling, which is the first in literature and has a constant approximation guarantee of 4 ,2/13 + 2. The rest of the chapter is organized as follows: In section 4.2, we describe a localized algorithm for alltoall data broadcast. Section 4.3 describes a distributed approximation algorithm for alltoone data aggregation along with the theoretical analysis. In Section 4.4, we describe a distributed approximation algorithm for alltoall data broadcasting along with the theoretical analysis of its approximation ratio. We provide the performance analysis of these algorithms in Section 4.5. Finally, Section 4.6 concludes the chapter. 4.2 Localized AllToAll Data Broadcast Scheduling Algorithm Similar to onetoall broadcast, we assume that time is divided into discrete Epochs and any hexagon with color ci is assigned the Tth Epoch, such that C, T mod k2, where k2 is the number of colors used to color the hexagon tiling. Each Epoch is divided into two parts EpochR and EpochT. EpochR is primarily used by a Supplier node to receive a message from a Provider in its neighborhood. Epochr is basically used for two purposes. Firstly, it is used by nodes in a hexagon to broadcast their own messages within their hexagon. Secondly, it can be used by some Supplier node to broadcast in its hexagon, a message which it received from one of its Provider. The preference for transmission is given to broadcast messages generated by the nodes within the hexagon. Each node maintains a Message List, which is a set of bits, such that it has a bit for each node in the network. When a node receives a message generated by some node with id i, it sets the bit at the ith location in its Message List. We now discuss how the time duration in an Epoch is used by the nodes in a hexagon. EpochR is further divided into Select time and Receive time. Select time is divided into 614 Comparison based on messages exchanged. . . . . . . . . ... 137 615 Comparison based on number of update messages at different phenomena expansion speed . . . . . . . .. . . . . . . . .. 138 616 Comparison based on energy consumption at different phenomena expansion spe ed . . . . . . . . . . . . . . . . . . . . 13 8 617 Comparison based on messages exchanged at different phenomena expansion spe ed . . . . . . . . . . . . . . . . . . . . 13 8 618 Snapshot of phenomena in WSN. . . . . . . . ... ........ 139 619 Estimated boundary with 0% message loss. . . . . . . . ..... 139 620 Estimated boundary with 15% message loss. . . . . . . . . ... 139 621 Estimated boundary with 30% message loss. . . . . . . . . ... 139 622 Estimated boundary with 45% message loss. . . . . . . . . ... 139 interference range to the transmission range and (/p+i 1) is the maximum degree of the conflict graph. In Chapter 2, we formulate data broadcasting in WSNs as Interferenceaware broadcast scheduling (lABS) problem with an objective to minimize the broadcast latency. We model WSN in 2D as a disk graph and in 3D as a Ball Graph. We consider a more realistic network model where the nodes may have different transmission ranges, while their interference ranges are a times of their transmission ranges, where a > 1. We propose 0(1)centralized approximation algorithms for lABS problem in 2D and 3D WSNs respectively. These approximation algorithms have the state of the art approximation ratio for the network model we considered. Further, in Chapter 3, based on the network and interference model introduced in Chapter 2, we study localized data broadcasting and propose a localized approximation algorithm for data broadcast. Our algorithm has a constant approximation guarantee of 2 r2 ,3 + 1) This is the first localized approximation ratio for data broadcasting in WSNs. We also extended our localized algorithm for 3D WSNs. Furthermore, in Chapter 4, we study the alltoall data broadcasting and alltoone data aggregation and propose: 1. A O(1)distributed approximation algorithm for alltoone data aggregation. 2. A O(1)distributed approximation algorithm for alltoall data broadcast. 3. A Localized algorithm for alltoall data broadcast. Alltoone data aggregation is a fundamental operation in WSNs, in which the data from all the nodes is aggregated in a sink node for further processing and forwarding. Our distributed algorithm for alltoone data aggregation is the first in literature and has a constant approximation guarantee of 2 2()3 + 1i Our distributed algorithm for alltoall data broadcasting is also the first in literature and has a constant approximation guarantee of 4 2( ) +1 2. 5' "C1^ A GHA ' * ApproxAlgo S40 vT LocalizedAlgo 20 0 1.5 2 2.5 3 Beta Figure 310. Effect of 3 on Average Latency Figure 39 shows optimality ratios of the broadcast for all three algorithms. The optimality ratio is the ratio of latency and the BFS height of the network (which serves as the trivial lower bound for broadcasting). The optimality ratio for GHA ranged from 1.0164 to 1.8265, for Approximation Algorithm it ranged between 1.3181 to 3.3840, which is very small in comparison to the upper bound discussed in Theorem 2.3. This shows that our approximation algorithm empirically shows a far better performance in comparison to its theoretical bound. The optimality ratio for our Localized Algorithm ranges between 1.6872 to 16.3568, which is much better than the theoretical upper bound provided in Theorem 3.2. Main advantages of our localized algorithm are, firstly, it has a 0(1) message complexity and secondly, it does not need any centralized control, therefore, it has much lower overheads and more efficiently adapts to network topology changes. Further, in its current state it can also handle multimessage multisource broadcasting. 3.3.2 Effect of 3 on Broadcast Latency Figure 310 shows the effect of increasing 3 on latencies of all three algorithms. We deploy 300 sensor nodes on a square area of side 500m. We vary 3 from 1.0 to 3.0 with an increment of 0.1 to closely monitor its effect. For every value of 3, we generate 100 network instances and averaged latencies produced by each algorithm. TABLE OF CONTENTS [ ACKNOW LEDGMENTS .................................. LIST OF FIGURES ................... ................. ABSTRACT .................... ..................... CHAPTER 1 INTRO D UCTIO N . . . . . . . . . . . . . . . . . . 1.1 Efficient Data Broadcasting and Aggregation ................ 1.2 Efficient InNetwork Detection and Tracking of Dynamic Phenomena . 2 CENTRALIZED APPROXIMATION ALGORITHM FOR INTERFERENCE AWARE BROADCAST SCHEDULING ....................... 2 .1 Introd uctio n . . . . . . . . . . . . . . . . . . 2.2 Network Model and Problem Definition . . . . . . . ..... ... 2.2.1 Netw ork M odel . . . . . . . . . . . . . . . 2.2.2 Problem Definition . . . . . . . . . . . . . . 2.3 Tiling and Coloring of 2Dimensional Plane Using Regular Hexagons . . 2.4 Tiling and Coloring of 3Dimensional Space . . . . . . . . . 2.5 Broadcast Scheduling Algorithm (BSA) . . . . . . . . . . 2.5.1 Algorithm Description .. . .. . .. . .. . .. . .. . 2.5.2 0(1)Approximation Ratio for InterferenceAware Broadcast Sched Problem in 2Dimension ........................ 2.5.3 0(1)Approximation Ratio for InterferenceAware Broadcast Sched Problem in 3Dimension ........................ 2.6 Centralized Greedy Heuristic for broadcast scheduling . . . . . . 2.7 C conclusion . . . . . . . . . . . . . . . . . 3 LOCALIZED APPROXIMATION ALGORITHM FOR INTERFERENCE AWARE BROADCAST SCHEDULING ...................... 3 .1 Introd uctio n . . . . . . . . . . . . . . . . . 3.2 Localized Algorithm for Broadcast Scheduling ............... 3.2.1 Localized Generation of Broadcasting Structure .......... 3.2.2 Broadcast Scheduling of Broadcast Message ........... 3.2.3 An Example Scenario .. ..................... 3.2.4 Localized Broadcast Scheduling Algorithm in 3Dimension ... 3.3 Experim ental Evaluation ........................... 3.3.1 Effect of Number of Sensor Nodes on Broadcast Latency ... 3.3.2 Effect of / on Broadcast Latency .................. 3.3.3 Effect of a on Broadcast Latency .................. 3.4 C conclusion . . . . . . . . . . . . . . . . . 24 26 26 28 28 36 40 40 uling 41 uling 43 45 45 . be satisfied in most or all cases. We found that for the Gator Tech Smart House Smart Floor, setting n equal to 2 or 3 ensures a reasonably good level of performance, where the number of false positives is comparatively low as compared to the number of correct detections and approximately 77% of all footsteps are successfully detected. 2500 Detected S2000 Missed S 1 * False Positive 1500 E ra 15000 0.1 0.2 0.4 0.6 08 1 PT (Thershold Probability) Figure 517. Effect of varying pT with n = 3 and m = 150 Figure 517 shows the effect of varying the threshold probability PT. We observe that as threshold probability increases, the number of false positives decreases since it filters out random spikes. Random spikes typically result in only a few readings of significant magnitude within a fixed size sliding window, hence, there is a sharp drop in the number of false positives even when we only increase pT from 0.1 to 0.2. However making the probability requirement more stringent also results in an increase in the number of false negatives/misses. This is due to the fact that since we are using a sliding window of fixed size, as the number of readings in the window that are required to lie within the phenomenadefined bounds [a, b] in order to satisfy the Probability Condition (defined in Section 5.2) increases, the chance of the Probability Condition getting satisfied decreases. For the Smart Floor we found that setting pT = 0.4 results in a reasonably good detection rate with a low number of false positives and misses. Figure 518 shows the effect of varying the sliding window size m. We observe that if the sliding window size is too low, this results in a large number of false positives 108 not affect the detection and tracking process and phenomena boundary will always be covered by the current set of active nodes. Figure 68. Xh Yh coordinate System for Hexagon tiling H 6.4 Localized Clustering and Data Aggregation In this section, we first describe a localized method for geographically clustering the WSN. We then discuss a data aggregation method to aggregate the phenomena boundary information at the cluster heads to form update messages. A. Localized network clustering: We locally generate a geographical clustering of the WSN. The generated clusters are disjoint and respectively located within nonoverlapping regular hexagons of sides r forming a hexagon tiling of the area covered by the WSN, as shown in Figure 68. On the basis of the hexagon centers, a new Xh Yh coordinate system can be generated with axis inclined at 600. This new coordinate system has two unit vectors i (jr, 0) and j ( 4r, r). A sensor node needs to find the hexagon in which it is located to identify its cluster. The location of each node v c V i.e (v, yv) on 2D is identified using some ad hoc positioning method [54, 55] or sensor nodes may be equipped with GPS functionality. Each node is aware of the CQP's location (xb, Yb) on the 2D plane. The CQP's location on Figure 512. Gator Tech Smart House Figure 513. Smart Floor Tile with force sensors and Atlas Platform Node 5.5 A Practical Application of Phenomena Detection and Tracking We felt that it would be interesting to describe a new realworld application of phenomena detection and tracking which is radically different from the gas cloud and oil slick simulations that are usually presented. The application that we describe involves the Smart Floor [62] in the Gator Tech Smart House (Figure 512) [63]. In addition, we use this application to evaluate the performance of our approaches as described later in section 6.5. The Smart Floor deployed in 2005, consists of a grid of piezoelectric force sensors deployed under the raised floor tiles of the house. Each tile has a single sensor connected to an Atlas Platform [64] ZigBee node placed below its center (Figure 513), which allows a step anywhere on the tile to be detected. The Smart Floor covers 103 CHAPTER 4 ALLTOALL DATA BROADCASTING AND ALLTOONE DATA AGGREGATION 4.1 Introduction In this chapter, we study alltoall data broadcasting and alltoone data aggregation in WSNs. We consider a WSN modeled as a disk graph G = (V, E), where each sensor node vi e V generates a message mi, we study following two problems: 1) Minimum latency alltoone aggregation scheduling and 2) Minimum latency alltoall broadcast scheduling. In minimum latency alltoone aggregation scheduling problem, it is required to aggregate at node vs all messages mi generated at node vi e V \ vs respectively. The earliest time at which the all messages reaches v, is known as alltoone aggregation latency and it should be minimized. In minimum latency alltoall broadcast scheduling, it is required to broadcast all messages mi generated at nodes vi e V respectively to all the nodes in the network. The earliest time at which all messages reach all nodes in the network, known as alltoall broadcast latency, should be minimized. The schedules generated for each of the above problems must satisfy the following constraints: 1. A schedule must specify for each node v, when it can transmit or receive a message m. 2. A node v can be scheduled to transmit a message m at time tj iff it had earlier successfully received the message m at time ti. 3. Two nodes u and v can be scheduled to transmit simultaneously iff their transmissions are interfereaware. The main contributions of this chapter are: 1. We present a localized algorithms for alltoall broadcast scheduling in WSNs. sets of interfering transmissions. For this, GHA considers exact transmission and interfering ranges of interfering sensor nodes. In case of Approximation Algorithm a layer by layer approach is used based on the BFS tree of the network. And in a time slot the identification and scheduling of interfering transmissions is done based on coloring of the hexagon tiling of 2D plane, which considers the the transmission range and the interference ranges as rTax and arT respectively. This possibly results in considering extra transmissions as interfering transmission, which might not be actually interfering. Further, in Figure 37 we see that the performance of the Localized Algorithm is not good for sparser networks, but as the network density increases the algorithm stabilized and after the point when number of sensor node become 80 the algorithm has latency close to 80. Though the Localized Algorithm does not use a layer by layer approach still its latency is a little higher, this is because, nodes need to wait for the time slots assigned to their hexagons in order to receive or transmit the broadcast message. In fact, we expected all three algorithms to respectively converge to fixed values after certain number of nodes. Intuitively, the expected latency is determined by the height of the BFS tree. Since the area of our network is fixed, after a certain number of nodes the height of the BFS tree cannot grow any further on increasing the number of nodes. Since a single transmission from a transmitter can inform all nodes in its neighborhood. Therefore, an increase in number of nodes without increasing the BFS height does not add much to the broadcast latency. Figure 38 shows the average height of the BFS trees in our sample networks for any given number of nodes. It can be observed in Figure 38, the BFS height of the network increases till the number of nodes reaches 40, after that it starts to decrease. This is because of the lower connectivity in sparser networks results in some longer paths, and when the network becomes denser the connectivity enhances and the path lengths becomes shorter. After the number of sensor nodes are around 375 the BFS height the remains close to 5. 10 20 30 40 50 60 10 20 30 40 50 60 Epochs  Epochs  Figure 611. Comparison based on Figure 612. Comparison based on number of boundary number of update nodes. messages. 500 12000________________ 120 A Proposed Protocol 10000 I 400 TOCOB E8000 A Proposed protocol & 300 )6000 m TOCOB (D 100 wU z 10 20 30 40 50 60 z 10 20 30 40 50 60 Epochs  Epochs Figure 613. Comparison based on Figure 614. Comparison based on energy consumption. messages exchanged. in the WSN communicate based on Zigbee protocol (IEEE 802.15.4). Each node has a single radio interface with transmission range 10m. The power consumption specifications for the sensor nodes are provided in Figure 610. We compared our proposed protocol with the TOCOB protocol proposed by Kim et. al [13]. The comparison was based on three important factors: 1) Boundary nodes and update messages send to the CQP, 2) Energy consumption and 3) Protocol messages exchanged by the nodes to implement the protocol. Simulations were performed in two different setups. In the first setup, we perform an Epochwise comparison of two protocols. We simulated the dynamic phenomena by spawning its three occurrences at locations (200,200), (400,200) and (400,300), 137 [65] R. Bose and A. Helal, "Observing walking behavior of humans using distributed phenomenon detection and tracking mechanisms," in Proceedings of 2nd Interna tional Workshop on Practical Applications of Sensor Networks, held in conjunction with the International Symposium on Applications and the Internet (SAINT), Turku (Finland), 2008. [66] M. Cardei, M. T. Thai, Y. Li, and W. Wu, "Energyeffcient target coverage in wireless sensor networks," in Proceedings of the 24th conference of the IEEE Communications Society (INFOCOM), 2005. [67] A. Omotayo, M. Hammad, and K. Barker, "Efficient data harvesting for tracing phenomena in sensor networks," in Proc. 18th International Conference on Scientific and Statistical Database Management (SSDBM), 2006. [68] K. K. Chintalapudi and R. Govindan, "Localized edge detection in sensor fields," in AdHoc Networks Journal, 2003. [69] D. Marthaler and A. L. Bertozzi, "Collective motion algorithms for determining environmental boundaries," in SIAM Conference on Applications of Dynamical Systems, 2003. [70] Z. Jin and A. L. Bertozzi, "Environmental boundary tracking and estimation using multiple autonomous vehicles," in Decision and Control, 2007 46th IEEE Conference on, Dec 2007, pp. 49184923. [71] A. Savvides, J. Fang, and D. Lymberopoulos, "Using mobile sensing nodes for dynamic boundary estimation," in MobiSys 2004 Workshop on Applications of Mobile Embedded Systems (WAMES 2004), June 2004. 150 hexagonal faces is and the distance between its two parallel square faces is Therefore, distances along the Xt, Yt and Zt axes are the multiple of /, /, and respectively. Centers of each truncated octahedron in the 3D space coincides with the integral coordinates in the Xt Yt Zt coordinate system. Hence, every truncated octahedron can be identified by coordinates (i,j, k) of its center as to(i,j, k). zt theta2 ththeetata / t Figure 210. The Xt Yt Zt Coordinate System The m2ncoloring Algorithm: We now present the m2ncoloring algorithm, illustrated as Algorithm 2, for the Distanced truncated octahedron coloring problem. The algorithm uses [m]2 [nl colors, where m, n e R+ and guarantees for any two truncated octahedrons to1, to2 e TOC, having same the color must have distance(to1, to2) > d = (m 1) = (n 1) Figure 211 shows the basic coloring pattern generated by the m2ncoloring algorithm for d = 1, where [m] = 3 and [n] = 3, hence, it uses 27 colors. For any arbitrary distance d e R+, the basic coloring pattern will have [m] = [(d + 1)1 and [n] = [d +11 the number of colors used are [(dG +1) 2 d[5 + 1. This basic coloring pattern is repeatedly used to color all the truncated octahedrons in 3D tiling. ACKNOWLEDGMENTS It is an immense pleasure for me to thank all those who made this dissertation possible. First of all, I would like to profoundly thank my committee chair and advisor Dr. My T. Thai for her encouragement, supervision and support, from initial to the concluding stage of my doctoral research. Her precious advices and moral support helped me to sail through different low and high phases of the PhD life. For this, I will always be grateful to her for the rest of my life. Further, I would like to thank members of my supervisory committee, Dr. Randy Y. C. Chow, Dr. Shigang Chen, Dr. Tamer Kahveci, and Dr. Panos M. Pardalos for their invaluable guidance. Finally, I would like to express gratitude to my family and friends for their unconditional help and emotional support. % . r' c % S , 'I I ~I d(,v % )>=rT^a+) Figure 21. Sufficient conditions for interferenceawareness based on transmitters. N6 trans s in m I \ i r j I ! =rim;(cs i) ..^.^.....T f + d(v,,,V >v=.,>r ,(. +1) Figure 22. Sufficient conditions for interferenceawareness based on receivers. 3. Simultaneous transmissions Vt > Vr and vr > v are interfering, if d(vrl, v) < r1 or d(vt2, Vr) < r^, else they are interferenceaware and do not interfere each other. Based on the above interference model, we describe sufficient conditions for interferenceaware transmissions in Lemma 1. Lemma 1. For simultaneous transmissions Vtl + vr and vt2 vr, sufficient conditions for ensuring interferenceawareness are, either d(vtl, vt2) > (c _1)rax or d(vri, Vr2) > (a 1)rrMax. Proof. If transmitters Vtl and vt2 have transmission ranges equal to r, their interference ranges will be rno Receivers vf r and v will be within rKT distance from their respective transmitters. truncated octahedron tiling of the 3Dspace, represented by the Xt Y Zt coordinate system described in Section 2.4. The truncated octahedron tiling is colored based on Algorithm 2 using (a (o 1)/ +12 (o 1)/ +1 colors, keeping distance d = (a + 1)r,,x. If coordinates of a sensor node v c V and the base station in 3D space are (xv, yv, z,) and (Xb, b, Zb) respectively, the coordinates of v i.e. (xv, yv, zv) and the truncated octahedron to(i,j, k) in which it is located in Xt Y Zt coordinate system can be computed as follows: zv = (z, zb)sin 03/r ,,(33) v = {(Yv Yb) (Zv Zb) COs (01/2)/ tan 03}/rin (34) xt = [(Xv Xb) {(Zv Zb) sin (01/2)/tan 03} 5 /tan]rn (35) The angles 01 and 03 are as defined in Section 2.4. The coordinates of to(i,j, k) are given as: i = L+ 1/2], j = yt+ 1/2, k = [z + 1/2] Node v can use Algorithm 2 to locally identify the color of to(i,j, k). Once all nodes v c V know their respective truncated octahedrons and colors, the localized broadcast scheduling algorithm for 2D WSNs can be used for performing interferenceaware broadcasting in 3D WSNs. Theorem 3.2. The approximation ratio for localized broadcasting algorithm for the IABS problem in 3D WSN is2 (a 1)/ +1 F/ +( 1)/ + I. expand smoothly as well to fully cover and track the phenomenon's movement. Also, at the border of the phenomenon, the DistPDT has a thicker green line than that of FDA, showing that DistPDT requires more candidate nodes due to our previous relaxed definition. In addition, at the inner area of the phenomenon, while all tracking nodes are active for DistPDT and FDA, ODA has some inactive tracking nodes. This is due to the optimization step to cover the entire area and satisfy the quorum but still minimize the energy consumption. During the overall 20 epochs, FDA involved 10.84% lesser active nodes compared to DistPDT. ODA further improves the performance by using 36.54% less active nodes compared to DistPDT. 5% 0% 2.86% 10% 0.245% 6.45% _ 15% 0.275% 11.43% Figure 541. Percentage of holes generated wrt percentage of update messages lost To evaluate the degree of fault tolerance of our proposed algorithms, we further ran the simulations allowing the loss of update message in the network and summarize the results in Figure 541. In addition, Figures 542547 pictorially show the holes generated for FDA and ODA while detecting phenomena cloud, when percentages of update messages lost are 5%, 10% and 15% respectively during the epoch t20. A hole is represented as a red ball and is generated when the detection status of a tracking sensor cannot be determined at the CQP based on the update messages received. We observed that our algorithms showed a reasonable performance when the network is vulnerable of message losses. Figure 541 shows the percentage of holes generated by FDA and ODA with respect to the percentage of update messages lost. As can be seen, the holes generates by FDA is very negligible, even only 0.275% at the rate of 15% of update message lost. As expected, ODA generates more holes. This is clearly 120 4. Idle Sensor: All sensors which do not belong to any of the above three categories are called idle sensors. These sensors are not engaged in phenomenon detection or tracking and do not perform any monitoring whatsoever. Typically, most sensors in the space will fall in this category since only selected clusters of sensors will be actively engaged in the detection and tracking of phenomena clouds at any given time. This ensures that the detection and tracking process is executed in a localized manner with minimal expenditure of energy. 0o 0 0 0 0 0 0 Initial Selection Initial Occurrence 0 0 0 S0 0 0 0 0 0 0 0 0 0 0 0 o 0Monitring0 00 0 0 0 0 0 0 0 0 0 0 00 0 0O 00 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 00 0 Shrinking of Growth of 0 o 0 0 Phenomena Phenomena 0 0 0 0 0 0 0 o Cloud Cloud 0 0 0 0 0 0 S 0 0 0 0 0 0 0 0 0 0 0 0 o Tracking Potential Candidate Candidate Idle Sensors Figure 53. Detection and Tracking of a Phenomena Cloud Remarks. We have modified the definitions of candidate and potential candidate sensors as compared to our initial definitions in the preliminary work [57]. More specifically, in [57], we defined that a candidate sensor is not required to satisfy the Probability Condition and a potential candidate sensor cannot have a tracking sensor, but only candidate sensor as its neighbors. Consequently, even if a candidate sensor does not satisfy the Probability Condition, it unnecessarily invokes all its idle and 37.76% in comparison to DistPDT. ODA improves the energy consumption of FDA by 34%, reflecting that applying the optimization step makes a significant help. In summary, for the first set of experiments, ODA performs the best and StreamPDT performs the worst in all terms: the number of active nodes, the number of exchange messages, the number of update messages, and energy consumption. Also notice that the graph for StreamPDT is a constant line when the phenomena clouds are enlarging because all sensor nodes in the grid remain active at all time regardless of the cloud's size. For the other three algorithms, when the phenomena expand, the graphs are increasing, but not linearly. s gorlthm ODA FDA DsPDT StreamPDT Grid Size 101X101 201X201 301X01 101X101 201X201 301 X 303 101X 101 21Xz201 301301 1011101 201X201 301X301 Ccmparslw Paramter Total 1.971 11"66 14975 23171 23134 23155 23171 21184 23155 255025 1010025 2265025 Update TotalEnergy 234 22 2U..43 233 69 328. 6 29.2S 328 6 W36 366 6 366. 4 307 D60 12180 0 27316.20 Consumption (JouIesI Total Active 18595 18612 18552 26795 26M30 26732 29942 29933 29907 255025 1010025 2265025 Nodes Total 15138 15146 15128 55 L33W 2550Z 26482 26481 26455 255025 1I01005 2265025 Exchanged Messaes Figure 525. Comparison based on different grid size. In the second set of simulations, we varied the grid size as shown in Figure 525. It can be observed that DistPDT, FDA, and ODA do not show much variation in all four comparison parameters with respect to increase in the grid size. This is derived from the fact that for these algorithms, the detection and tracking process is localized to the immediate neighborhood of phenomena cloud at any given time and does not require all sensor nodes to remain unnecessarily active. In contrast, StreamPDT requires all nodes in the network to remain active and send update messages about their detecting status to the CQP. Therefore, as the grid size increases, the more active nodes and the larger network traffic. Consequently, the performance of StreamPDT degrades. The simulation results show that DistPDT, FDA, and ODA are scalable to the size of grids 115 BIOGRAPHICAL SKETCH Ravi Tiwari was born in 1978, in the historic city named Agra, located in north central India. He received his Bachelor of Engineering degree in computer science and engineering in the year 2001 from Dr. Bhim Rao Ambedkar University (Formally Agra University), Agra, India. In 2004, he received his Master of Engineering degree with specialization in communication, controls and networking from Rajeev Gandhi Technical University, Bhopal, India. 2. In the second set of simulations, we varied the size of the sensor grid from 101 x 101 to 301 x 301 and simulated the random movement and expansion of phenomena cloud for 25 epochs in order to show the scalability of our proposed algorithms. 3. In the third set of simulations, we simulated the random movement and expansion of phenomena cloud for 5 epochs on a small rectangular sensor grid of size 10 x 10 to compare the performance of our algorithms with the optimal solution generated by the Integer Program introduced in Section 5.4.1. 4. Finally, the fourth set of simulations is to verify the functioning and performance of each of above mentioned algorithms pictorially through snapshots taken during their executions. We simulated the random expansion of phenomena cloud for 20 epochs on a medium sized rectangular grid of 51 x 51 sensors deployed over an area of 500m x 500m. We also discuss the packet lost tolerance of our proposed algorithms in this set of simulations. We connected each sensor to an Atlas ZigBee node, whose hardware is based on Atmel Zlink RCB design. At the beginning of each simulation, we randomly spawned phenomena cloud in different areas on the sensor grid. During each epoch, the variation of phenomena cloud motion and size were simulated by randomly changing shape, size and direction of motion of its boundary. Hence, the simulation can be viewed as a random walk of phenomenon cloud over a sensor grid. Our simulations introduce a high degree of uncertainty regarding phenomenon cloud movement and test the performance of detection and tracking algorithms to the fullest extent. During each epoch, we logged four statistics which are 1) the number of active sensors involved, 2) the number of network messages exchanged between sensors for the innetwork implementation of proposed algorithms, 3) the number of updates sent to the Centralized Query Processor (CQP), and 4) energy consumption. We calculated the energy consumption of nodes as a function of processing costs (including sampling sensors) and network costs (incurred of Xh Yh plane and adds it to set S of cocolor hexagons. It then sequentially rotates the Xh Yh plane by 600 for five times to find rest of closest cocolor hexagons of h(i',j') that are h(i' + (i +j),j' i), h(ii , ( j) j), h(i' (i +j), j' + ), h(i' j,j' + (i +j)) and adds them to the set S. Due to the symmetric property of the rotation, distances between h(i',j') and its closest cocolor hexagons remain the same. Any hexagon which is identified for the first time is added to the set S and above steps are recursively repeated on it. The Figure 26 shows cocolor hexagons of h(0, 0) identified by Algorithm 1 for distance d = v', where / = 2, j = 3. Six closest cocolor hexagons of h(0, 0) are h(i,j), h((i +j), i), h(j, (i +j)j), h(i, j), h((i + j), i), and h(j, (i +j)). We can see that centers of cocolor hexagons of h(0, 0) form a triangular sublattice S and a rhombic sublattice Rh of the lattice structure generated by centers of hexagons in H. Unit vectors of sublattice Rh are A = i + jj and B = j/ (i +j)j. The number of possible classes i.e. the index of sublattice Rh in H, which is the number of disjoint sublattices similar to Rh in H is given as Idet(A, B) = i2 +j2 + ij [49]. Thus, there are {Rhl, Rh2... Rh(2+j2+U)} disjoint sublattices similar to Rh in H, union of which form H. If we assign each of them a unique color, all hexagons in H will be colored with i2 +j2 + ij colors and the closest distance between two cocolor hexagons will be at least d R+. In Theorem 2.1, we prove that the hexagon coloring generated this way is the optimal solution for Distanced hexagon coloring problem. Lemma 2. Algorithm 1 optimally identifies cocolor hexagons for a given distance deR+. Proof. Lets consider the hexagon tiling of an area. We need to identify maximum number of cocolor hexagons on this area, such that any two cocolor hexagon are at least at a given distance d R+. For this, Algorithm 1, computes a pair (i,j) and produces a set S of cocolor hexagons, whose centers form an equilateral triangular lattice of side length '/(i2 +j2 +i), as shown in Figure 26. The number of Figure 511. Clustering on the basis of hexagon lattice 1. All the core tracking nodes in a cluster select a cluster head, this can be selected on the basis of maximum energy left or on any other arbitrary factor [61]. 2. Each elected cluster head performs a one hop broadcast to inform its presence. Consequently, all nodes in the neighbor clusters are informed about the presence of this cluster head. 3. At this step, each node in a cluster can have at most seven cluster heads in its neighborhood. Now all the core tracking nodes send back to the cluster heads the extra required number of cluster heads they need to satisfy the minimum quorum condition. 4. If any of the core tracking nodes in a cluster does not satisfy the minimum quorum condition, then the last cluster head in the cluster again invokes the cluster head election protocol within the cluster to generate an extra cluster head. This is repeated until all the nodes in a cluster satisfy the minimum quorum condition. 5. Finally, all the cluster heads in a cluster are scheduled to be active, whereas all the other core tracking nodes in the cluster are scheduled to sleep in order to conserve the energy. 6. If any active cluster head fails or goes down because of getting depleted of energy, then a new cluster head is elected to replace it. 102 Sensor Node Neighbor Potential 1 Candidate Candidate Tracking Not Idle None Not Applicable Ai Send alert Potential whenever Not None readings satisfy Not Candidate None rbabiliy Applicable Probability Condition Send alerts/ receive alerts Receive alerts whenever their Send alert from neighbor readings satisfy whenever whenever its Phenomena readings do Candidate readings satisfy Condition or not satisfy Probability whenever Probability Condition readings do not Condition satisfy Probability Condition Send alert Send alerts/ whenever the receive alerts Phenomena whenever Trackig Not Applicable Condition or their readings Probability do not satisfy Condition is not Probability satisfied Condition Figure 54. Action Taken by a Sensor Node with respect to its Neighbors which are not idle neighbors as potential candidates, thereby causing excessive resource usage. In contrast, in this paper, a candidate sensor must satisfy the Probability Condition and a potential candidate sensor can has at least either one tracking or candidate sensor in its neighborhood. Therefore, only those idle sensors are invoked as potential candidates which have phenomena occurring in their vicinity. This slightly modification have an impact on the performance in terms of energy and resource consumption which we show later in section 6.5. 5.3.2 Keeping Tabs on the Neighborhood Each sensor node keeps track of the category of its neighbors. This is done in a peertopeer fashion, where a sensor transitioning from one category to another notifies its neighbors via a 1hop broadcast without involving the centralized query processor. We used ZigBee communication protocol in our system, which natively supports 1hop broadcasting. The category of a sensor and its neighbors determines their mutual responsibilities towards each other. For example, a candidate sensor node A has evaluates the effectiveness of our detection strategy in a real world sensor deployment and analyzes the effect of varying phenomena parameters described in Section 5.2.2. The second set of experiments uses simulation to evaluate the resource usage and power consumption of our approaches compared with the streambased method. We relied on simulation in this case because we wanted to measure resource usage and power consumption in large sensor networks of varying sizes. And it was not practically feasible for us to physically deploy sensors in such large numbers for the purpose of experimentation. 5.6.1 Effectiveness of Detection Strategy In this first set of experiments, we study the effectiveness of our phenomenon detection and tracking mechanism in a realworld sensor deployment inside the Gator Tech Smart House. 5.6.1.1 Experimental setup We chose to evaluate effectiveness by performing experiments using the Smart Floor (previously described in Section 5.5) where human footsteps are represented as phenomena clouds and phenomenon detection and tracking is used to monitor the location of a resident in the house. We observed the effect of phenomenon definition parameters (PT, m and n, defined in Section 5.2.2) on the detection efficiency of our technique. We varied the values of each of these parameters and studied their effect by logging the number of false positives, false negatives/misses and correct detections of a human step. In order to aid our evaluation, we restricted movement to a 100 sq. ft. area in the living room of the smart house and had test subjects walk along a clearly marked path on the floor. This allowed us to log the actual steps that a person was taking and collect statistics on correct detections and detection errors. 5.6.1.2 Results and analysis The experimental results are presented as 3 graphs shown in Figures 516, 517 and 518. Figure 516 shows the effect of varying parameter n which determines 106 Proof. As I (o 1)3 1+ ~ (a 1) + 1] colors are required by Algorithm 2 to color the truncated octahedron tiling. Based on this, the theorem can be proved similar to Theorem 3.1. O 3.3 Experimental Evaluation In this section, through simulations, we present the experimental evaluation of localize approximation algorithm for onetoall broadcast scheduling proposed in this chapter and centralized approximation algorithm and greedy heuristic for broadcast scheduling proposed in Chapter 2. We randomly generated 11, 000 network instances with different setups and ran our algorithms to evaluate their performance in terms of the broadcast latency. We study the behavior of our proposed algorithms based on three important parameters: 1) Number of sensor nodes in the network, 2) Ratio /, and 3) Ratio a. We implemented the approximation algorithm (ApproxAlgo) introduced in Section 2.5, the localized algorithm (LocalizedAlgo) introduced in Section 3.2, and the centralized greedy heuristic (GHA) introduced in Section 2.6. Although, these three algorithms work for 2D as well as 3D WSNs, but we simulated them only on 2D WSNs. 3.3.1 Effect of Number of Sensor Nodes on Broadcast Latency In the first set of experiments, we consider a square area of sides 500m and randomly deployed N nodes on it, where N varies from 10 to 500, rn = 100m, and a= f = 2.0. Figure 37 shows plots of broadcast latencies produced by ApproxAlgo, LocalizedAlgo and GHA with respect to number of sensor nodes in WSN. The latency value for any number of nodes is averaged after running each algorithm on a set of 100 network instances. As it was expected the latency for the greedy heuristic is the smallest. There are two main reasons for this: firstly, GHA does not follow the layer by layer broadcasting approach. Secondly, for any time slot GHA follows the manual identification, selection and elimination of simultaneous transmissions among different SMiddle Region Figure 51. Dissection of the Phenomena Cloud constitute a phenomenon are denoted by a and b respectively. For example, a hydrogen gas cloud can have a = 20% volume and b = 100% volume. PT is the threshold probability, m is the observation count and n is the minimum quorum. A sensor's reading is said satisfying the Probability Condition, iff it is lying in the range [a, b] with probability greater than PT during the last m observations (that is, in a sliding window of size m). A sensor is said to participate in a phenomenon cloud (or satisfy the Phenomenon Condition) P = (a, b, PT, m, n), iff it and at least n neighbor sensors satisfy the Probability Condition. This criterion ensures that a sensor must have a sufficient number of neighbors in agreement with it before it can claim the existence of a phenomenon cloud, thereby reducing the occurrence of false positives. We define Phenomenon Set to be the set of sensors satisfying the Phenomenon Condition. We consider a phenomenon cloud is composed of multiple regions as shown in Figure 51. The innermost region, called the Core region of the cloud is where the phenomenon is most strongly observed. Clearly, the sensors lying in the core region satisfy the Phenomenon Condition and hence, are members of the Phenomenon Set. The Middle region is the outer border of the phenomena cloud where the Prob ability Condition is satisfied but the Phenomenon Condition is not yet satisfied. The Outer region denotes the fringes where uncertainty regarding the occurrence of the phenomenon is highest, hence, the outer fringe is the region where the phenomena is sparse and is not detected. Section 5.3.1 describes the roles assigned to the sensors a tradeoff between the energy consumption and fault tolerance. In order to reduce the energy consumption and message complexity, ODA leaves enough active core tracking sensors to sastified the required quorum whereas all tracking sensor nodes in FDA are active. We can slightly modify ODA to be more fault tolerance by allowing more core tracking sensors to be active. More specifically, at step (4) in section 5.4.2.2, instead of repeating until the minimum quorum n is satisfied, we can repeat the process until all active nodes in a cluster satisfy an quorum condition where a > 1. The bigger a is, the more active nodes are, the lesser holes generated. Let us further look into the snapshots (Figure 542547) to see the location of these holes. The holes were mostly created in the inner part of the core tracking region. This is partially because we only allow some core tracking nodes (which locate in the inner region) to be inactive. When update messages of some active core tracking nodes get lost, it results in lack of information about these active core tracking nodes and the sleeping core tracking nodes which they were covering. As only a few holes are generated at the boundary of the core tracking region, consequently, the region where the phenomena cloud is currently located can easily be identified at the CQP even if 15% of update messages are lost, as shown in Figure 547. 5.7 Related Work In an early stage of the phenomena detection and tracking using WSNs, the phenomenon is static and confined to a set of points or within a certain area, often known as the coverage problem (see [23, 66] and references therein). Towards nowadays, as the phenomena are dynamic, have irregular shapes, and invariant movements, there has been recently an on going research on detection and tracking of phenomena cloud [12, 13, 19, 42, 4446, 67, 68]. The most closely related work is NilePDT [46], which is a Phenomena Detection and Tracking (PDT) framework running on top of centralized Nile data stream management system, developed by Indiana Center for Database Systems (ICDS) at CHAPTER 2 CENTRALIZED APPROXIMATION ALGORITHM FOR INTERFERENCE AWARE BROADCAST SCHEDULING 2.1 Introduction Due to its imperative motivation in Wireless Sensor Networks (WSNs), broadcast scheduling problem has been extensively studied by many researchers [1, 15, 32, 35, 36]. Existing works consider network and interference models, which are not practical. Either they assume that all sensors have the same transmission range [32, 35, 36] or sensors may have different transmission ranges but their interference ranges are equal to their transmission ranges [15]. However, in practice, depending upon their energy level or functionality, sensor nodes may have different transmission ranges and their interference ranges are always greater than their transmission ranges. Furthermore, existing solutions consider WSNs are always deployed in 2D plane. In contrast, there are many cases when sensor nodes acquire locations in 3D space. For instance, fire sensors deployed at different levels on trees in forests [47], underwater sensors deployed at different depths in seas to collect vital information about aquatic life [48]. Considering deficiencies in the existing research, in this chapter, we study the broadcast scheduling problem for WSNs in 2D and 3D. We consider a more realistic network model, in which each sensor node v has a transmission range r~ eG [rT,, r,,Tx] (where r = > 1) and its interference range rv = ar (where a > 1). This model has not been considered for broadcast scheduling problem in the existing literature. Since broadcast scheduling is NPhard [15], we propose O(1)centralized approximation algorithms for WSNs in 2D and 3D respectively. For this, we study two sub problems: 1) Tiling and coloring 2D plane using regular hexagons, and 2) Tiling and coloring 3D space using truncated octahedrons. Solutions to these two problems lead to O(1)approximation ratios in 2D and 3D respectively. Our O(1)centralized approximation algorithm is the first approximation algorithm for 3D WSNs and in 2D our algorithm has the best approximation ration for the model we considered. Xh Yh coordinate system is (0, 0). Based on this, a node v e V identifies its coordinates (xv, yv) and the integral coordinates h(i,j) of its hexagon in Xh Yh coordinate system as follows: h Yv rV x, {xv Y v/ (61) tan 600 2 yh = yvsin 600/3 (62) 2 The coordinates of the hexagon h(i,j) in which node v is located is given as: /= {xv I}/ (63) tan 600 2 2(63) j= ysin 600/ (64) 2 2 During the inception of the WSN, each sensor node v c V identifies its location (xv,, yv) and hexagon h(i,j) and exchanges this information with its neighbors. The nodes located within the same hexagon form a cluster. On the basis of factors such as the maximum energy contained, a cluster head can be elected (smallest id is used to break the ties). Based on the node ids, the cluster head forms a sorted list of nodes in the cluster along with their respective locations. The cluster head then sends a message containing this list along with the hexagon coordinates of the cluster to the CQP. The CQP forms a hashmap indexed on the basis of hexagon coordinates and stores in it the sorted list of nodes in the hexagon. B. Data Aggregation and Reporting: The cluster head generates a bitarray called Report array. The Report array contains a bit for each node in the hexagon, arranged in sorted order of their ids. If a cluster head has B nodes in its hexagon, as shown in Figure 69, it receives BINFO messages from them and generates the Report array, setting the bits corresponding to the B nodes in the hexagon. It then sends this Re port array to the CQP along with its hexagon coordinates in a PINFO message. The 135 Figure 25. Closest points pi and P2 in two hexagons * pl is the mid point of the right side of h(O, 0) and p2 is the mid point of the left side of (i,j), in Figure 25 (i = 7,j = 0). Without loss of generality, we consider / < j, therefore, we get rid of the third case. Also we exclude the case i = 0, j = 1. We compute (i,j) for the given d e R+ as follows: * Identify two pairs (il,jl) and (i2,j2) as follows: Compute (il > 0,jl > 0) in first quadrant of Xh Yh plane using the inequality d2 < 3((il 2a)2 + (. 2a)2 + (il 2a)(ji 2a)), such that i2 +j2 +j i is minimum among all integral solutions of this inequality, where a is as shown in Figure 25 and is equal to . Compute (2 = 0,J2 > 1) in first quadrant of Xh Yh plane using the inequality d2 < (j2 1)2, such that j2 is minimum among all integral solutions of this inequality. Finally, if (i2 + il +j2) < (i2 + 122 +j,2), we select /i,ji as i,j else we select i2,J2 as i, J. We now introduce the cocolor hexagon algorithm, illustrated in Algorithm 1. In Lemma 2, we prove that for any arbitrary distance d R+, Algorithm 1 optimally identifies cocolor hexagons (i.e. hexagons having the same color) for any given hexagon h(i',j') in H. The Algorithm 1, for the given d e R+, first computes (i,j) using the above method and identifies the closest cocolor hexagon h(i' + i,j' j) of h(i',j') in the first quadrant Purdue University. NilePDT is designed for detecting and tracking phenomenon clouds such as gas clouds, oil spills and chemical waste spillage. NilePDT uses two custom database operators, namely, SNScan and SNJoin to perform phenomenon detection and tracking. The SNScan operator scans all the sensors in the network and chooses candidate sensors which have a high probability of detecting the phenomenon. The SNJoin operator then evaluates each of these candidate sensors and checks if they join with other candidates a certain number of times and hence detect a phenomenon event. NilePDT uses feedback control to continuously tune the SNScan and SNJoin parameters to maximize efficiency of the detection process. The main drawback of the NilePDT approach is that it takes a streaming database view of the process. It does not consider any mechanisms for controlling the flow of data at the source sensors themselves or address power consumption and network bandwidth issues inside the sensor network. Furthermore, it requires all sensors to pump readings to the SNScan operator to allow it to choose phenomenon candidates, which can lead to potentially massive scalability issues. In this paper, we have compared our algorithms to this work, referred at StreamPDT Omotayo et al. [67] describe a data harvesting framework for tracing phenomena. They propose algorithms for maintaining a data farm on the nodes by maximizing the utilization of their onboard nonvolatile storage, for enabling backtracking to determine the cause of a phenomenon. McErlean et. al. [42] propose a distributed event detection and tracking algorithm for moving objects using WSNs. However, this system assumes the prior availability of optimal adhoc routing mechanisms and is primarily designed for detecting individual discrete objects with welldefined shape and size, as opposed to phenomenon clouds whose shape and size typically cannot be defined in exact terms. There are also some work studying the boundary of the phenomena clouds instead of detecting and tracking the entire area [12, 1922, 6871]. As these studies are not in the scope of this paper (we detect and track the entire area), we only briefly mention 122 very short time messages, the probability for Response Messages from multiple Providers to collide is very low. On receiving a Response Message, the Supplier node broadcasts a Receiving Message. This message indicates the corresponding Provider to start transmitting and to all other Supplier nodes in the hexagon, it indicates to stop attempting in the current Epoch. During the Receive time the broadcast message is received by the Supplier node from its corresponding Provider. Since the size of the broadcast message is very large in comparison to control messages, the Select time is negligible in comparison to the Receive time. If the Supplier node does not receive a Response Message from any of its Providers, in subsequent Trices other Supplier nodes in the hexagon attempt to receive the broadcast message from their respective Providers. After receiving the broadcast message in EpochR, during EpochT, the Supplier node broadcasts the message m to all other nodes in the hexagon. 3.2.3 An Example Scenario Without loss of generality we consider that all the nodes in the WSN have the same transmission range r and the distance d = (a + 1)r = r/3. We consider the hexagon tiling of the 2D plane, with hexagons of sides Now following Algorithm 7, we have k = 3 and the number of colors used to color the hexagon tiling will be k2 = 9, these are {C1, C2... C9}. We can see in Figure 35 the hexagons at a distance less than d are having different colors. Figure 35 basically shows an example where a WSN is deployed on the 2D plane, the nodes are represented as points. The mapping of the WSN nodes on the hexagon tiling along with the formation of the broadcast structure shown in Figure 35. Figure 36 shows the broadcast schedule generated when a source node s in the hexagon h(0, 0) initiate the broadcast. Following is the epochwise description of the generate broadcast schedule: Epoch 1 : The source node s in h(0, 0) broadcasts the broadcast message to all the nodes in h(0, 0). CHAPTER 3 CENTRALIZED APPROXIMATION ALGORITHM FOR INTERFERENCE AWARE BROADCAST SCHEDULING 3.1 Introduction In this chapter, considering the network and interference model defined in Chapter 2, we study localized broadcast scheduling in WSNs. Existing works only provide centralized solutions [1, 15, 32, 35, 36, 38, 40, 51, 52]. In addition, most of them consider sensor nodes have the same transmission range and their interference range is equal to their transmission range. The major drawback of these centralized solutions is that they fail to adapt to topology changes in case of dynamic networks. This can be easily accommodated by localized algorithms with much lesser overheads. In this paper, we study the localized broadcast scheduling considering the protocol interference model [53] to model the interference environment. We consider each sensor node has a transmission range rf c [ri rx] (where r = > 1) and its interference range is a times of its transmission ranges (where a > 1). We propose a novel approach to locally partition and color the WSN into clusters. Our approach is based on tiling and coloring the 2D plane covered by WSN nodes using regular hexagons. This approach is used in our algorithms to generate interferenceaware transmission schedules for transmitter nodes. In Section 3.2.1, we discuss this approach in detail. Based on this approach we proposed the first localized approximation algorithm which has a constant approximation guarantee of 2 r 1) + i 2. Furthermore, we extended our localized algorithm to work for 3D WSNs. In Section 3.2.4, we present this extension along with the theoretical analysis of the approximation ratio for localized broadcast scheduling in 3D WSNs. The rest of the chapter is organized as follows: In section 3.2, we present our localized approximation algorithm for broadcast scheduling. Section 3.3, provides the performance evaluation of the localized approximation algorithm described in Section Algorithm 5 Greedy Heuristic Algorithm (GHA) (G = (V, E), r, a, /, s) 1: INFORMED = {s}, ACTIVE = {s}, TIME = 0 2: Priority Queue PQ : key(u e PQ) = IN(u) \ INFORMEDI 3: while INFORMED z V do 4: PQ ACTIVE, S  5: while (PQ z 0) do 6: u  ExtractMin(PQ) 7: ACTIVE + ACTIVE \ {u} 8: if (N(u) \ INFORMED / 0) then 9: From PQ remove all nodes v whose transmissions would conflict with the scheduled transmission of u, as follows: 10: Vv e PQ & Vw e N(v) \ INFORMED, if (d(u, w)) < arT then PQ PQ \ {v} 11: Vx e N(u) \ INFORMED & Vy E PQ, if (d(y, x)) < arT then PQ + PQ \ {y} 12: Schedule u as follows: 13: S SU{u} 14: for (w c N(u) \ INFORMED) do 15: INFORMED + INFORMED U {w} 16: ACTIVE + ACTIVE U {w} 17: end for 18: end if 19: end while TIME TIME + 1 20: Schedule S in time slot TIME 21: end while interference ranges are a times of their transmission ranges (where a > 1). We devise efficient coloring methods for coloring a hexagonal tiling in 2D plane and a truncated octahedron tiling in 3D space, based on which we propose O(1)approximation algorithms for lABS problem in 2D and 3D WSNs respectively. Our O(1)approximation algorithm for 3D WSNs is the first in literature and our O(1)approximation algorithm for 2D is the best in literature for the network and interference model we considered. Finally, we present an efficient greedy heuristic to study the effect of various priority metrics for greedily selecting a transmission among multiple interfering transmissions. discussion for the rest of this paper, we assume that sensor nodes are deployed in such a manner that each sensor has a sufficient number of neighbors to potentially avoid false positives. 5.3.5 Monitoring for Initial Occurrences The query processor pushes the phenomenon cloud parameters on to each of the selected initial potential candidate sensor nodes in the network. At the beginning of every epoch, each potential candidate node monitors its readings and sends a 1 hop broadcast message if it satisfies the Probability Condition and transitions into a candidate sensor node. In order to enable sensor nodes to send or receive alert broadcasts to and from multiple neighbors simultaneously during the same epoch, a slotted approach is used to ensure collision avoidance similar to what is described in [58]. Each epoch is subdivided into multiple subepochs and each node only broadcasts alerts during its assigned subepoch. The candidate sensor node aggregates alerts received via broadcasts from its neighbors and determines if it satisfies the Phenomenon Condition. A candidate sensor satisfies the Phenomenon Condition if its readings satisfy the Probability Condition and it also receives broadcast alerts from at least n neighbors which also satisfy the Probability Condition in the same epoch. 5.3.6 Notification of Initial Occurrence If an initial potential candidate node has satisfied the Probability Condition, it transitions to a candidate sensor node. Furthermore, when a candidate sensor node satisfies the Phenomenon Condition, it notifies the query processor residing in the base station that it has detected presence of a phenomenon cloud. The query processor adds the candidate node to the PhenomenonSet and the candidate sensor transitions to a tracking sensor node using rule R1 given in Section 5.3.3. With a new application and a broader concept of phenomena clouds, early studies on boundary detection and tracking of welldefined shapes are no longer sufficient [12, 13, 19, 44, 45]. Only one work recently studied on similar applications, called NilePDT (a streambased mechanism) may be applicable [46]. However, this centralized approach does not take into account the cost of acquiring and transmitting sensor readings and typically requires participation from all sensors in the network. Unfortunately, sensor sampling costs and networking and processing overheads can have a critical effect on the practical viability of the entire smart space This raises a need for a distributed innetwork detection mechanism, where the detection and tracking process is localized to the immediate neighborhood of a phenomenon at any given time and does not require all the sensor nodes to remain unnecessarily active. Along this direction, we introduce a mathematical model and innetwork distributed mechanisms with the following specific contributions: 1. Analyzing the structure of phenomena clouds and proposing a set of parameters to comprehensively describe them without requiring complex models. 2. Presenting an energyefficient and distributed algorithm, called Full Density Algorithm (FDA) for realtime detection and tracking of phenomena clouds, which do not require customization of the network routing layers. The proposed algorithm works in an autonomous manner without requiring intervention from the centralized query processor residing in the base station and hence, is suitable for disconnected mode of operation, when continuous communication with the base station cannot be maintained. Plus, the proposed algorithm can be used in a new application domain, i.e, detection a walking motion. 3. Introducing a mathematical model based on Integer Program (IP) to further optimize the energy consumption during the phenomena cloud detection and tracking process. This model provides an excellent benchmark for evaluating the performance of the proposed algorithms. Figure 32. Hexagon coloring generated by Algorithm 7 for k = 4, colors assigned to the hexagons are represented by numbers. 2. A set PP, c (N(v) \ HN(v)) (Possible Providers), which is a set of nodes in v's neighboring hexagons, its contains a single node from each neighboring hexagon. 3. A set Cv of ordered pairs (v,, ci), where vi e PPv and ci is the hexagon color of vi. After generating these sets, node v broadcasts the set Cv to its neighbors in HN(v). Based on Cs it received from its neighbors vi e HN(v), node v generates a set L = {(vi, C,) I v c HN(v)}, where C, is the set of colors in the neighborhood of nodes vi e HN(v), and runs Algorithm 8, to identify the set of Supplier nodes in its hexagon. Note that every node in HN(v) generates the same copy of L, so each of them identify the same set of Supplier nodes. The correctness of Algorithm 8 depends on whether the set of Supplier nodes generated for a hexagon have possible providers in all neighboring hexagons. This happens only if any two Suppliers nodes in a hexagon having respective possible providers of the same color belonging to the same hexagon. We prove this in Lemma 7. 3.2 and the centralized approximation algorithm and the greedy heuristic described in Chapter 2. Finally, Section 3.4 concludes the chapter. 3.2 Localized Algorithm for Broadcast Scheduling In this section, we introduce a localized algorithm for broadcast scheduling in 2D WSNs and provide its extension for 3D WSNs. The algorithm first generates a broadcasting structure, on top of which message broadcasting can be performed whenever needed. As the broadcasting structure is not a tree rooted at some specific source node, it supports broadcast initiated by any node as the source node. We first discuss the localized construction of the broadcasting structure followed by description of the protocol for broadcasting a message. Algorithm 6 Localized Algorithm for generating a Broadcasting Structure Step 1: Every node vi e V locally identifies the hexagon h in which it is located along with its color. Step 2: Node v, then broadcasts its id, color and hexagon coordinates to its one hop neighbors. Step 3: Based on the color and hexagon information from onehop neighbors, v, generates HN(vi), PP, and a set of ordered pairs C,. Step 4 Node vi, broadcasts its C, to its neighbors in HN(vi), based on similar information from its neighbors in HN(vi), it generates a list L = {(vj, Cj) Ivj HN(vi)}. Step 5: Node vi runs Algorithm 8 to identify the set of Supplier node in its hexagon. Step 6: If the node vi is a Supplier node, it sends a Provider Request message to all its neighbors in PP,. Step 7: A node u e PP, on receiving a Provider Request message responds with a Provider Response message and becomes a Provider node for v. The edge connecting a Supplier node and a Provider node becomes a Provider edge. Step 8: The set of Supplier nodes, Provider nodes, and Provider edges together forms the broadcasting structure G = (Vb, Eb). 3.2.1 Localized Generation of Broadcasting Structure In this section, we describe the construction of the broadcasting structure, illustrated as Algorithm 6. We assume that the subgraph generated by the bidirectional links in G = (V, E) is connected. Further, the 2D plane is partitioned into regular hexagons of sides r forming a hexagon tiling which can be represented by the Xh h coordinate system, described in Section 2.3. 1,483.33 2,243.86 2,383.36 8,806.56 117,097 182,650 194,160 732,050 104,533 170,086 181,736 732,05 Figure 524. Comparison based on overall 50 Epochs Figure 520 evaluates the performances of the four algorithms in terms of the number of active nodes involved in the detection and tracking process. As can be seen, ODA shows the best performance and StreamPDT has the worst performance. Poor performance of StreamPDT is due to the fact that it uses centralized processing, in oppose to the innetwork processing used by our proposed algorithms. Consequently, StreamPDT requires all sensor nodes to remain active at all the time. In contrast, DistPDT only needs a set of potential candidate, candidate and tracking nodes to remain active, which results in comparatively a better performance. FDA performs slightly better than DistPDT as it stringently activates the candidates and potential candidates, resulting in more efficient resource usage. ODA shows the best performance, as it further optimizes the resource usage of FDA by reducing coverage redundancies in the core tracking region. More specifically, FDA needs 75% less active nodes in comparison to StreamPDT and 6% less active nodes in comparison to DistPDT over the period of 50 epochs, as shown in Figure 524. Likewise, Figure 524 also reveals that ODA needs 84% less active nodes in comparison to StreamPDT and 40% less active nodes in comparison to DistPDT over the period of 50 epochs. ODA shows a performance enhancement of 36% over FDA due to the optimization step. Figure 521 shows the epochwise comparison of the four algorithms based on the number of update messages send to the CQP. As the number of update messages 113 103,97E 169,531 169,531 732,05( PAGE 1 ONBROADCASTSCHEDULINGANDDYNAMICPHENOMENADETECTIONINWIRELESSSENSORNETWORKSByRAVITIWARIADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2010 PAGE 2 c2010RaviTiwari 2 PAGE 3 Tomyparents,MrsShashiTiwariandMrVasudevTiwari 3 PAGE 4 ACKNOWLEDGMENTS Itisanimmensepleasureformetothankallthosewhomadethisdissertationpossible.Firstofall,IwouldliketoprofoundlythankmycommitteechairandadvisorDr.MyT.Thaiforherencouragement,supervisionandsupport,frominitialtotheconcludingstageofmydoctoralresearch.HerpreciousadvicesandmoralsupporthelpedmetosailthroughdifferentlowandhighphasesofthePhDlife.Forthis,Iwillalwaysbegratefultoherfortherestofmylife.Further,Iwouldliketothankmembersofmysupervisorycommittee,Dr.RandyY.C.Chow,Dr.ShigangChen,Dr.TamerKahveci,andDr.PanosM.Pardalosfortheirinvaluableguidance.Finally,Iwouldliketoexpressgratitudetomyfamilyandfriendsfortheirunconditionalhelpandemotionalsupport. 4 PAGE 5 TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 16 1.1EfcientDataBroadcastingandAggregation ................ 17 1.2EfcientInNetworkDetectionandTrackingofDynamicPhenomena ... 21 2CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCEAWAREBROADCASTSCHEDULING ....................... 24 2.1Introduction ................................... 24 2.2NetworkModelandProblemDenition .................... 26 2.2.1NetworkModel ............................. 26 2.2.2ProblemDenition ........................... 28 2.3TilingandColoringof2DimensionalPlaneUsingRegularHexagons ... 28 2.4TilingandColoringof3DimensionalSpace ................. 36 2.5BroadcastSchedulingAlgorithm(BSA) ................... 40 2.5.1AlgorithmDescription ......................... 40 2.5.2O(1)ApproximationRatioforInterferenceAwareBroadcastSchedulingProblemin2Dimension ........................ 41 2.5.3O(1)ApproximationRatioforInterferenceAwareBroadcastSchedulingProblemin3Dimension ........................ 43 2.6CentralizedGreedyHeuristicforbroadcastscheduling ........... 45 2.7Conclusion ................................... 45 3LOCALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCEAWAREBROADCASTSCHEDULING ....................... 47 3.1Introduction ................................... 47 3.2LocalizedAlgorithmforBroadcastScheduling ................ 48 3.2.1LocalizedGenerationofBroadcastingStructure ........... 48 3.2.2BroadcastSchedulingofBroadcastMessage ............ 52 3.2.3AnExampleScenario ......................... 54 3.2.4LocalizedBroadcastSchedulingAlgorithmin3Dimension ..... 58 3.3ExperimentalEvaluation ............................ 60 3.3.1EffectofNumberofSensorNodesonBroadcastLatency ..... 60 3.3.2EffectofonBroadcastLatency ................... 63 3.3.3EffectofonBroadcastLatency ................... 64 3.4Conclusion ................................... 66 5 PAGE 6 4ALLTOALLDATABROADCASTINGANDALLTOONEDATAAGGREGATION 67 4.1Introduction ................................... 67 4.2LocalizedAllToAllDataBroadcastSchedulingAlgorithm ......... 68 4.3DistributedAllToOneDataAggregationSchedulingAlgorithm ...... 70 4.4DistributedAllToAllBroadcastSchedulingAlgorithm ........... 73 4.5ExperimentalEvaluation ............................ 74 4.5.1ResultsforVaryingtheNumberofSensorNodes .......... 75 4.5.2ResultsforVarying .......................... 77 4.5.3ResultsforVarying .......................... 79 4.6Conclusion ................................... 80 5DETECTIONANDTRACKINGOFPHENOMENACLOUD:NEWLOCALIZEDAPPROACHESANDAPPLICATIONS ....................... 81 5.1Introduction ................................... 81 5.2PhenomenaCloud:ChallengesandRepresentation ............ 83 5.2.1MajorChallenges ............................ 84 5.2.2Representation ............................. 84 5.3ProposedSolutionforDetectionandTracking ................ 86 5.3.1ClassicationofSensors ........................ 86 5.3.2KeepingTabsontheNeighborhood .................. 89 5.3.3TransitionRules ............................. 90 5.3.4InitialSelectionofPotentialCandidateSensors ........... 91 5.3.5MonitoringforInitialOccurrences ................... 92 5.3.6NoticationofInitialOccurrence .................... 92 5.3.7GrowthofPhenomenonCloud .................... 93 5.3.8ShrinkingofPhenomenonCloud ................... 94 5.3.9RealTimeMonitoringbyApplications ................ 95 5.4OptimizingEnergyConsumptionandResourceUtilization ......... 95 5.4.1TheIntegerProgramFormulation ................... 96 5.4.2OptimizedDensityAlgorithm ...................... 98 5.4.2.1Clusteringmethod ...................... 99 5.4.2.2Localizedprotocol ...................... 101 5.5APracticalApplicationofPhenomenaDetectionandTracking ....... 103 5.6PerformanceEvaluation ............................ 105 5.6.1EffectivenessofDetectionStrategy ................. 106 5.6.1.1Experimentalsetup ..................... 106 5.6.1.2Resultsandanalysis ..................... 106 5.6.2ResourceandPowerConsumption .................. 109 5.6.2.1Experimentalsetup ..................... 110 5.6.2.2Resultsandanalysis ..................... 112 5.7RelatedWork .................................. 121 5.8Conclusion ................................... 123 6 PAGE 7 6LOCALIZEDENERGYEFFICIENTDETECTIONANDTRACKINGOFDYNAMICPHENOMENABOUNDARY ............................. 126 6.1Introduction ................................... 126 6.2SystemModel ................................. 128 6.3DetectingandTrackingofDynamicPhenomenaBoundary ......... 128 6.4LocalizedClusteringandDataAggregation ................. 134 6.5PerformanceEvaluation ............................ 136 6.6Conclusion ................................... 141 7CONCLUSION .................................... 142 REFERENCES ....................................... 145 BIOGRAPHICALSKETCH ................................ 151 7 PAGE 8 LISTOFFIGURES Figure page 21Sufcientconditionsforinterferenceawarenessbasedontransmitters. ..... 27 22Sufcientconditionsforinterferenceawarenessbasedonreceivers. ...... 27 23Comparisonofdifferentplanetilingpolygon.Figuresa,b,canddrespectivelyshowasquare,arhombus,atriangleandahexagon,havingmaximumdistancewithinthemequalto1. ................................ 29 24ThenewXh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhcoordinatesystem ........................ 30 25Closestpointsp1andp2intwohexagons ..................... 31 26CoColorHexagonsofh(0,0)fori=2andj=3.TheindexofsublatticeRhinHi.e.jdet(A,B)j=i2+j2+ij=19. ....................... 34 27ComparisonofnumberofcolorsusedtocolorthehexagontilingusingourschemeandScottet.al[ 1 ]. ............................. 35 28Comparisonofdifferentspacingllingpolyhedra.Figuresa,b,canddrespectivelyshowatruncatedoctahedron,arhombicdodecahedron,acubeandahexagonalprism,havingmaximumdistancewithinthemequalto1. ............. 37 29Thetilingofspaceusingtruncatedoctahedrons .................. 37 210TheXt)]TJ /F3 11.955 Tf 11.95 0 Td[(Yt)]TJ /F3 11.955 Tf 11.96 0 Td[(ZtCoordinateSystem ....................... 38 211Coloringpatternford=1,dme=3anddne=3,Colorsassignedtothetruncatedoctahedronsarerepresentedbynumbers. ............... 39 31ElementsoftheBroadcastingStructure. ...................... 49 32HexagoncoloringgeneratedbyAlgorithm 7 fork=4,colorsassignedtothehexagonsarerepresentedbynumbers. ...................... 50 33AnExampleshowingthefunctioningofapartofthebroadcaststructure. ... 51 34AnEpoch ....................................... 53 35Abroadcaststructure ................................ 55 36Databroadcastingontopofabroadcaststructure ................ 55 37EffectofnumberofnodesonAverageLatency .................. 61 38AverageBFSheight ................................. 61 39Averageoptimalityratio ............................... 61 8 PAGE 9 310EffectofonAverageLatency ........................... 63 311EffectofonAverageLatency ........................... 65 312Comparisonofvariousheuristicsalgorithms .................... 66 41EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. ............................ 75 42EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. ............................ 76 43EffectofNo.ofNodesonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. ............................ 76 44EffectofonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. .............................. 77 45EffectofonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. .............................. 78 46EffectofonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. .............................. 78 47EffectofonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. .............................. 79 48EffectofonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. .............................. 80 49EffectofonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. .............................. 80 51DissectionofthePhenomenaCloud ........................ 85 52ClassicationoftheParticipatingSensors ..................... 86 53DetectionandTrackingofaPhenomenaCloud .................. 88 54ActionTakenbyaSensorNodewithrespecttoitsNeighborswhicharenotidle 89 55RatioofTotalActiveSensorstoCloudSizeinaRectangularSensorGrid ... 93 56Partitionshapeassquare. .............................. 100 57Partitionshapeasrhombus. ............................. 100 58PartitionshapeasEquilateralTriangle. ....................... 100 59PartitionshapeasRegularHexagon. ........................ 100 510TheHexagonLattice ................................. 100 9 PAGE 10 511Clusteringonthebasisofhexagonlattice ..................... 102 512GatorTechSmartHouse .............................. 103 513SmartFloorTilewithforcesensorsandAtlasPlatformNode .......... 103 514RippleEffectofaFootStepontheSmartFloor .................. 104 515WalkingmotionasaPhenomena .......................... 104 516EffectofvaryingnwithpT=0.4andm=150 ................... 107 517EffectofvaryingpTwithn=3andm=150 .................... 108 518Effectofvaryingmwithn=3andPT=0.4 .................... 109 519PowerConsumptionSpecicationsforAtlas .................... 110 520Epochwisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. ................................ 112 521EpochwisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) ........................ 112 522Epochwisecomparisonbasedonnumberofmessagesexchangedbetweenonehopneighborstoimplementthealgorithms. ................. 112 523EpochwisecomparisonbasedontheEnergyConsumption. .......... 112 524Comparisonbasedonoverall50Epochs ...................... 113 525Comparisonbasedondifferentgridsize. ...................... 115 526Epochwisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. ................................ 116 527EpochwisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) ........................ 116 528Epochwisecomparisonbasedonnumberofmessagesexchangedbetweenonehopneighborstoimplementthealgorithms. ................. 116 529EpochwisecomparisonbasedontheEnergyConsumption. .......... 116 530Comparisonbasedonoverall5Epochs ...................... 117 531SnapshotsofexpandingphenomenacloudduringEpochst10,t15,t20. ..... 117 532ActiveSensorsduringEpocht10,forDistPDT. ................... 117 533ActiveSensorsduringEpocht10,forFDA. ..................... 118 10 PAGE 11 534ActiveSensorsduringEpocht10,forODA. ..................... 118 535ActiveSensorsduringEpocht15,forDistPDT. ................... 118 536ActiveSensorsduringEpocht15,forFDA. ..................... 118 537ActiveSensorsduringEpocht15,forODA. ..................... 118 538ActiveSensorsduringEpocht20,forDistPDT. ................... 118 539ActiveSensorsduringEpocht20,forFDA. .................... 119 540ActiveSensorsduringEpocht20,forODA. ..................... 119 541Percentageofholesgeneratedwrtpercentageofupdatemessageslost .... 120 542DetectionandTrackingwith5%updatemessagelostforFDA. ......... 125 543DetectionandTrackingwith5%updatemessagelostforODA. ......... 125 544DetectionandTrackingwith10%updatemessagelostforFDA. ......... 125 545DetectionandTrackingwith10%updatemessagelostforODA. ......... 125 546DetectionandTrackingwith15%updatemessagelostforFDA. ......... 125 547DetectionandTrackingwith15%updatemessagelostforODA. ......... 125 61ClassicationofSensorNodesintheWSN .................... 129 62TypesofNodesintheWSN ............................. 129 63TypesofmessagesintheWSN ........................... 130 64TheTransitionRules ................................. 130 65StateTransitionDiagramforaSensornode .................... 131 66Expansionofthephenomenacloud ........................ 131 67Shrinkingofthephenomenacloud ......................... 133 68Xh)]TJ /F3 11.955 Tf 11.95 0 Td[(YhcoordinateSystemforHexagontilingH ................. 134 69Dataaggregationbasedonclusteringgeneratedbythehexagonaltiling .... 136 610Powerconsumptionspecicationsforasensornode ............... 136 611Comparisonbasedonnumberofboundarynodes. ................ 137 612Comparisonbasedonnumberofupdatemessages. ............... 137 613Comparisonbasedonenergyconsumption. .................... 137 11 PAGE 12 614Comparisonbasedonmessagesexchanged. ................... 137 615Comparisonbasedonnumberofupdatemessagesatdifferentphenomenaexpansionspeed. ................................... 138 616Comparisonbasedonenergyconsumptionatdifferentphenomenaexpansionspeed. ......................................... 138 617Comparisonbasedonmessagesexchangedatdifferentphenomenaexpansionspeed. ......................................... 138 618SnapshotofphenomenainWSN. ......................... 139 619Estimatedboundarywith0%messageloss. .................... 139 620Estimatedboundarywith15%messageloss. ................... 139 621Estimatedboundarywith30%messageloss. ................... 139 622Estimatedboundarywith45%messageloss. ................... 139 12 PAGE 13 AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyONBROADCASTSCHEDULINGANDDYNAMICPHENOMENADETECTIONINWIRELESSSENSORNETWORKSByRaviTiwariAugust2010Chair:MyT.ThaiMajor:ComputerEngineering MajorityofnetworkapplicationsdesignedontopofWirelessSensorNetworks(WSNs)involvedetectionandtrackingofsomephysicalphenomena.Additionally,theyutilizesomeprimitiveservicessuchasbroadcastingandaggregationfordisseminatingandcollectinginformation. Broadcastingisanoperationtopromulgatesomeinformationfromasourcenodetoallothernodesinthenetwork.Incontrast,aggregationisanoperationtocollectthesensedinformationfromallnodesinthenetworkataspecicsinknode.SensornodesinWSNscommunicateviaradiotransmissions.DuetoWirelessBroadcastAdvantage(WBA)ofradiotransmissions,performingefcientdatabroadcastingordataaggregationwithminimumlatencyisnontrivialandprovedtobeNPhard.Floodingisastraightforwardapproachwhichcanbeused.Unfortunately,itgeneratesredundanttransmissions,contentionsandcollisions,whichaggravatesthenetworkthroughputandresultsinabroadcaststorm.Broadcastschedulingandaggregationschedulingaremoreintelligentandeffectivemechanismstoperformefcientbroadcastingandaggregationrespectively.Thesearebasedonschedulingtheinterferingtransmissions,whichavoidsbroadcaststormandimprovesnetworkthroughput. Existingresearchesonbroadcastschedulingandaggregationschedulingprovidecentralizedsolutions,whichcannotbeimplementedlocally.Additionally,theyconsiderveryelementarynetworkandinterferencemodels,inwhich,eitherallsensornodeshave 13 PAGE 14 thesametransmissionrangeortheirtransmissionrangesareequaltotheirinterferenceranges.Theseassumptionsarenotpractical.Furthermore,theyentirelyignoretheexistenceofWSNsin3D. MostoftheexistingresearchonphenomenadetectionandtrackingusingWSNsassumethephenomenaareinvariantinshape,sizeandmotion.However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgases,whicharecharacterizedbynondeterministicvariationsinshape,sizeanddirectionofmotion.Thesedynamicphenomenaaretermedasphenomenacloud.Duetotheabsenceofanywelldenedmodelforphenomenaclouds,theirdetectionandtrackingthroughWSNsisextremelychallenging.Sincesensornodeshavelimitedenergyandprocessingpower,theefcientdetectionandtrackingofphenomenacloudwithanobjectivetomaximizenetworklifetimeisachallengingoptimizationproblem. Thefocusofthisdissertationismainlyonfollowingtwoimperativeoptimizationproblems: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena. Themaincontributionsofthisdissertationare: 1.AconstantapproximationalgorithmforbroadcastschedulinginWSNs,whichhasthestateoftheartapproximationratio. 2.TherstconstantlocalizedapproximationalgorithmforbroadcastschedulinginWSNs. 3.Therstconstantdistributedapproximationalgorithmforalltoonedataaggregation. 4.Therstconstantdistributedapproximationalgorithmforalltoallbroadcastscheduling. 5.Alocalizedinnetworkalgorithmfordetectionandtrackingofphenomenacloud. 14 PAGE 15 6.Anenergyefcientlocalizedalgorithmfordetectionandtrackingofphenomenacloudboundary. 15 PAGE 16 CHAPTER1INTRODUCTION AWirelessSensorNetwork(WSN)isacollectionofsensornodesdeployedtosensesomephenomena,collectinformationandsendittothebasestationforfurtherprocessingonmultihoppaths.WSNshavelotsofapplicationsinvariouseldswherecontinuousmonitoringisextremelycriticalandcannotbeperformedbyhumansduetoissueslikerisk,reachability,accuracyandcost.Duetorecentadvancementsinmicroelectronicsandwirelesstechnologies,varioustypesofcosteffectivesensornodesaremodeledandrealizedfordifferentapplicationssuchasenvironmentandhabitatmonitoring[ 2 8 ],healthmonitoring[ 9 11 ],criticalmilitaryoperationslikesurveillanceandreconnaissancetokeeptrackofenemy.Recently,theuseofWSNsisstudiedforapplicationsinvolvingdynamicphenomenasuchasoilspills,mudow,etc[ 12 13 ].MostlyallnetworkapplicationsdesignedontopofWSNsinvolvedetectionandtrackingofsomephysicalphenomena.Additionally,theyutilizesomeprimitiveserviceslikebroadcastingandaggregationfordisseminatingandcollectinginformation. Broadcastingisanoperationtopromulgatesomeinformationfromasourcenodetoallothernodesinthenetwork.Incontrast,aggregationisanoperationtocollectthesensedinformationfromallnodesataspecicnode.SensornodesinWSNscommunicateviaradiotransmissions.Thebroadcastnatureofradiotransmissions,calledWirelessBroadcastAdvantage(WBA)[ 14 ],enablesatransmittingsensortobroadcastamessagetoallreceivingsensorswithinitstransmissionrangeinasingletransmission.However,morethanonesensortransmittingsimultaneouslymayresultininterferenceatreceivers.Consequently,performingefcientdatabroadcastingordataaggregationwithminimumlatencyisnontrivialinWSNsandprovedtobeNPhard[ 15 ].However,onestraightforwardapproachtoperformdatabroadcastingoraggregationisooding[ 16 17 ].Unfortunately,itgeneratesredundanttransmissions,contentionsandcollisionsinthenetwork,whichaggravatesthenetworkthroughputandresultsin 16 PAGE 17 abroadcaststorm[ 18 ].Amoreintelligentapproachtoperformefcientdatabroadcastordataaggregationistoscheduletheinterferingtransmission.Thisavoidsbroadcaststormandconsiderablyimprovesnetworkthroughputandlatency.IntheexistingliteratureonWSNs,broadcastschedulingandaggregationschedulingareformulatedastwoimportantoptimizationproblemswithobjectivetominimizelatency. MostoftheexistingresearchonphenomenadetectionandtrackingusingWSNsassumethephenomenaisinvariantinshape,sizeandmotion[ 19 23 ].However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgasesthatarecharacterizedbynondeterministicvariationsinshape,sizeanddirectionofmotion.Thesedynamicphenomenaaretermedasphenomenacloud.Duetotheabsenceofanywelldenedmodelforphenomenaclouds,theirdetectionandtrackingthroughWSNsisextremelychallenging.Sincesensornodeshavelimitedenergyandprocessingpower,theefcientdetectionandtrackingofphenomenacloudwithanobjectivetomaximizenetworklifetimeisachallengingoptimizationproblem. Theinherentlydistributednatureofsensornodesintroducesmanyintriguingandchallengingoptimizationproblemswhichhaveenormousresearchpotential.EfcientlysolvingtheseproblemsispivotalforresourcefullydesigningcriticalapplicationsforWSNs.ThefocusofthisdissertationismainlyonfollowingtwoimperativeoptimizationproblemsinWSNs: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena(phenomenacloud). Intherestofthischapter,weprovideadetailedintroductionandbackgroundforthesetwoproblems. 1.1EfcientDataBroadcastingandAggregation DatabroadcastinganddataaggregationaretwomostprimitiveoperationsinmultihopWSNs.Thepurposeofdatabroadcastingistoconveyamessagefromasourcetoallothernodes.Itslatencydirectlygovernstheperformanceofvarious 17 PAGE 18 delayconstraintdistributedprotocolsinWSNssuchasroutediscovery,servicediscovery,broadcastingupdatesetc,whichrequiredatapromulgation.Incontrast,dataaggregationisperformedtoefcientlycollectthesensedinformationfromallsensornodesatasinknodeorabasestationforfurtherprocessingorforwarding. AWSNcanbecloselymodeledusingagraphG=(V,E),wheretheverticesinsetVrepresentnetworknodesandedgesinsetErepresentthecommunicationlinks.Thedatabroadcastinwirelessnetworkhasbeenstudiedusingdifferentkindsofgraphmodelswithanobjectivetominimizethebroadcastlatency.ThetheoreticallowerboundonminimumlatencyistheradiusRofthenetworkwithrespecttothesourcenodevs2V.In[ 24 ],Chlamtacet.al.provedthattheminimumlatencybroadcastscheduleproblemisNPhardforgeneralgraphs.Thereareseveraladditive[ 25 ],[ 26 ],andmultiplicative[ 27 ],[ 28 ],[ 24 ],[ 29 ]approximationalgorithmsproposedforthisproblemingeneralgraphs.In[ 30 ]Elkinet.al.provedthattheminimumlatencybroadcastschedulingproblemcannothavean(logn)multiplicativeapproximationunlessNPBPTIME(nO(loglogn)).In[ 31 ],theyalsoprovedthatitisimpossibletohaveanopt(G)+log2(n)additiveapproximationalgorithmunlessNPBPTIME(nO(loglogn)).However,forwirelessnetworks,restrictivegraphmodelssuchasUnitDiskGraphs(UDG)andDiskGraphs(DG)in2DandUnitBallGraphs(UBG)andBallGraphs(BG)in3D,aremoresuitable.TheUDGandUBGmodelsawirelessnetworkwhosenodeshavethesametransmissionrange,theDGandBGmodelsthewirelessnetworkswherethenodeshavedifferenttransmissionranges. In[ 15 ],Gandhiet.al.studiedthebroadcastschedulingprobleminDiskGraph(DG)andprovedthattheminimumlatencybroadcastschedulingproblemisNPhard.In[ 32 ],Scottet.al.presentedasolutionforUDG,usingthegeometricpropertyofUDGtheyprovealowerboundof16R)]TJ /F4 11.955 Tf 12.3 0 Td[(15.Further,theyextendthepipelinedbroadcastingalgorithmin[ 33 ]forgeneralgraphtoUDGandgetalowerboundofR+O(log(R)).Thepipelinedbroadcastalgorithmin[ 33 ]isbasedonstandardrankingalgorithm[ 34 ] 18 PAGE 19 forassigningrankstothenodesofBFStree.In[ 35 ],Chenet.alstudiedthisprobleminamorerealisticmodel,theyconsideredtransmissionrangeissmallerthaninterferencerange.TheyproposedanO(2)approximationratio,whereistheratioofinterferencerangeandtransmissionrange,with>1.In[ 36 ]Rezaet.alstudiedthisproblem,considering>1proposedanO(2)approximationwithabetteranalysis.Apartfromtheinterferenceandtransmissionrangetheyalsoconsideredthecarriersensingrange.Usinga2Diskmodel,Scottet.al.studiedthebroadcastschedulingproblemandproposedanapproximationalgorithmwithratio6l2 3(rI rT+2)m2[ 1 ].Theyconsidered>1andeachnodehasthesametransmissionrangerTandtheirinterferencerangerI=rT. Unfortunately,almostallabovementionedworksconsideredthesametransmissionrangeforallnodes.Only[ 15 ]consideredadiskgraphmodel,buttheyconsideredtransmissionrangeandinterferencerangetobesame,whichisnotapracticalassumption,asinterferencerangeisalwaysgreaterthanthetransmissionrange.Furthermore,allexistingworksstudyingbroadcastschedulinginwirelessnetworksmodelthenetworkasa2Dplanargraphinwhichthenodesexistsin2Dplane.However,thisisnotappropriateinallcases,asmostofthetimethenodesacquirelocationsin3D.Furthermore,allexistingworksinbroadcastschedulingprovidecentralizedsolutionswithsomeapproximationguarantees.Thereisnolocalizedapproximationalgorithmintheexistingliterature. Intheexistingliterature,alltooneaggregationschedulingismostlystudiedinUDGwithinterferencerangeequaltothetransmissionrange.In[ 37 ],Chenet.al.proposeda()]TJ /F4 11.955 Tf 12.54 0 Td[(1)approximationalgorithm,whereisthemaximumnodedegree.Basedonmaximalindependentset,Huanget.al.[ 38 ]proposedanalgorithmwithlatencyboundof23R+)]TJ /F4 11.955 Tf 12 0 Td[(18,whichwasimprovedto16R+)]TJ /F4 11.955 Tf 12 0 Td[(14byXuet.al.[ 39 ].In[ 40 ],Wanet.al.consideredthatforanynode,theinterferencerangeisgreaterthanthetransmissionrangeandproposedanalgorithmwithlatency+1(15R+)]TJ /F4 11.955 Tf 12.08 0 Td[(4),whereistheratioof 19 PAGE 20 interferencerangetothetransmissionrangeand(+1)]TJ /F4 11.955 Tf 12.33 0 Td[(1)isthemaximumdegreeoftheconictgraph. InChapter 2 ,weformulatedatabroadcastinginWSNsasInterferenceawarebroadcastscheduling(IABS)problemwithanobjectivetominimizethebroadcastlatency.WemodelWSNin2Dasadiskgraphandin3DasaBallGraph.Weconsideramorerealisticnetworkmodelwherethenodesmayhavedifferenttransmissionranges,whiletheirinterferencerangesaretimesoftheirtransmissionranges,where>1.WeproposeO(1)centralizedapproximationalgorithmsforIABSproblemin2Dand3DWSNsrespectively.Theseapproximationalgorithmshavethestateoftheartapproximationratioforthenetworkmodelweconsidered. Further,inChapter 3 ,basedonthenetworkandinterferencemodelintroducedinChapter 2 ,westudylocalizeddatabroadcastingandproposealocalizedapproximationalgorithmfordatabroadcast.Ouralgorithmhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2.ThisistherstlocalizedapproximationratiofordatabroadcastinginWSNs.Wealsoextendedourlocalizedalgorithmfor3DWSNs. Furthermore,inChapter 4 ,westudythealltoalldatabroadcastingandalltoonedataaggregationandpropose: 1.AO(1)distributedapproximationalgorithmforalltoonedataaggregation. 2.AO(1)distributedapproximationalgorithmforalltoalldatabroadcast. 3.ALocalizedalgorithmforalltoalldatabroadcast. AlltoonedataaggregationisafundamentaloperationinWSNs,inwhichthedatafromallthenodesisaggregatedinasinknodeforfurtherprocessingandforwarding.Ourdistributedalgorithmforalltoonedataaggregationistherstinliteratureandhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2.Ourdistributedalgorithmforalltoalldatabroadcastingisalsotherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. 20 PAGE 21 1.2EfcientInNetworkDetectionandTrackingofDynamicPhenomena Contemporarywirelesssensornetwork(WSN)researchdoneintheareaofdetectionandtrackinghasprimarilyconcentratedonobservingmotionofobjectswhoseshapeandsizeareinvariant[ 41 43 ].However,manyreallifeeventssuchasoilspills,gasclouds,orrandomwalkingmotionofpeople,henceforthcalledPhenomenaClouds,arecharacterizedbynondeterministic,dynamictemporalvariationsofcloudshape,sizeanddirectionofmotionalongmultipleaxes.Theseeventscannotbemodeledinwelldenedterms.Thus,itisdifculttoapplyexistingmechanismsinsuchsituations. Furthermore,theutilityofphenomenaclouddetectionandtrackingisnotrestrictedonlytoapplicationdomainsinvolvinggascloudsoroilspills.Infact,theycanalsobeutilizedinsituationswherethequalityofdataoriginatingfromindividualsensorscannotbetrustedinisolation.Insuchcases,therawsensordataoriginatingfromthesystemistypicallyextremelynoisywhichmakesitverydifculttodistinguishactualeventsfromrandomstimuli.Hence,aquorumofmultiplesensors,whicharelocatedincloseproximitytoeachother,isrequiredtoreducetheprobabilityoffalsepositives.ThroughourcollectiveresearchandsystemsexperienceovertheyearsinbuildingSmartSpacesatUniversityofFlorida'sMobileandPervasiveComputingLaboratory,wehavefoundasignicantutilityinapplyingthephenomenacloudconceptforefcientlyandaccuratelymonitoringvariouseventsinthespace,suchasdetectionofbarefootwalking,whichisacriticalapplicationfordiabetespatients. Withanewapplicationandbroaderconceptofphenomenaclouds,earlystudiesonboundarydetectionandtrackingofwelldenedshapesarenolongersufcient[ 12 13 19 44 45 ].Onlyoneworkrecentlystudiedonsimilarapplications,calledNilePDT(astreambasedmechanism)maybeapplicable[ 46 ].However,thiscentralizedapproachdoesnottakeintoaccountthecostofacquiringandtransmittingsensorreadingsandtypicallyrequiresparticipationfromallsensorsinthenetwork.Unfortunately,sensorsamplingcostsandnetworkingandprocessingoverheadscanhaveacriticaleffect 21 PAGE 22 onthepracticalviabilityoftheentiresmartspace.Thisraisesaneedforadistributedinnetworkdetectionmechanism,wherethedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofaphenomenonatanygiventimeanddoesnotrequireallthesensornodestoremainunnecessarilyactive. Alongthisdirection,inChapter 5 ,weintroduceamathematicalmodelandinnetworkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergyefcient,localized,innetworkalgorithmforrealtimedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizingtheenergyconsumptionofthephenomenacloudsdetectionandtracking.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 4.Providinganovellocalizedalgorithmwhichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinarealworldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 22 PAGE 23 6.Validatingourapproachesusingbothrealworldapplicationsandsimulationstoanalyzeitsperformanceandresourcerequirementsaswellascomparingitwiththatofstreambasedapproaches. Furthermore,inChapter 6 ,weprovideanenergyefcientlocalizedinnetworkdetectionandtrackingprotocolfortrackingtheboundaryofthephenomenacloud.Thisprotocolismorerelevantforscenariossuchasoilspills,gasleakage,etc,whereitismoresensibletodetectandtrackonlythephenomenaboundaryengulngtheaffectedareainsteadoftrackingtheentirephenomena.Simulationresultsareprovidedtoshowthattheproposedprotocolismoreefcientthantheexistingworks.Finally,inChapter 7 ,weprovideabriefsummaryofthisdissertationandconcludeit. 23 PAGE 24 CHAPTER2CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCEAWAREBROADCASTSCHEDULING 2.1Introduction DuetoitsimperativemotivationinWirelessSensorNetworks(WSNs),broadcastschedulingproblemhasbeenextensivelystudiedbymanyresearchers[ 1 15 32 35 36 ].Existingworksconsidernetworkandinterferencemodels,whicharenotpractical.Eithertheyassumethatallsensorshavethesametransmissionrange[ 32 35 36 ]orsensorsmayhavedifferenttransmissionrangesbuttheirinterferencerangesareequaltotheirtransmissionranges[ 15 ].However,inpractice,dependingupontheirenergylevelorfunctionality,sensornodesmayhavedifferenttransmissionrangesandtheirinterferencerangesarealwaysgreaterthantheirtransmissionranges.Furthermore,existingsolutionsconsiderWSNsarealwaysdeployedin2Dplane.Incontrast,therearemanycaseswhensensornodesacquirelocationsin3Dspace.Forinstance,resensorsdeployedatdifferentlevelsontreesinforests[ 47 ],underwatersensorsdeployedatdifferentdepthsinseastocollectvitalinformationaboutaquaticlife[ 48 ]. Consideringdecienciesintheexistingresearch,inthischapter,westudythebroadcastschedulingproblemforWSNsin2Dand3D.Weconsideramorerealisticnetworkmodel,inwhicheachsensornodevhasatransmissionrangerTv2rTmin,rTmax(whererTmax rTmin=>1)anditsinterferencerangerIv=rTv(where>1).Thismodelhasnotbeenconsideredforbroadcastschedulingproblemintheexistingliterature. SincebroadcastschedulingisNPhard[ 15 ],weproposeO(1)centralizedapproximationalgorithmsforWSNsin2Dand3Drespectively.Forthis,westudytwosubproblems:1)Tilingandcoloring2Dplaneusingregularhexagons,and2)Tilingandcoloring3Dspaceusingtruncatedoctahedrons.SolutionstothesetwoproblemsleadtoO(1)approximationratiosin2Dand3Drespectively.OurO(1)centralizedapproximationalgorithmistherstapproximationalgorithmfor3DWSNsandin2Douralgorithmhasthebestapproximationrationforthemodelweconsidered. 24 PAGE 25 Inordertostudythetilingandcoloringof2Dplaneusingidenticalregularhexagons,weconsiderahexagontilingHofthe2Dplane.WecolorallhexagonsinH,suchthatthedistancebetweenanytwohexagonsh1andh2havingthesamecolorisatleastd2R+.Thisdistanceismeasuredbetweentwoclosestpointsp1andp2on2Dplane,wherep1isinh1andp2isinh2.Weprovideanoptimalsolutiontothisproblemforanyarbitrarydistanced2R+. Furthermore,tostudythetilingandcoloringof3Dspaceusingtruncatedoctahedrons,weconsideratilingTOCof3Dspaceusingidenticaltruncatedoctahedrons.AlltruncatedoctahedronsinTOCarecolored,suchthatthedistancebetweenanytwotruncatedoctahedronsto1andto2havingthesamecolorisatleastd2R+.Similarto2D,thisdistanceismeasuredbetweentwoclosestpointsp1andp2in3Dspace,wherep1isinto1andp2isinto2. Wealsoproposeanefcientcentralizedgreedyheuristicalgorithmforbroadcastschedulingproblem.Ourheuristicalgorithmconsidersallsensorsthathavereceivedthebroadcastmessageaspotentialtransmitters.Further,toselectamongtheinterferingtransmissions,itprovideshigherprioritytothetransmissionwhichcoversmoreuninformednodes.InoursimulationsinChapter 3 ,weperformacomparativeanalysisofperformancesoftheheuristicalgorithmunderdifferentprioritymetricsforgreedilyschedulingtheinterferingtransmissions. Therestofthechapterisorganizedasfollows:InSection 2.2 ,wedescribethenetworkandtheinterferencemodelalongwiththeformaldenitionoftheinterferenceawarebroadcastschedulingproblem.Weintroducethetilingandcoloringof2DplaneusingregularhexagonsinSection 2.3 .Section 2.4 describesthetilingandcoloringof3Dspaceusingidenticaltruncatedoctahedrons.TheO(1)centralizedapproximationalgorithmsforbroadcastschedulingin2Dand3DWSNs,alongwiththeoreticalanalysisaredescribedinSection 2.5 .InSection 2.6 ,weintroducean 25 PAGE 26 efcientcentralizedheuristicforbroadcastscheduling.Finally,Section 2.7 concludesthechapter. 2.2NetworkModelandProblemDenition 2.2.1NetworkModel WeassumethateachsensornodevihastransmissionrangerTi2[rTmin,rTmax]andinterferencerangerIi=rTi(>1),whererTminandrTmaxaretheminimumandmaximumtransmissionrangesintheWSNrespectivelyandrTmax rTmin=>1. The2DNetworkModel:In2D,theWSNisrepresentedbyadirecteddiskgraphG=(V,E),whereVisasetofsensornodesdeployedonthe2DplaneandEisthesetofdirectedcommunicationlinks.Eachnodevi2Visassociatedwithtwoopendisks,thetransmissiondiskDTiandtheinterferencediskDIicenteredatvi,withradiusrTiandrIirespectively.IfanodevjislocatedwithinDTi,thereexistsadirectedlink(vi,vj)2E.Additionally,ifviisalsolocatedwithinDTjthen(vj,vi)2Eandthereexistsabidirectionallinkbetweenviandvj. The3DNetworkModel:Similarto2D,in3D,theWSNisrepresentedbyadirectedballgraphG=(V,E).AtransmissionballBTiandaninterferenceballBIiareassociatedwitheverysensornodevi2VcenteredatviwithradiusrTiandrIirespectively.IfanodevjislocatedwithinBTi,thereexistsadirectedlink(vi,vj)2E.Further,ifviisalsolocatedwithinBTjthen(vj,vi)2Eandthereexistsabidirectionallinkbetweenviandvj. Basedontheabovenetworkmodel,wedenetheinterferencemodelasfollows: 1.IftheEuclideandistancebetweenatransmittervt1andareceivervr1i.e.d(vt1,vr1) PAGE 27 Figure21. Sufcientconditionsforinterferenceawarenessbasedontransmitters. Figure22. Sufcientconditionsforinterferenceawarenessbasedonreceivers. 3.Simultaneoustransmissionsvt1!vr1andvt2!vr2areinterfering,ifd(vt1,vr2) PAGE 28 Ifwehaved(vt1,vt2)(+1)rTmaxasshowninFigure 21 ,accordingtotriangularinequalityd(vt1,vr2)rTmaxandd(vt2,vr1)rTmax.Thiswillensurethattransmissionsvt1!vr1andvt2!vr2willbeinterferenceaware. Ifwehaved(vr1,vr2)(+1)rTmaxasshowninFigure 22 ,accordingtotriangularinequalityd(vt1,vr2)rTmaxandd(vt2,vr1)rTmax.Thiswillensurethattransmissionsvt1!vr1andvt2!vr2willbeinterferenceaware. Hence,toensuresimultaneoustransmissionsvt1!vr1andvt2!vr2donotinterfereeachother,itissufcienttohaved(vt1,vt2)(+1)rTmaxord(vr1,vr2)(+1)rTmax. 2.2.2ProblemDenition InterferenceAwareBroadcastScheduling(IABS)problem:GivenamultihopWSNG=(V,E)andasensornodevs2Vhavingamessagem.TheIABSproblemistogenerateaninterferenceawarebroadcastscheduleforbroadcastingthemessagemfromvstoallothersensornodes.Theinterferenceawarebroadcastschedulemustsatisfyfollowingconditions: Thesourcenodevsisscheduledtotransmitduringthersttimeslott1. Anodeu,ifscheduledtotransmitintimeslottj,musthavereceivedthemessageminsomeearliertimeslotti,wherei PAGE 29 Figure23. Comparisonofdifferentplanetilingpolygon.Figuresa,b,canddrespectivelyshowasquare,arhombus,atriangleandahexagon,havingmaximumdistancewithinthemequalto1. tilingregularpolygons:1)Square,2)Rhombus,3)EquilateralTriangleand4)RegularHexagon,astheunitpartitionshapeandcomparetheirareas,asshowninFigure 23 .Weobservethataregularhexagonofsides1 2hasthemaximumarea.Consequently,weselectitastheunitpartitionshape.Figure 24 showstheregularhexagontilingof2Dplane. Weformallydenetheregularhexagontilingandcoloringof2DplaneasDistancedHexagoncoloringproblem: DistancedHexagonColoringproblem:GivenaregularhexagontilingHof2Dplaneandadistanced2R+,ndtheminimumnumberofcolorsneededtocolorH,suchthattwohexagonsh1,h22HhavingthesamecolormusthavetheEuclideandistancedistance(h1,h2)d.Thedistancedistance(h1,h2)ismeasuredbetweentwoclosestpointsp1andp2,where,p1lieswithinh1andp2lieswithinh2. 29 PAGE 30 Figure24. ThenewXh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhcoordinatesystem InordertostudytheDistancedHexagonColoringproblem,weconsideranewXh)]TJ /F3 11.955 Tf 458.7 23.91 Td[(YhcoordinatesystembasedonhexagoncentersinH.AxesoftheXh)]TJ /F3 11.955 Tf 12.36 0 Td[(Yhcoordinatesystemareinclinedat60oanditstwounitvectorsare^i(p 3 2,0)and^j(p 3 4,3 4),asshowninFigure 24 .Eachhexagonh2HinXh)]TJ /F3 11.955 Tf 12.81 0 Td[(Yhcoordinatesystemcanbeidentiedbycoordinatesofitscenterash(i,j).TheEuclideandistancebetweentwohexagoncentersh(i1,j1)andh(i2,j2)isgivenasp 3 2p (i1)]TJ /F3 11.955 Tf 11.96 0 Td[(i2)2+(i1)]TJ /F3 11.955 Tf 11.96 0 Td[(i2)(j1)]TJ /F3 11.955 Tf 11.95 0 Td[(j2)+(j1)]TJ /F3 11.955 Tf 11.95 0 Td[(j2)2.TheEuclideandistanceofahexagoncenterh(i,j)fromtheoriginh(0,0)isgivenasp 3 2p i2+ij+j2. AstherststeptoprovidethesolutionforDistancedHexagoncoloringproblem,weidentifytheclosesthexagonh(i,j)toh(0,0)intherstquadrantofXh)]TJ /F3 11.955 Tf 12.48 0 Td[(Yhplane,suchthattwoclosestpoints,p1inh(0,0)andp2inh(i,j)areatleastatadistanced2R+. Weobservethatclosestpointsp1andp2canappearinthreewaysasshowninFigure 25 : p1istheupperrightcornerofh(0,0)andp2isthelowerleftcornerofh(i,j),inFigure 25 (i=3,j=5). p1isthemidpointofupperrightsideofh(0,0)andp2isthemidpointoflowerleftsideofh(i,j),inFigure 25 (i=0,j=7). 30 PAGE 31 Figure25. Closestpointsp1andp2intwohexagons p1isthemidpointoftherightsideofh(0,0)andp2isthemidpointoftheleftsideof(i,j),inFigure 25 (i=7,j=0). Withoutlossofgenerality,weconsiderij,therefore,wegetridofthethirdcase.Alsoweexcludethecasei=0,j=1.Wecompute(i,j)forthegivend2R+asfollows: Identifytwopairs(i1,j1)and(i2,j2)asfollows: Compute(i1>0,j1>0)inrstquadrantofXh)]TJ /F3 11.955 Tf 12.06 0 Td[(Yhplaneusingtheinequalityd23 4((i1)]TJ /F4 11.955 Tf 12.3 0 Td[(2a)2+(j1)]TJ /F4 11.955 Tf 12.29 0 Td[(2a)2+(i1)]TJ /F4 11.955 Tf 12.3 0 Td[(2a)(j1)]TJ /F4 11.955 Tf 12.3 0 Td[(2a)),suchthati21+j21+i1j1isminimumamongallintegralsolutionsofthisinequality,whereaisasshowninFigure 25 andisequalto1 3. Compute(i2=0,j2>1)inrstquadrantofXh)]TJ /F3 11.955 Tf 12.06 0 Td[(Yhplaneusingtheinequalityd23 4(j2)]TJ /F4 11.955 Tf 12.43 0 Td[(1)2,suchthatj22isminimumamongallintegralsolutionsofthisinequality. Finally,if(i21+i1j1+j21)<(i22+i2j2+j22),weselecti1,j1asi,jelseweselecti2,j2asi,j. Wenowintroducethecocolorhexagonalgorithm,illustratedinAlgorithm 1 .InLemma 2 ,weprovethatforanyarbitrarydistanced2R+,Algorithm 1 optimallyidentiescocolorhexagons(i.e.hexagonshavingthesamecolor)foranygivenhexagonh(i0,j0)inH. TheAlgorithm 1 ,forthegivend2R+,rstcomputes(i,j)usingtheabovemethodandidentiestheclosestcocolorhexagonh(i0+i,j0+j)ofh(i0,j0)intherstquadrant 31 PAGE 32 ofXh)]TJ /F3 11.955 Tf 12.35 0 Td[(YhplaneandaddsittosetSofcocolorhexagons.ItthensequentiallyrotatestheXh)]TJ /F3 11.955 Tf 12 0 Td[(Yhplaneby60oforvetimestondrestofclosestcocolorhexagonsofh(i0,j0)thatareh(i0+(i+j),j0)]TJ /F3 11.955 Tf 12.32 0 Td[(i),h(i0+j,j0)]TJ /F4 11.955 Tf 12.32 0 Td[((i+j)j),h(i0)]TJ /F3 11.955 Tf 12.32 0 Td[(i,j0)]TJ /F3 11.955 Tf 12.32 0 Td[(j),h(i0)]TJ /F4 11.955 Tf 12.32 0 Td[((i+j),j0+i),h(i0)]TJ /F3 11.955 Tf 12.42 0 Td[(j,j0+(i+j))andaddsthemtothesetS.Duetothesymmetricpropertyoftherotation,distancesbetweenh(i0,j0)anditsclosestcocolorhexagonsremainthesame.AnyhexagonwhichisidentiedforthersttimeisaddedtothesetSandabovestepsarerecursivelyrepeatedonit. TheFigure 26 showscocolorhexagonsofh(0,0)identiedbyAlgorithm 1 fordistanced=p 31 2,wherei=2,j=3.Sixclosestcocolorhexagonsofh(0,0)areh(i,j),h((i+j),)]TJ /F3 11.955 Tf 9.3 0 Td[(i),h(j,)]TJ /F4 11.955 Tf 9.29 0 Td[((i+j)j),h()]TJ /F3 11.955 Tf 9.3 0 Td[(i,)]TJ /F3 11.955 Tf 9.3 0 Td[(j),h()]TJ /F4 11.955 Tf 9.3 0 Td[((i+j),i),andh()]TJ /F3 11.955 Tf 9.3 0 Td[(j,(i+j)).Wecanseethatcentersofcocolorhexagonsofh(0,0)formatriangularsublatticeSandarhombicsublatticeRhofthelatticestructuregeneratedbycentersofhexagonsinH.UnitvectorsofsublatticeRhareA=i^i+j^jandB=j^i)]TJ /F4 11.955 Tf 12.7 0 Td[((i+j)^j.Thenumberofpossibleclassesi.e.theindexofsublatticeRhinH,whichisthenumberofdisjointsublatticessimilartoRhinHisgivenasjdet(A,B)j=i2+j2+ij[ 49 ].Thus,therearefRh1,Rh2...Rh(i2+j2+ij)gdisjointsublatticessimilartoRhinH,unionofwhichformH.Ifweassigneachofthemauniquecolor,allhexagonsinHwillbecoloredwithi2+j2+ijcolorsandtheclosestdistancebetweentwococolorhexagonswillbeatleastd2R+.InTheorem 2.1 ,weprovethatthehexagoncoloringgeneratedthiswayistheoptimalsolutionforDistancedhexagoncoloringproblem. Lemma2. Algorithm 1 optimallyidentiescocolorhexagonsforagivendistanced2R+. Proof. Letsconsiderthehexagontilingofanarea.Weneedtoidentifymaximumnumberofcocolorhexagonsonthisarea,suchthatanytwococolorhexagonareatleastatagivendistanced2R+.Forthis,Algorithm 1 ,computesapair(i,j)andproducesasetSofcocolorhexagons,whosecentersformanequilateraltriangularlatticeofsidelengthp 3 2p (i2+j2+ij),asshowninFigure 26 .Thenumberof 32 PAGE 33 Algorithm1Cocolorhexagonalgorithm(H,d,h(i0,j0),c) Input:ThehexagonallatticeH,distanced,hexagonh(i0,j0)andacolornumbercassignedtoh(i0,j0). Output:AsetSofcocolorhexagonsofh(i0,j0) Computei,j S ; Queue h(i0,j0); while(Queueisnotempty)do h(a,b) Queue.Remove() S S[h(a,b); Color(h(a,b)) c InserteachofthefollowinghexagonsintheQueueiftheyarenotinsertedinthequeue: h(a+i,b+j) h(a+(i+j),b)]TJ /F3 11.955 Tf 11.96 0 Td[(i) h(a+j,b)]TJ /F4 11.955 Tf 11.95 0 Td[((i+j)j) h(a)]TJ /F3 11.955 Tf 11.95 0 Td[(i,b)]TJ /F3 11.955 Tf 11.96 0 Td[(j) h(a)]TJ /F4 11.955 Tf 11.95 0 Td[((i+j),b+i) h(a)]TJ /F3 11.955 Tf 11.95 0 Td[(j,b+(i+j)) endwhile returnS; cocolorhexagonsinSisproportionaltothenumberofequilateraltrianglesofsidesp 3 2p (i2+j2+ij)inthetriangularlattice. LetsconsideranothermethodwhichprovidesabettersolutionthanAlgorithm 1 .Thismethodidentiesasetofcocolorhexagoncentersformingaregularorirregulartriangulartilingoftheareainwhichatleastonetriangleisnonequilateral.However,itissimpletoobservethatforthesamesmallestsidelength,theareaofanequilateraltriangleisalwayssmallerthantheareaofanynonequilateraltriangle.Hence,thenumberofnonoverlappingtrianglesinthetilingstructuregeneratedwiththenewmethodwillbeboundedbythenumberofequilateraltriangleofsidesp 3 2p (i2+j2+ij)inthetriangularlatticegeneratedbyAlgorithm 1 .Thisresultsinthenewmethodidentifyinglessernumberofcocolorhexagons,incomparisontoAlgorithm 1 .Hence,acontradiction. 33 PAGE 34 Figure26. CoColorHexagonsofh(0,0)fori=2andj=3.TheindexofsublatticeRhinHi.e.jdet(A,B)j=i2+j2+ij=19. Theorem2.1. ThecoloringgeneratedbytheabovemethodisanoptimalsolutiontotheDistancedHexagonCenterColoringproblem. Proof. AccordingtoLemma 2 ,Algorithm 1 optimallyidentiescocolorhexagonswhichformsarhombiclatticeRhwithunitvectorsA=i^i+j^jandB=j^i)]TJ /F4 11.955 Tf 12.81 0 Td[((i+j)^j.ThenumberofsublatticessimilartoRhinHisgivenasjdet(A,B)j=i2+j2+ij[ 49 ].Therefore,theminimumnumberofcolorsneededtocolorHarei2+j2+ij.Ifweusei2+j2+ij)]TJ /F4 11.955 Tf 12.87 0 Td[(1colorsthenatleasttworhombicsublatticeswillbeassignedsamecolor.Asthedistancebetweenthehexagonsindifferentrhombicsublatticesisnotguaranteedtobeatleastd,itwillnotbethesolutionforDistancedhexagoncoloringproblem.Therefore,theoptimalnumberofcolorsneededwillbei2+j2+ij,hence,theprovidedsolutionisoptimal. 34 PAGE 35 Theorem2.2. ThenumberofcolorsforDistancedHexagoncoloringproblemforanarbitrarydisboundedby4 3d2+8 3d+4 3 Proof. Considerthehexagonh(0,0)andoneofitsclosestcocolorneighborsintherstquadrantofXh)]TJ /F3 11.955 Tf 12.17 0 Td[(Yhcoordinatesystemish(i,j).Withoutlossofgenerality,weconsider(ji),weexcludethecasewheni=0,j=1,thuswehavetwocases:1)i=0,j>1and2)i>0,j>0. Case1:Weusej2colorstoobtainthedistanced(j)]TJ /F4 11.955 Tf 12.83 0 Td[(1)p 3 2.Therefore,thenumberofcolorisequalto4 3d2+4 p 3d+1<4 3d2+8 3d+4 3 Case2:AsshownintheproofofTheorem 2.1 ,thenumberofcolorsusedisi2+ij+j2andtheguaranteedminimumdistancebetweenclosestpointsoftwococolorhexagonsisasfollows: ds 3 4(i)]TJ /F4 11.955 Tf 13.15 8.08 Td[(2 3)2+(i)]TJ /F4 11.955 Tf 13.15 8.08 Td[(2 3)(j)]TJ /F4 11.955 Tf 13.15 8.08 Td[(2 3)+(j)]TJ /F4 11.955 Tf 13.15 8.08 Td[(2 3)2=r 3 4(i2+ij+j2+4 3)]TJ /F4 11.955 Tf 11.95 0 Td[(2(i+j)) Itiseasytoprovethati2+ij+j24 3d2+8 3d+4 3fori,j>0.Theequalityhappensiffi=j. Figure27. ComparisonofnumberofcolorsusedtocolorthehexagontilingusingourschemeandScottet.al[ 1 ]. 35 PAGE 36 In[ 1 ],Scottet.al.proposeda3k2hexagoncoloringschemeforDistancedhexagoncoloringproblem.Figure 27 ,showsthecomparisonbetweentheirsolutionandtheoptimalsolutiongeneratedbyourproposedscheme.ItcanbeseenthatmostlyourcoloringschemeperformsfarbetterthanScottet.al.Onlywheni=j,thenumberofcolorsusedbyScottet.alisequaltothenumberofcolorsusedbyourscheme. 2.4TilingandColoringof3DimensionalSpace Inthissection,westudythetilingandcoloringof3Dspaceusingtruncatedoctahedrons,whichformsthekernelpartofoursolutionforIABSproblemin3DWSNs. Aregulartilingofthe3Dspaceresultsinpartitioningof3Dspaceintoidenticalcells.Basedonourrequirements,thediameterofaunitcellshouldbe1anditsvolumeshouldbeaslargeaspossible.Therefore,toidentifytheshapeoftheunitpartitioncell,wecomparevolumesofthefourpossiblespacetilingprimarypolyhedra[ 50 ]:1)TruncatedOctahedron,2)RhombicDodecahedron,3)Cubeand4)HexagonalPrism,consideringtheirdiametersareequalto1asshowninFigure 28 .Weobservethatthetruncatedoctahedronofsides1 p 10hasthemaximumvolume.Hence,weselectedtruncatedoctahedronasthepartitionshape.Figure 29 showsthetilingof3Dspaceusingtruncatedoctahedrons. Similarto2D,weformallydenethetilingandcoloringof3DspaceusingtruncatedoctahedronsasDistancedtruncatedoctahedroncoloringproblem: Distancedtruncatedoctahedroncoloringproblem:GivenatilingTOCof3Dspaceusingtruncatedoctahedronsofsides1 p 10andadistanced2R+,ndtheminimumnumberofcolorsneededtocolorTOC,suchthattwotruncatedoctahedronsto1andto2havingthesamecolormusthavethedistancedistance(to1,to2)d.Thedistancedistance(to1,to2)istheEuclideandistancebetweentwoclosestpointsp1andp2in3Dspace,suchthatp1lieswithinto1andp2lieswithinto2. InordertostudytheDistancedtruncatedoctahedroncoloringproblem,weintroduceanewXt)]TJ /F3 11.955 Tf 12.81 0 Td[(Yt)]TJ /F3 11.955 Tf 12.81 0 Td[(Ztcoordinatesystemin3Dspace,inwhich,Xt,Yt,and 36 PAGE 37 Figure28. Comparisonofdifferentspacingllingpolyhedra.Figuresa,b,canddrespectivelyshowatruncatedoctahedron,arhombicdodecahedron,acubeandahexagonalprism,havingmaximumdistancewithinthemequalto1. Figure29. Thetilingofspaceusingtruncatedoctahedrons ZtaxesareinclinedasshowninFigure 210 .TheanglebetweenXtandYtaxesis1=cos)]TJ /F7 7.97 Tf 6.58 0 Td[(1()]TJ /F7 7.97 Tf 6.59 0 Td[(1 3),whereas,anglesbetweenXtandZtaxesandYtandZtaxesareequalto2=cos)]TJ /F7 7.97 Tf 6.59 0 Td[(1(1 p 3).TheanglebetweentheZtaxisandtheXt)]TJ /F3 11.955 Tf 12.48 0 Td[(Ytplaneis3=45o.Thesidelengthofthetruncatedoctahedronis1 p 10,thedistancebetweenitstwoparallel 37 PAGE 38 hexagonalfacesisq 3 5andthedistancebetweenitstwoparallelsquarefacesis2 p 5.Therefore,distancesalongtheXt,YtandZtaxesarethemultipleofq 3 5,q 3 5,and2 p 5respectively.Centersofeachtruncatedoctahedroninthe3DspacecoincideswiththeintegralcoordinatesintheXt)]TJ /F3 11.955 Tf 12.74 0 Td[(Yt)]TJ /F3 11.955 Tf 12.75 0 Td[(Ztcoordinatesystem.Hence,everytruncatedoctahedroncanbeidentiedbycoordinates(i,j,k)ofitscenterasto(i,j,k). Figure210. TheXt)]TJ /F3 11.955 Tf 11.96 0 Td[(Yt)]TJ /F3 11.955 Tf 11.95 0 Td[(ZtCoordinateSystem Them2ncoloringAlgorithm:Wenowpresentthem2ncoloringalgorithm,illustratedasAlgorithm 2 ,fortheDistancedtruncatedoctahedroncoloringproblem.Thealgorithmusesdme2dnecolors,wherem,n2R+andguaranteesforanytwotruncatedoctahedronsto1,to22TOC,havingsamethecolormusthavedistance(to1,to2)d=(m)]TJ /F4 11.955 Tf 13.01 0 Td[(1)q 3 5=(n)]TJ /F4 11.955 Tf 13.02 0 Td[(1)2 p 5,Figure 211 showsthebasiccoloringpatterngeneratedbythem2ncoloringalgorithmford=1,wheredme=3anddne=3,hence,ituses27colors.Foranyarbitrarydistanced2R+,thebasiccoloringpatternwillhavedme=l(dq 5 3+1)manddne=ldp 5 2+1mthenumberofcolorsusedarel(dq 5 3+1)m2ldp 5 2+1m.Thisbasiccoloringpatternisrepeatedlyusedtocolorallthetruncatedoctahedronsin3Dtiling. 38 PAGE 39 Figure211. Coloringpatternford=1,dme=3anddne=3,Colorsassignedtothetruncatedoctahedronsarerepresentedbynumbers. Algorithm2m2ncoloringAlgorithm(TOC,d) dme=l(dq 5 3+1)m dne=ldp 5 2+1m forallhexagonTOC(i,j,k)do if(i<0)then i0=(dme)]TJ /F4 11.955 Tf 19.93 0 Td[(1)+(imoddme) else i0=(imoddme) endif if(j<0)then j0=(dme)]TJ /F4 11.955 Tf 19.93 0 Td[(1)+(jmoddme) else j0=(jmoddme) endif if(k<0)then k0=(dne)]TJ /F4 11.955 Tf 19.93 0 Td[(1)+(kmoddne) else k0=(kmoddne) endif ColorTOC(i,j,k) k0dme2+j0dme+i0+1 endfor 39 PAGE 40 2.5BroadcastSchedulingAlgorithm(BSA) WenowpresentourcentralizedBroadcastSchedulingAlgorithm(BSA)forIABSproblem.BSAisapplicableto2Daswellas3DWSNs.Inthissection,werstdescribeBSAfollowedbyitstheoreticalanalysisforO(1)approximationratiosin2Dand3DWSNsrespectively. 2.5.1AlgorithmDescription BSAtakesthegraphG=(V,E),representingtheWSNandthesourcenodevs2Vasinputs.Itgeneratesasoutput,theinterferenceawarebroadcastscheduleforbroadcastingthemessagemfromvstoalltheothernodes. BSA,incaseof2DWSNs,considersatilingof2DplanewithregularhexagonofsidesrTmin 2andcolorsitusingthemethoddescribedinSection 2.3 ,assumingd=(+1)rTmax.Incaseof3DWSNs,itconsidersatilingof3DspacewithtruncatedoctahedronsofsidesrTmin p 10.Further,assumingd=(+1)rTmax,itcolorsthetilingusingm2ncoloringalgorithmdescribedinSection 2.4 .Allnodesareassignedthecoloroftheirhexagonsortruncatedoctahedronsinwhichtheyarelocated,incaseof2Dor3DWSNsrespectively. Consideringvsasroot,BSAgeneratesaBFStreeofG=(V,E)topartitionitintoasetoflayersfL1,L2,...,LRg(whereRistheheightoftheBFStree).Afterthis,BSAstartsthebroadcastbysequentialitytransferringthebroadcastmessagembetweenconsecutivelayersstartingfromlayerL1=fsg.Consequently,allnodesinthenetworkreceivethebroadcastmessage. Duringthersttimeslott1,thesourcenodevs2L1transmitsthebroadcastmessagetoallnodesinlayerL2.Afterthis,BSArunsR)]TJ /F4 11.955 Tf 12.39 0 Td[(2iterationsoftheInterlayerSchedulingAlgorithm(ISA).Ineachiteration,ISAgeneratesaninterferenceawareschedulefortransmissionsbetweentwoconsecutivelayers.TheISAisillustratedinAlgorithm 4 40 PAGE 41 TheISAtakestwoconsecutivelayersLiandLjasinputsandgeneratesaninterferenceawaretransmissionschedulefromLitoLj.Inordertodothis,ISArstgeneratesamaximalindependentsetMIS(Lj)ofthesubgraphG[Lj]inducedbynodesinLj,suchthatMIS(Lj)isthedominatingsetofG[Lj].ISAgeneratesthescheduleintwophases.Intherstphase,basedontheircolors,nodesinMIS(Lj)arescheduletoreceivethebroadcastmessagemfromtheirparentsinLi.Inthesecondphase,basedontheircolors,nodesinMIS(Lj)arescheduledtotransmit,sothatallnodesinLjnMIS(Lj)receivethebroadcastmessagem. Algorithm3BSA(G(V,E),s) Incaseof2D(3D)WSNs,generatehexagon(truncatedoctahedron)tilingandcolorit. Toallnodesin2D(3D)WSN,assignthecoloroftheirrespectivehexagon(truncatedoctahedron)inwhichtheyarelocated. RunBFSrootedatvstopartitiongraphG=(V,E)intodistinctlayersfL1,L2,...LRg. Intimeslot1,L1=fsgtransmitstoallnodesinL2. Time 1;i 2 whilei6=R)]TJ /F4 11.955 Tf 11.95 0 Td[(1do Time Time+ILTS(Li,Li+1) i i+1 endwhile 2.5.2O(1)ApproximationRatioforInterferenceAwareBroadcastSchedulingProblemin2Dimension Lemma3. ThetransmissionscheduleproducedbyISAfor2DWSNsisinterferenceaware. Proof. WhenISAisappliedtoa2DWSN,eachhexagoncanhaveonlyoneMIS(Lj)nodeandhexagonshavingthesamecolorareatleastatadistanced=(+1)rTmax.AsMIS(Lj)nodesofthesamecolorstransmitsorreceivesimultaneously,theysatisfysufcientconditionsforinterferenceawarenessdescribedinLemma 1 ,whichresultsininterferenceawaretransmissionschedule. 41 PAGE 42 Algorithm4ISA(Li,Lj) GenerategraphG(Lj)inducedbythenodesinLj. MIS GenMIS(G(Lj)) c Numberofcolorsusedtocolorhexagon(truncatedoctahedron)tilingincaseof2D(3D)WSNs. Time InitializeS1,S2,...,Scto forallu2MISdo Selectanodew2N)]TJ /F4 11.955 Tf 7.09 4.34 Td[((u)\Li Scolor(u) Scolor(u)[fwg endfor fori 1tocdo Sitransmits endfor Time Time+c. InitializeS1,S2,...,Scto forallu2MISdo Scolor(u) Scolor(u)[fug endfor fori 1tocdo Sitransmits endfor Time Time+c. returnTime Lemma4. MIS(Lj)nodesinISAarecoloredusingatmostl4 3(+1)22+8(+1) 3+4 3mcolorsin2DWSN. Proof. EveryMIS(Lj)nodeacquiresthecolorofthehexagoninwhichitislocated.Whensidesofthehexagonare1 2,accordingtoTheorem 2.2 foranydistanced2Rthenumberofcolorsneededtocolorthehexagontilingisboundedby4 3d2+8 3d+4 3.Thus,whensidesofthehexagonarermin 2thenumberofcolorsusedareboundedby4d2 3r2min+8d 3rmin+4 3.BasedonsufcientconditionsforinterferenceawarenessinLemma 1 ,dis(+1)rTmax.Hence,thenumberofcolorsneededwillbe:l4 3(+1)22+8(+1) 3+4 3m. Theorem2.3. TheBSAalgorithmprovidesanapproximationratio2l4 3(+1)22+8(+1) 3+4 3mforIABSproblemin2DWSNs. 42 PAGE 43 Proof. Intherstphase,theISAtakesatmostl4 3(+1)22+8(+1) 3+4 3mtimeslotstoscheduleallnodesinMIS(Lj)toreceivethebroadcastmessagemformtheirparentsinLiwithoutinterference.Ittakesanotherl4 3(+1)22+8(+1) 3+4 3mtimeslots,inthesecondphase,toschedulesallnodesinMIS(Lj)totransmitthebroadcastmessagemtonodesinLjnMIS(Lj).Hence,ittakestotal 2l4 3(+1)22+8(+1) 3+4 3mtimeslotstotransferthebroadcastmessagemfromlayerLitolayerLj. BSArunsR)]TJ /F4 11.955 Tf 13.04 0 Td[(2iterationsofISA,hence,thetotalnumberoftimeslotsorthebroadcastlatencyofBSAisgivenas: 1+(R)]TJ /F4 11.955 Tf 11.96 0 Td[(2)2l4 3(+1)22+8(+1) 3+4 3m ThetheoreticallowerboundoftheIABSproblemisR.Hence,theapproximationratiois: 2l4 3(+1)22+8(+1) 3+4 3m. Corollary1. Ifratiosandarebounded,theapproximationratiooftheBSAalgorithmforIABSproblemin2DWSNsisO(1). 2.5.3O(1)ApproximationRatioforInterferenceAwareBroadcastSchedulingProblemin3Dimension Lemma5. ThetransmissionscheduleproducedbyISAin3DWSNsisinterferenceaware. Proof. ThiscanbeprovedsimilartoLemma 3 .WhenISAisappliedina3DWSN,eachtruncatedoctahedroncanhaveonlyoneMIS(Lj)nodeandtruncatedoctahedronshavingthesamecolorareatleastatadistanced=(+1)rTmax.AsMIS(Lj)nodesofthesamecolor,transmitorreceivesimultaneously,theysatisfysufcientconditionsforinterferenceawarenessdescribedinLemma 1 ,whichresultsininterferenceawaretransmissionschedule. Lemma6. MIS(Lj)nodesinISAarecoloredusingatmostlq 3 5(+1)+1m2lq 4 5(+1)+1mcolorsin3DWSNs. 43 PAGE 44 Proof. EveryMIS(Lj)nodeisassignedthecolorofthetruncatedoctahedroninwhichitislocated.Consequently,themaximumnumberofcolorsassignedtoMIS(Lj)nodesareboundedbythenumberofcolorsneededtocolorthetruncatedoctahedrontiling. Asdescribedinsection 2.4 ,whentruncatedoctahedronstilingthe3Dspacehavesidelength1 p 10,foradistanced=(m)]TJ /F4 11.955 Tf 12.07 0 Td[(1)q 3 5=(n)]TJ /F4 11.955 Tf 12.08 0 Td[(1)q 4 5,them2ncoloringalgorithmusesdme2dnecolors. Therefore,whentruncatedoctahedronsofsidelengthrTmin p 10tilethe3Dspace,dme2dnecolorscanbeusedford=(m)]TJ /F4 11.955 Tf 11.98 0 Td[(1)rTminq 5 3=(n)]TJ /F4 11.955 Tf 11.98 0 Td[(1)rTminq 5 4.BaseonLemma 1 ,dis(+1)rTmax.Consequently,wehavem=q 3 5(+1)+1andn=q 4 5(+1)+1. Hence,thenumberofcolorsneededareboundedbylq 3 5(+1)+1m2lq 4 5(+1)+1m Theorem2.4. TheBSAalgorithmprovidesanapproximationratio2lq 3 5(+1)+1m2lq 4 5(+1)+1mforIABSproblemin3DWSNs. Proof. Intherstphase,theISAtakeslq 3 5(+1)+1m2lq 4 5(+1)+1mtimeslotstoscheduleallnodesinMIS(Lj)toreceivethebroadcastmessagemfromtheirparentsinLiwithoutinterference.Similarly,inthesecondphase,ittakesanotherlq 3 5(+1)+1m2lq 4 5(+1)+1mtimeslotstoscheduleallnodesinMIS(Lj)totransmitthebroadcastmessagemtonodesinLjnMIS. Hence,ittaketotal2lq 3 5(+1)+1m2lq 4 5(+1)+1mtimeslotstotransferthebroadcastmessagemfromLitoLj. BSArunsR)]TJ /F4 11.955 Tf 12.41 0 Td[(2iterationsofISA,so,thetotalnumberoftimeslotsneededorthebroadcastlatencyofBSAisgivenas: 1+(R)]TJ /F4 11.955 Tf 11.96 0 Td[(2)2lq 3 5(+1)+1m2lq 4 5(+1)+1m Furthermore,thetheoreticallowerboundofthebroadcastschedulingproblemisR. Hence,theapproximationratiois:2lq 3 5(+1)+1m2lq 4 5(+1)+1m. 44 PAGE 45 Corollary2. Ifratiosandarebounded,theapproximationratiooftheBSAalgorithmforIABSproblemin3DWSNsisO(1). 2.6CentralizedGreedyHeuristicforbroadcastscheduling Inthissection,weintroduceacentralizedGreedyHeuristicAlgorithm(GHA)forbroadcastschedulinginWSNs.GHAdoesnotfollowalayerbylayerapproachusedinAlgorithm 2.5 ,inwhichallnodesinaBFSlayermustbeinformedbeforethebroadcastproceedstosubsequentlayers.Instead,GHAconsidersthesetofallinformednodesatanypointintimeaspotentialtransmitters.consequently,GHAschedulessimultaneoustransmissionsinmultiplelayers.Thus,itavailstheadvantageofspatialdistributionoftransmittersbyschedulingmorenonconictingtransmissionsineachtimeslot.Furthermore,GHAusesamanualinterferenceavoidancetechniquebasedoncheckingindividualtransmitterswhethertheyareviolatingsufcientconditionsforinterferenceawarenessdescribedinLemma 1 .Thishelpsinincreasingthenumberofsimultaneousinterferenceawaretransmissionsineachtimeslot. Inordertoselectoneoutofpossibleinterferingtransmissions,mostofexistingheuristicsandapproximationalgorithms[ 15 32 35 ]usevarietyofcriteriatogivehigherprioritytoparticulartransmissionsinasetofinterferingtransmissions.Usually,higherpriorityisgiventotransmitterswithmoreneighborsinthenetwork,ortransmitterswithmorechildrenintheBFStree.Ontheotherhand,sincetheultimategoalofthebroadcastschedulingistoinformallnodesinthenetwork,wetriedtofollowagreedyruleforlocallyoptimizingtheprogressrateofthebroadcastbyinformingasmanynodespossiblewitheachnewtransmission.Thisgreedyrulegivesprioritytotransmitterswhichhavethehighestnumberofuninformedneighborsatthatpointintime.ThepseudocodeforGHA,whichemploysthisgreedyoptimization,isgiveninAlgorithm 5 2.7Conclusion Inthischapter,westudythebroadcastschedulingin2Dand3DWSNs.Weconsiderthatsensornodesmayhavedifferenttransmissionrangesandtheir 45 PAGE 46 Algorithm5GreedyHeuristicAlgorithm(GHA)(G=(V,E),r,,,s) 1: INFORMED=fsg,ACTIVE=fsg,TIME=0 2: PriorityQueuePQ:key(u2PQ)=jN(u)nINFORMEDj 3: whileINFORMED6=Vdo 4: PQ ACTIVE,S 5: while(PQ6=)do 6: u ExtractMin(PQ) 7: ACTIVE ACTIVEnfug 8: if(N(u)nINFORMED6=)then 9: FromPQremoveallnodesvwhosetransmissionswouldconictwiththescheduledtransmissionofu,asfollows: 10: 8v2PQ&8w2N(v)nINFORMED,if(d(u,w))rTuthenPQ PQnfvg 11: 8x2N(u)nINFORMED&8y2PQ,if(d(y,x))rTythenPQ PQnfyg 12: Scheduleuasfollows: 13: S S[fug 14: for(w2N(u)nINFORMED)do 15: INFORMED INFORMED[fwg 16: ACTIVE ACTIVE[fwg 17: endfor 18: endif 19: endwhileTIME TIME+1 20: ScheduleSintimeslotTIME 21: endwhile interferencerangesaretimesoftheirtransmissionranges(where>1).Wedeviseefcientcoloringmethodsforcoloringahexagonaltilingin2Dplaneandatruncatedoctahedrontilingin3Dspace,basedonwhichweproposeO(1)approximationalgorithmsforIABSproblemin2Dand3DWSNsrespectively.OurO(1)approximationalgorithmfor3DWSNsistherstinliteratureandourO(1)approximationalgorithmfor2Disthebestinliteratureforthenetworkandinterferencemodelweconsidered.Finally,wepresentanefcientgreedyheuristictostudytheeffectofvariousprioritymetricsforgreedilyselectingatransmissionamongmultipleinterferingtransmissions. 46 PAGE 47 CHAPTER3CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCEAWAREBROADCASTSCHEDULING 3.1Introduction Inthischapter,consideringthenetworkandinterferencemodeldenedinChapter 2 ,westudylocalizedbroadcastschedulinginWSNs.Existingworksonlyprovidecentralizedsolutions[ 1 15 32 35 36 38 40 51 52 ].Inaddition,mostofthemconsidersensornodeshavethesametransmissionrangeandtheirinterferencerangeisequaltotheirtransmissionrange.Themajordrawbackofthesecentralizedsolutionsisthattheyfailtoadapttotopologychangesincaseofdynamicnetworks.Thiscanbeeasilyaccommodatedbylocalizedalgorithmswithmuchlesseroverheads.Inthispaper,westudythelocalizedbroadcastschedulingconsideringtheprotocolinterferencemodel[ 53 ]tomodeltheinterferenceenvironment.WeconsidereachsensornodehasatransmissionrangerTv2rTmin,rTmax(whererTmax rTmin=>1)anditsinterferencerangeistimesofitstransmissionranges(where>1). WeproposeanovelapproachtolocallypartitionandcolortheWSNintoclusters.Ourapproachisbasedontilingandcoloringthe2DplanecoveredbyWSNnodesusingregularhexagons.Thisapproachisusedinouralgorithmstogenerateinterferenceawaretransmissionschedulesfortransmitternodes.InSection 3.2.1 ,wediscussthisapproachindetail.Basedonthisapproachweproposedtherstlocalizedapproximationalgorithmwhichhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2.Furthermore,weextendedourlocalizedalgorithmtoworkfor3DWSNs.InSection 3.2.4 ,wepresentthisextensionalongwiththetheoreticalanalysisoftheapproximationratioforlocalizedbroadcastschedulingin3DWSNs. Therestofthechapterisorganizedasfollows:Insection 3.2 ,wepresentourlocalizedapproximationalgorithmforbroadcastscheduling.Section 3.3 ,providestheperformanceevaluationofthelocalizedapproximationalgorithmdescribedinSection 47 PAGE 48 3.2 andthecentralizedapproximationalgorithmandthegreedyheuristicdescribedinChapter 2 .Finally,Section 3.4 concludesthechapter. 3.2LocalizedAlgorithmforBroadcastScheduling Inthissection,weintroducealocalizedalgorithmforbroadcastschedulingin2DWSNsandprovideitsextensionfor3DWSNs.Thealgorithmrstgeneratesabroadcastingstructure,ontopofwhichmessagebroadcastingcanbeperformedwheneverneeded.Asthebroadcastingstructureisnotatreerootedatsomespecicsourcenode,itsupportsbroadcastinitiatedbyanynodeasthesourcenode.Werstdiscussthelocalizedconstructionofthebroadcastingstructurefollowedbydescriptionoftheprotocolforbroadcastingamessage. Algorithm6LocalizedAlgorithmforgeneratingaBroadcastingStructure Step1:Everynodevi2Vlocallyidentiesthehexagonhinwhichitislocatedalongwithitscolor. Step2:Nodevithenbroadcastsitsid,colorandhexagoncoordinatestoitsonehopneighbors. Step3:Basedonthecolorandhexagoninformationfromonehopneighbors,vigeneratesHN(vi),PPviandasetoforderedpairsCvi. Step4Nodevi,broadcastsitsCvitoitsneighborsinHN(vi),basedonsimilarinformationfromitsneighborsinHN(vi),itgeneratesalistL=fhvj,Cjijvj2HN(vi)g. Step5:NodevirunsAlgorithm 8 toidentifythesetofSuppliernodeinitshexagon. Step6:IfthenodeviisaSuppliernode,itsendsaProviderRequestmessagetoallitsneighborsinPPi. Step7:Anodeu2PPionreceivingaProviderRequestmessagerespondswithaProviderResponsemessageandbecomesaProvidernodeforv.TheedgeconnectingaSuppliernodeandaProvidernodebecomesaProvideredge. Step8:ThesetofSuppliernodes,Providernodes,andProvideredgestogetherformsthebroadcastingstructureG=(Vb,Eb). 3.2.1LocalizedGenerationofBroadcastingStructure Inthissection,wedescribetheconstructionofthebroadcastingstructure,illustratedasAlgorithm 6 .WeassumethatthesubgraphgeneratedbythebidirectionallinksinG=(V,E)isconnected.Further,the2DplaneispartitionedintoregularhexagonsofsidesrTmin 2formingahexagontilingwhichcanberepresentedbytheXh)]TJ /F3 11.955 Tf 12.17 0 Td[(Yhcoordinatesystem,describedinSection 2.3 48 PAGE 49 ThebroadcastingstructureisasubgraphGb=(Vb,Eb),whichspreadsoverallhexagonsinwhichWSNnodesarelocated.Ithastwokindsofnodes;SuppliernodesandProvidernodes,whichareconnectedthroughProvideredges(referFigure 31 ). Figure31. ElementsoftheBroadcastingStructure. Allnodesv2Videntifytheirlocations(xv,yv)on2Dplaneusingsomelocalizationmethod[ 54 55 ]ortheymaybeequippedwithGPSdevicesforthis.Theyalsoknowthelocationofthebasestation(xb,yb)in2Dplane,whichislocatedat(0,0)intheXh)]TJ /F3 11.955 Tf 11.98 0 Td[(Yhcoordinatesystem.Eachv2Vlocallycomputestheintegralcoordinatesofthehexagonh(i,j)inwhichitislocatedinXh)]TJ /F3 11.955 Tf 11.96 0 Td[(Yhcoordinatesystemasfollows: i=$f(xv)]TJ /F3 11.955 Tf 11.95 0 Td[(xb))]TJ /F4 11.955 Tf 13.15 8.09 Td[((yv)]TJ /F3 11.955 Tf 11.95 0 Td[(yb) tan60og=rTminp 3 2+1 2% (3) j=$(yv)]TJ /F3 11.955 Tf 11.96 0 Td[(yb)sin60o=rTminp 3 2+1 2% (3) Afteridentifyingh(i,j),nodevidentiesthecolorofh(i,j)usingAlgorithm 7 ,whichcolorsthehexagontilingusingk2=l(+1) p 3=2+1m2colorsandguaranteesthatanytwohexagonsatclosestdistanced<(+1)rTmaxhavedifferentcolors.Figure 32 showsanexampleofhexagoncoloringgeneratedbyAlgorithm 7 .Nodevbroadcastitsid,hexagoncoordinatesh(i,j)andcolortoitsonehopneighborsandbasedonsimilarinformationitreceivesfromitsonehopneighbors,itgenerates: 1.AsetHN(v)N(v),whichisasetofnodeslocatedinthesamehexagoninwhichvislocated. 49 PAGE 50 Figure32. HexagoncoloringgeneratedbyAlgorithm 7 fork=4,colorsassignedtothehexagonsarerepresentedbynumbers. 2.AsetPPv(N(v)nHN(v))(PossibleProviders),whichisasetofnodesinv0sneighboringhexagons,itscontainsasinglenodefromeachneighboringhexagon. 3.AsetCvoforderedpairshvi,cii,wherevi2PPvandciisthehexagoncolorofvi. Aftergeneratingthesesets,nodevbroadcaststhesetCvtoitsneighborsinHN(v).BasedonCvisitreceivedfromitsneighborsvi2HN(v),nodevgeneratesasetL=fhvi,Ciijvi2HN(v)g,whereCiisthesetofcolorsintheneighborhoodofnodesvi2HN(v),andrunsAlgorithm 8 ,toidentifythesetofSuppliernodesinitshexagon.NotethateverynodeinHN(v)generatesthesamecopyofL,soeachofthemidentifythesamesetofSuppliernodes.ThecorrectnessofAlgorithm 8 dependsonwhetherthesetofSuppliernodesgeneratedforahexagonhavepossibleprovidersinallneighboringhexagons.ThishappensonlyifanytwoSuppliersnodesinahexagonhavingrespectivepossibleprovidersofthesamecolorbelongingtothesamehexagon.WeprovethisinLemma 7 50 PAGE 51 WhenanodevisaSuppliernode,itbroadcastsaProviderRequestmessagetoallitsneighborsinPPv.Thenodesvj2PPvrespondwithaProviderResponsemessageandbecomeProvidernodesforvandedgesconnectingthemtovbecomeProvideredges.ThesetofSuppliernodes,ProvidernodesandProvideredgesformthebroadcaststructureGb=(Vb,Eb)fortheWSN. Figure33. AnExampleshowingthefunctioningofapartofthebroadcaststructure. Figure 33 showsaportionofthebroadcaststructurewithrespecttoasinglehexagonwhosecoloris11.BlacknodesdepictSuppliernodes,graynodesdepictProvidernodesandwhitenodesarerestofnodesinthehexagon.TheedgesshownareProvideredges.TheSuppliernodev1isberesponsibletoreceiveandforwardthebroadcastmessageinitshexagon,ifanyoneofitsProviderinneighboringhexagonswithcolorsf10,14,15,20,21,24gwhohasalreadyreceivedthebroadcastmessage. 51 PAGE 52 Similarly,nodesv2andv3willberesponsibletoreceiveandforwardfromneighboringhexagonswithcolorsf12,13,16,17,21,22,25gandf1,2,3,6,7,8grespectively. Lemma7. IfanytwoSuppliersnodess1ands2inahexagonhavetheirrespectivepossibleprovidersp12PPs1andp22PPs2ofthesamecolor,p1,p2belongtothesamehexagon. Proof. Letp1andp2belongtodifferenthexagonsh1andh2respectivelyofthesamecolor.BasedonAlgorithm 7 ,closestdistancebetweenh1andh2mustbeatleast(+1)rTmax.Butifp1istheneighborofs1andp2istheneighborofs2,thenthemaximumpossibledistancebetweenh1andh2willberTmax,whichisacontradiction. Algorithm7HexagonColoringAlgorithm(H,,) 1: k=l(+1) p 3=2+1m 2: forAllh(i,j)2Hdo 3: if(i<0)then 4: i0=(k)]TJ /F4 11.955 Tf 11.95 0 Td[(1)+(imodk) 5: else 6: i0=(imodk) 7: endif 8: if(j<0)then 9: j0=(k)]TJ /F4 11.955 Tf 11.95 0 Td[(1)+(jmodk) 10: else 11: j0=(jmodk) 12: endif 13: Color(h(i,j))=j0k+i0k+1 14: endfor 3.2.2BroadcastSchedulingofBroadcastMessage Inthissection,wedescribetheprotocolforbroadcastingamessagemfromthesourcenodevs,toallothernodes. WeassumethattimeisdividedintosufcientlylargediscretetimeslotscalledEpochs.AllhexagonswithcolorciareassignedTthEpochs,suchthatciTmodk2,wherek2isthenumberofcolorsusebyAlgorithm 7 tocolorthehexagontiling.During 52 PAGE 53 Algorithm8SupplierIdenticationAlgorithm:Runslocallyonallv2V. INPUT:AsetL=fhvi,Ciijvi2HN(v)g,whereCiisthesetofcolorsintheneighborhoodofnodevi2HN(v). OUTPUT:SetoforderedpairsofSuppliernodesforv0shexagonandtherespectiveneighboringcolorstheycovertoreceivebroadcastmessage. Ch Svi2HN(v)Ci. Supplier= whileCh6=do Selectanodevi2LcoveringmaximumcolorsinCh(breakthetiesonthebasisofsmallerid). C0i=SetofcolorsinChthatarecoveredbyvi. Supplier=Supplier[vi,C0i Ch=ChnC0i endwhile ReturnSupplier Figure34. AnEpoch someEpochassignedtoitshexagon,thesourcenodevs2Vinitiatesthebroadcastbytransmittingthemessagemtoallnodesinitshexagon. AsshowninFigure 34 ,eachEpochisdividedintotwopartsEpochRandEpochT.EpochRisprimarilyusedbyaSuppliernodeinahexagonforreceivingthebroadcastmessagefromoneofitsProvidernodes.Further,itusesEpochTforbroadcastingthereceivedmessagetoallothernodesinitshexagon.EpochRisfurtherdividedintotwoparts;SelecttimeandReceivetime.SelecttimeforahexagonisdividedintosmallertimeslotscalledTrices,equaltothenumberofSuppliernodesinit.TheseTricesareallocatedtoSuppliernodesinincreasingorderoftheirids. DuringitscorrespondingTrice,aSuppliernodebroadcastsaRequestMessagetoallitsProvidersneighborsandifanyofthemhaveearlierreceivedthebroadcastmessagem,theyrespondwithResponseMessages.AsResponseMessagesare 53 PAGE 54 veryshorttimemessages,theprobabilityforResponseMessagesfrommultipleProviderstocollideisverylow.OnreceivingaResponseMessage,theSuppliernodebroadcastsaReceivingMessage.ThismessageindicatesthecorrespondingProvidertostarttransmittingandtoallotherSuppliernodesinthehexagon,itindicatestostopattemptinginthecurrentEpoch.DuringtheReceivetimethebroadcastmessageisreceivedbytheSuppliernodefromitscorrespondingProvider.Sincethesizeofthebroadcastmessageisverylargeincomparisontocontrolmessages,theSelecttimeisnegligibleincomparisontotheReceivetime.IftheSuppliernodedoesnotreceiveaResponseMessagefromanyofitsProviders,insubsequentTricesotherSuppliernodesinthehexagonattempttoreceivethebroadcastmessagefromtheirrespectiveProviders.AfterreceivingthebroadcastmessageinEpochR,duringEpochT,theSuppliernodebroadcaststhemessagemtoallothernodesinthehexagon. 3.2.3AnExampleScenario WithoutlossofgeneralityweconsiderthatallthenodesintheWSNhavethesametransmissionrangerandthedistanced=(+1)r=rp 3.Weconsiderthehexagontilingofthe2Dplane,withhexagonsofsidesr 2.NowfollowingAlgorithm 7 ,wehavek=3andthenumberofcolorsusedtocolorthehexagontilingwillbek2=9,thesearefC1,C2...C9g.WecanseeinFigure 35 thehexagonsatadistancelessthandarehavingdifferentcolors. Figure 35 basicallyshowsanexamplewhereaWSNisdeployedonthe2Dplane,thenodesarerepresentedaspoints.ThemappingoftheWSNnodesonthehexagontilingalongwiththeformationofthebroadcaststructureshowninFigure 35 .Figure 36 showsthebroadcastschedulegeneratedwhenasourcenodesinthehexagonh(0,0)initiatethebroadcast.Followingistheepochwisedescriptionofthegeneratebroadcastschedule: Epoch1:Thesourcenodesinh(0,0)broadcaststhebroadcastmessagetoallthenodesinh(0,0). 54 PAGE 55 Figure35. Abroadcaststructure Figure36. Databroadcastingontopofabroadcaststructure 55 PAGE 56 Epoch2:DuringtheEpochRtheSuppliernodea5inh(1,0)receivesthebroadcastmessagefromtheProvidernodea1inh(0,0).DuringEpochTtheSuppliernodea5broadcaststhebroadcastmessagetoalltheothernodesinh(1,0). Epoch3:TheSuppliernodesa10inh(2,0)anda13inh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,0)receivesthebroadcastmessageduringtheEpochRfromtheirrespectiveProvidernodesa7anda3.Further,duringEpochT,theSuppliernodesa10anda13broadcastthebroadcastmessagetoalltheothernodesinh(2,0)andh()]TJ /F4 11.955 Tf 9.29 0 Td[(1,0),respectively. Epoch4:DuringEpochRaSuppliernodea15inh(0,1)receivesthebroadcastmessagefromitsProviderneighbora6inh(1,0).DuringEpochTtheSuppliernodea15broadcaststhebroadcastmessagetoalltheothernodesinh(0,1). Epoch5:DuringEpochRtheSuppliernodesa18anda16inh(1,2)andh(1,)]TJ /F4 11.955 Tf 9.29 0 Td[(2),respectively,receivesthebroadcastmessagefromtheirrespectiveProviderneighborsa7and14inh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,0)andh(1,0).DuringEpochTtheSuppliernodesa18anda16broadcaststhebroadcastmessagetoalltheothernodesinh(1,2)andh(1,)]TJ /F4 11.955 Tf 9.29 0 Td[(2),respectively. Epoch6:DuringEpochRtheSuppliernodesa23anda21inh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,1)andh(2,1),respectively,receivesthebroadcastmessagefromtheirrespectiveProviderneighborsa4anda19inh(0,0)andh(1,1).DuringEpochTtheSuppliernodesa23anda21broadcaststhebroadcastmessagetoalltheothernodesinh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,1)andh(2,1),respectively. Epoch7:DuringEpochRtheSuppliernodesa27,a26anda25inh(0,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),(3,)]TJ /F4 11.955 Tf 9.3 0 Td[(1)andh(0,2),respectively,receivethebroadcastmessagefromtheirrespectiveProviderneighborsa2,a11anda15inh(0,0),(2,0)andh(0,1).DuringEpochTtheSuppliernodesa27,a26anda25broadcastthebroadcastmessagetoalltheothernodesinh(0,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),(3,)]TJ /F4 11.955 Tf 9.3 0 Td[(1)andh(0,2),respectively. Epoch8:DuringEpochRtheSuppliernodesa30,a28anda29inh(1,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),()]TJ /F4 11.955 Tf 9.3 0 Td[(2,2)andh(1,2),respectively,receivethebroadcastmessagefromtheirrespectiveProvider 56 PAGE 57 neighborsa9,a17anda20inh(1,0),()]TJ /F4 11.955 Tf 9.3 0 Td[(2,1)andh(1,1).DuringEpochTtheSuppliernodesa30,a28anda29broadcastthebroadcastmessagetoalltheothernodesinh(1,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),()]TJ /F4 11.955 Tf 9.3 0 Td[(2,)]TJ /F4 11.955 Tf 9.3 0 Td[(2)andh(1,2),respectively. Epoch9:DuringEpochRtheSuppliernodea33,a32,a31anda34inh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),()]TJ /F4 11.955 Tf 9.3 0 Td[(1,2),h(2,2)and(2,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),respectively,receivethebroadcastmessagefromtheirrespectiveProviderneighborsa40,a24,a22anda8inh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,0),()]TJ /F4 11.955 Tf 9.3 0 Td[(1,1),h(2,1)andh(1,0).DuringEpochTtheSuppliernodesa33,a32,a31anda34broadcastthebroadcastmessagetoalltheothernodesinh()]TJ /F4 11.955 Tf 9.3 0 Td[(1,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),()]TJ /F4 11.955 Tf 9.3 0 Td[(1,2),h(2,2)and(2,)]TJ /F4 11.955 Tf 9.3 0 Td[(1),respectively. Epoch10:DuringEpochRtheSuppliernodea39inh(3,0)receivesthebroadcastmessagefromitsProviderneighbora12inh(2,0).DuringEpochTtheSuppliernodesa39broadcaststhebroadcastmessagetoalltheothernodesinh(3,0). AsinalltheEpochs,whilereceivingandtransmittingthebroadcastmessage,alltheSuppliernodesfollowthesufcientconditionsforinterferenceawarenessintroducedinLemma 1 ,hence,therewillbenointerferenceduringthebroadcastingofthebroadcastmessage. Lemma8. Thereisnointerferencewhen:1)anySuppliernodereceivesbroadcastmessagemfromitsProvider,2)anySuppliernodetransmitsthebroadcastmessagemtoothernodesinitshexagon. Proof. Case1:AssumethataSuppliernodevsupreceivingbroadcastmessagefromitsrespectiveProvidervproisinterferedbyanodevi.ThiswouldmeanthatviandvpromustbetransmittingatthesametimeduringtheEpochRofanEpoch.Therefore,thereceiverofvi,sayvj(whichshouldbeaSuppliernode)andvsup,mustbeinhexagonswiththesamecolor.Thisgivesrisetotwopossibilities:1)Bothvjandvsupareinthesamehexagon.Inthiscase,onlyoneofthemcanbescheduledtoreceive,henceacontradiction.2)vjandvsupareindifferenthexagonsofsamecolor.Butinthiscasethedistancebetweenvjandvswillbegreaterthanorequalto(+1)rTmax.Therefore,accordingtoLemma 1 ,vicannotinterferevs,henceacontradiction. 57 PAGE 58 Case2:AssumethatthetransmissionsoftwoSuppliernodes,vsup1andvsup2areinterfering(whichoccursiftheyaretransmittingatthesametimeduringtheEpochTofanEpoch).Thisispossibleonlyifvsup1andvsup2belongtothesamecolorhexagons.Thisgiverisetotwopossibilities:1)Bothvsup1andvsup2areinthesamehexagon,inthiscasevsup1andvsup2cannotbescheduledtotransmitatthesametime,hence,thisisacontradiction.2)vsup1andvsup2areindifferenthexagonsofsamecolor.Inthiscasethedistancebetweenvsup1andvsup2isatleast(+1)rTmaxandaccordingtoLemma 1 theycannotinterfereeachother. Theorem3.1. TheapproximationratioforlocalizedbroadcastingalgorithmfortheIABSproblemin2DWSNis2l(+1) p 3=2+1m2. Proof. ThetheoreticallowerboundofIABSproblemisR,i.e.theradiusofthenetworkwithrespecttothesourcenode.Forcomparingthelatencyoflocalizedalgorithmwiththetheoreticallowerbound,weconsidertheBFStreeofthegraphG=(V,E)rootedatvs,whichdividesthenetworkintolayersL1,L2,...,LR.Accordingtoourlocalizedalgorithm,withinl(+1) p 3=2+1m2Epochs,allnodesinhexagonsinwhichnodesinlayerL2arelocatedwillreceivethemessagemfromthehexagoninwhichthesourcenodevs2L1islocated.Andwithinnextl(+1) p 3=2+1m2Epochs,nodesinallhexagonsinwhichnodesinL3arelocatedwillreceivethebroadcastmessagemfromhexagonsinwhichnodesinL2arelocated,andsoon.After(R)]TJ /F4 11.955 Tf 12.97 0 Td[(1)l(+1) p 3=2+1m2EpochsnodesinhexagonsinwhichnodesinLRarelocatedwillreceivethemessagem.AseachEpochhastwotimeslotsEpochRandEpochTduringwhichthebroadcastmessageistransmitted,hence,thebroadcastlatencyofthelocalizedalgorithmis2(R)]TJ /F4 11.955 Tf 11.95 0 Td[(1)l(+1) p 3=2+1m2.Thus,theapproximationratiois2l(+1) p 3=2+1m2. 3.2.4LocalizedBroadcastSchedulingAlgorithmin3Dimension Thelocalizedbroadcastschedulingalgorithmcanbeappliedto3DWSNs,ifweconsiderthe3DspaceispartitionedintotruncatedoctahedronsofsidesrTmin p 10,forminga 58 PAGE 59 truncatedoctahedrontilingofthe3Dspace,representedbytheXt)]TJ /F3 11.955 Tf 12.08 0 Td[(Yt)]TJ /F3 11.955 Tf 12.08 0 Td[(ZtcoordinatesystemdescribedinSection 2.4 .ThetruncatedoctahedrontilingiscoloredbasedonAlgorithm 2 usinglq 3 5(+1)+1m2lq 4 5(+1)+1mcolors,keepingdistanced=(+1)rTmax.Ifcoordinatesofasensornodev2Vandthebasestationin3Dspaceare(xv,yv,zv)and(xb,yb,zb)respectively,thecoordinatesofvi.e.(xtv,ytv,ztv)andthetruncatedoctahedronto(i,j,k)inwhichitislocatedinXt)]TJ /F3 11.955 Tf 12.27 0 Td[(Yt)]TJ /F3 11.955 Tf 12.27 0 Td[(Ztcoordinatesystemcanbecomputedasfollows: ztv=(zv)]TJ /F3 11.955 Tf 11.96 0 Td[(zb)sin3=rTmin2 p 5(3) ytv=f(yv)]TJ /F3 11.955 Tf 11.95 0 Td[(yb))]TJ /F4 11.955 Tf 11.95 0 Td[((zv)]TJ /F3 11.955 Tf 11.96 0 Td[(zb)cos(1=2)=tan3g=rTminr 3 5(3) xtv=[(xv)]TJ /F3 11.955 Tf 11.95 0 Td[(xb))222(f(zv)]TJ /F3 11.955 Tf 11.96 0 Td[(zb)sin(1=2)=tan3g)]TJ /F10 11.955 Tf 101.25 12.11 Td[(r 5 3ytv=tan1]=rTminr 3 5(3) Theangles1and3areasdenedinSection 2.4 .Thecoordinatesofto(i,j,k)aregivenas: i=xtv+1=2,j=ytv+1=2,,k=ztv+1=2 NodevcanuseAlgorithm 2 tolocallyidentifythecolorofto(i,j,k).Onceallnodesv2Vknowtheirrespectivetruncatedoctahedronsandcolors,thelocalizedbroadcastschedulingalgorithmfor2DWSNscanbeusedforperforminginterferenceawarebroadcastingin3DWSNs. Theorem3.2. TheapproximationratioforlocalizedbroadcastingalgorithmfortheIABSproblemin3DWSNis2lq 3 5(+1)+1m2lq 4 5(+1)+1m. 59 PAGE 60 Proof. Aslq 3 5(+1)+1m2lq 4 5(+1)+1mcolorsarerequiredbyAlgorithm 2 tocolorthetruncatedoctahedrontiling.Basedonthis,thetheoremcanbeprovedsimilartoTheorem 3.1 3.3ExperimentalEvaluation Inthissection,throughsimulations,wepresenttheexperimentalevaluationoflocalizeapproximationalgorithmforonetoallbroadcastschedulingproposedinthischapterandcentralizedapproximationalgorithmandgreedyheuristicforbroadcastschedulingproposedinChapter 2 .Werandomlygenerated11,000networkinstanceswithdifferentsetupsandranouralgorithmstoevaluatetheirperformanceintermsofthebroadcastlatency.Westudythebehaviorofourproposedalgorithmsbasedonthreeimportantparameters:1)Numberofsensornodesinthenetwork,2)Ratio,and3)Ratio. Weimplementedtheapproximationalgorithm(ApproxAlgo)introducedinSection 2.5 ,thelocalizedalgorithm(LocalizedAlgo)introducedinSection 3.2 ,andthecentralizedgreedyheuristic(GHA)introducedinSection 2.6 .Although,thesethreealgorithmsworkfor2Daswellas3DWSNs,butwesimulatedthemonlyon2DWSNs. 3.3.1EffectofNumberofSensorNodesonBroadcastLatency Intherstsetofexperiments,weconsiderasquareareaofsides500mandrandomlydeployedNnodesonit,whereNvariesfrom10to500,rTmin=100m,and==2.0. Figure 37 showsplotsofbroadcastlatenciesproducedbyApproxAlgo,LocalizedAlgoandGHAwithrespecttonumberofsensornodesinWSN.Thelatencyvalueforanynumberofnodesisaveragedafterrunningeachalgorithmonasetof100networkinstances.Asitwasexpectedthelatencyforthegreedyheuristicisthesmallest.Therearetwomainreasonsforthis:rstly,GHAdoesnotfollowthelayerbylayerbroadcastingapproach.Secondly,foranytimeslotGHAfollowsthemanualidentication,selectionandeliminationofsimultaneoustransmissionsamongdifferent 60 PAGE 61 Figure37. EffectofnumberofnodesonAverageLatency Figure38. AverageBFSheight Figure39. Averageoptimalityratio 61 PAGE 62 setsofinterferingtransmissions.Forthis,GHAconsidersexacttransmissionandinterferingrangesofinterferingsensornodes.IncaseofApproximationAlgorithmalayerbylayerapproachisusedbasedontheBFStreeofthenetwork.Andinatimeslottheidenticationandschedulingofinterferingtransmissionsisdonebasedoncoloringofthehexagontilingof2Dplane,whichconsidersthethetransmissionrangeandtheinterferencerangesasrTmaxandrTmaxrespectively.Thispossiblyresultsinconsideringextratransmissionsasinterferingtransmission,whichmightnotbeactuallyinterfering. Further,inFigure 37 weseethattheperformanceoftheLocalizedAlgorithmisnotgoodforsparsernetworks,butasthenetworkdensityincreasesthealgorithmstabilizedandafterthepointwhennumberofsensornodebecome80thealgorithmhaslatencycloseto80.ThoughtheLocalizedAlgorithmdoesnotusealayerbylayerapproachstillitslatencyisalittlehigher,thisisbecause,nodesneedtowaitforthetimeslotsassignedtotheirhexagonsinordertoreceiveortransmitthebroadcastmessage. Infact,weexpectedallthreealgorithmstorespectivelyconvergetoxedvaluesaftercertainnumberofnodes.Intuitively,theexpectedlatencyisdeterminedbytheheightoftheBFStree.Sincetheareaofournetworkisxed,afteracertainnumberofnodestheheightoftheBFStreecannotgrowanyfurtheronincreasingthenumberofnodes.Sinceasingletransmissionfromatransmittercaninformallnodesinitsneighborhood.Therefore,anincreaseinnumberofnodeswithoutincreasingtheBFSheightdoesnotaddmuchtothebroadcastlatency.Figure 38 showstheaverageheightoftheBFStreesinoursamplenetworksforanygivennumberofnodes.ItcanbeobservedinFigure 38 ,theBFSheightofthenetworkincreasestillthenumberofnodesreaches40,afterthatitstartstodecrease.Thisisbecauseofthelowerconnectivityinsparsernetworksresultsinsomelongerpaths,andwhenthenetworkbecomesdensertheconnectivityenhancesandthepathlengthsbecomesshorter.Afterthenumberofsensornodesarearound375theBFSheighttheremainscloseto5. 62 PAGE 63 Figure310. EffectofonAverageLatency Figure 39 showsoptimalityratiosofthebroadcastforallthreealgorithms.TheoptimalityratioistheratiooflatencyandtheBFSheightofthenetwork(whichservesasthetriviallowerboundforbroadcasting).TheoptimalityratioforGHArangedfrom1.0164to1.8265,forApproximationAlgorithmitrangedbetween1.3181to3.3840,whichisverysmallincomparisontotheupperbounddiscussedinTheorem 2.3 .Thisshowsthatourapproximationalgorithmempiricallyshowsafarbetterperformanceincomparisontoitstheoreticalbound.TheoptimalityratioforourLocalizedAlgorithmrangesbetween1.6872to16.3568,whichismuchbetterthanthetheoreticalupperboundprovidedinTheorem 3.2 .Mainadvantagesofourlocalizedalgorithmare,rstly,ithasaO(1)messagecomplexityandsecondly,itdoesnotneedanycentralizedcontrol,therefore,ithasmuchloweroverheadsandmoreefcientlyadaptstonetworktopologychanges.Further,initscurrentstateitcanalsohandlemultimessagemultisourcebroadcasting. 3.3.2EffectofonBroadcastLatency Figure 310 showstheeffectofincreasingonlatenciesofallthreealgorithms.Wedeploy300sensornodesonasquareareaofside500m.Wevaryfrom1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreveryvalueof,wegenerate100networkinstancesandaveragedlatenciesproducedbyeachalgorithm. 63 PAGE 64 TheplotforLocalizedAlgorithm,inFigure 310 ,showsthatwhenthevalueofvariesfrom1.0to1.8,thelatencyincreasesrapidlyfrom54to80.Thisismainlybecause,increasingincreasesthenumberofcolorsusedtocolorthehexagontiling.Hence,thenumberoftimeslotsanodehastowaittogetachancetotransmitorreceivethebroadcastmessagealsoincreases.Thisincreasesthebroadcastlatency.Atthesametime,increasingincreasesthesizeoftheneighborhoodofasensornodeandsowithasingletransmissionanodecancovermoreuninformednodeinitsneighborhood.Thisbalancesouttheadverseeffectofincreaseinhexagoncolorsonthelatencyandhence,withfurtherincreaseinthereisnoincreaseinthebroadcastlatency. Interestingly,weseethatwithincreaseinthelatencyoftheApproximationAlgorithmdecreases,thisisbecausewhenincreasesthesizeoftheneighborhoodsofsensornodesalsoincrease,whichresultsindecreasingoftheradiusofthenetwork.Andasourapproximationalgorithmfollowsalayerbylayerapproach,hence,itslatencydirectlydependsupontheheightoftheBFStree,i.e.theradiusofthegraph.Itcanbenoticedthatincreasingalsoincreasesthenumberofinterferingtransmissions,butasweknowthatincaseofApproximationAlgorithm,inagiventimeslottransmissionstakeplaceonlywithintwoconsecutiveBFSlayerbutnotintheentirenetwork.Therefore,theeffectofincreasingonbroadcastlatencyisnotsignicant. IncreasingdoesnothavemucheffectonthelatencyofGHA,thismaybebecauseGHAdoesnotfollowthelayerbylayerapproach,hence,itisnotaffectedbytheradiusofthenetwork.Although,increasingincreasesthesizeoftheneighborhoodofanodebutitalsoincreasesthenumberofinterferingtransmission,whichnulliesthegoodeffect. 3.3.3EffectofonBroadcastLatency Figure 311 showstheeffectofvaryingonlatenciesofallthreealgorithms.Wedeploy300sensornodesonasquareareaofside500m.Theparametervariesfrom 64 PAGE 65 Figure311. EffectofonAverageLatency 1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreveryvalueofwegenerate100networkinstancesandaveragerespectivelatenciesproducedbyouralgorithms.Figure 311 showsthathasaneffectsimilartoonLocalizedAlgorithm.Thiscanbeexplainedasthenumberofcolorsneededtocolorthehexagontilingisdirectlyproportionalto,sohasadirectimpactonthelatencyofLocalizedAlgorithm. Further,inFigure 311 weseethattherearenotmuchvariationsinthelatencyofApproximationAlgorithmonchanging.ThisisbecausedoesnothaveanyeffectontheBFSheightofthenetwork,itonlyincreasestheinterferencerangeofanode.AsweknowthatincaseofApproximationAlgorithm,inagiventimeslotthetransmissionsareconsideredwithintwoconsecutiveBFSlayersbutnotintheentirenetwork,therefore,theeffectofonbroadcastlatencyisnotnoticeable.IncaseofGHA,weseeagradualincreaseinlatencywithrespectto.Thisisthedirecteffectofincreaseininterferingtransmissionswithincreasein. Figure 312 comparestheperformanceofvariousheuristicalgorithms,basedondifferentcriteriausedforschedulingvariousinterferingtransmissions.Foreachcriterion,theaverageoptimalityratiooverallthe11,000samplegraphsislisted.Itisinterestingtoseethatmanyofchosenoptimizationcriteriaactuallydegradetheperformanceofthealgorithm.Thisisbecausethecriteriawhicharebasedonthetopologyofthe 65 PAGE 66 Figure312. Comparisonofvariousheuristicsalgorithms network,arelikelytoprovidehigherprioritytophysicallyadjacentnodesinthenetworktotransmit.Thiscanaggravatethethespreadingofbroadcastmessageinthenetwork.Figure 312 showsthatitisbettertoprioritizenodeswhicharefartherfromthesourceratherthannodeswhichareclosertothesource.Thisisinlinewiththeobservationthatfarthernodesaremoreeffectiveinrapidlyspreadingthebroadcastmessageinthenetwork. 3.4Conclusion Inthischapter,westudiedlocalizedbroadcastschedulingintheinterferenceenvironmentmodeledbyprotocolinterferencemodel.Westudiedminimumlatencybroadcastschedulingandproposedtherstlocalizedapproximationalgorithms.Ourlocalizedalgorithmhasanapproximationguaranteeofl2(+1) p 3+1m2. 66 PAGE 67 CHAPTER4ALLTOALLDATABROADCASTINGANDALLTOONEDATAAGGREGATION 4.1Introduction Inthischapter,westudyalltoalldatabroadcastingandalltoonedataaggregationinWSNs.WeconsideraWSNmodeledasadiskgraphG=(V,E),whereeachsensornodevi2Vgeneratesamessagemi,westudyfollowingtwoproblems:1)Minimumlatencyalltooneaggregationschedulingand2)Minimumlatencyalltoallbroadcastscheduling. Inminimumlatencyalltooneaggregationschedulingproblem,itisrequiredtoaggregateatnodevsallmessagesmigeneratedatnodevi2Vnvsrespectively.Theearliesttimeatwhichtheallmessagesreachesvsisknownasalltooneaggregationlatencyanditshouldbeminimized. Inminimumlatencyalltoallbroadcastscheduling,itisrequiredtobroadcastallmessagesmigeneratedatnodesvi2Vrespectivelytoallthenodesinthenetwork.Theearliesttimeatwhichallmessagesreachallnodesinthenetwork,knownasalltoallbroadcastlatency,shouldbeminimized. Theschedulesgeneratedforeachoftheaboveproblemsmustsatisfythefollowingconstraints: 1.Aschedulemustspecifyforeachnodev,whenitcantransmitorreceiveamessagem. 2.Anodevcanbescheduledtotransmitamessagemattimetjiffithadearliersuccessfullyreceivedthemessagemattimeti. 3.Twonodesuandvcanbescheduledtotransmitsimultaneouslyifftheirtransmissionsareinterfereaware. Themaincontributionsofthischapterare: 1.WepresentalocalizedalgorithmsforalltoallbroadcastschedulinginWSNs. 67 PAGE 68 2.Wepresentadistributedalgorithmsforalltoonedataaggregationschedulingandalltoalldatabroadcastscheduling.Ourdistributedalgorithmforalltoonedataaggregationschedulingistherstinliteratureandhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2. 3.Wealsopresentadistributedalgorithmforalltoallbroadcastscheduling,whichistherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. Therestofthechapterisorganizedasfollows:Insection 4.2 ,wedescribealocalizedalgorithmforalltoalldatabroadcast.Section 4.3 describesadistributedapproximationalgorithmforalltoonedataaggregationalongwiththetheoreticalanalysis.InSection 4.4 ,wedescribeadistributedapproximationalgorithmforalltoalldatabroadcastingalongwiththetheoreticalanalysisofitsapproximationratio.WeprovidetheperformanceanalysisofthesealgorithmsinSection 4.5 .Finally,Section 4.6 concludesthechapter. 4.2LocalizedAllToAllDataBroadcastSchedulingAlgorithm Similartoonetoallbroadcast,weassumethattimeisdividedintodiscreteEpochsandanyhexagonwithcolorciisassignedtheTthEpoch,suchthatCiTmodk2,wherek2isthenumberofcolorsusedtocolorthehexagontiling.EachEpochisdividedintotwopartsEpochRandEpochT.EpochRisprimarilyusedbyaSuppliernodetoreceiveamessagefromaProviderinitsneighborhood.EpochTisbasicallyusedfortwopurposes.Firstly,itisusedbynodesinahexagontobroadcasttheirownmessageswithintheirhexagon.Secondly,itcanbeusedbysomeSuppliernodetobroadcastinitshexagon,amessagewhichitreceivedfromoneofitsProvider.Thepreferencefortransmissionisgiventobroadcastmessagesgeneratedbythenodeswithinthehexagon.EachnodemaintainsaMessageList,whichisasetofbits,suchthatithasabitforeachnodeinthenetwork.Whenanodereceivesamessagegeneratedbysomenodewithidi,itsetsthebitattheithlocationinitsMessageList. WenowdiscusshowthetimedurationinanEpochisusedbythenodesinahexagon.EpochRisfurtherdividedintoSelecttimeandReceivetime.Selecttimeisdividedinto 68 PAGE 69 smallertimeslotscallerTrices,equaltothenumberofdesignatedProvidernodesforthehexagon.DuringtheSelecttime,theSuppliernodesareallocatedtheTricesonthebasisoftheirdesignatedProvidernodesintheincreasingorderoftheidsoftheProvidernodes.DuringtheirallocatedTrice,aSuppliernodesnegotiateswithitsrespectiveProvidersforthatTricetoreceiveanewmessage. InordertonegotiatewithitsProvider,aSuppliernodeduringitsallocatedTricesendsaRequestMessage.AlongwiththeRequestMessage,itsendsitsMessageList.BasedonthereceivedMessageList,theProvidernodechecksforanynewmessageitcanprovide.Ifithasany,itsendstheidofthatmessageintheResponseMessagetothecorrespondingSuppliernode.OnreceivingtheResponseMessage,theSuppliernodeupdatesitsMessageListandbroadcastsitintheReceivingMessage.ThepurposeoftheReceivingMessageisthreefold.Firstly,itacknowledgestherespectiveProvidertosendthemessage.Secondly,itbroadcastitsupdatedMessageListtoallthenodesinthehexagon.Thirdly,itnotiestheotherSuppliernodesnottoattempttoreceivefromtheirProvidersinthecurrentEpoch.Afterthisnegotiation,theProvidertransmitsthemessagetotheSupplierduringtheReceivetimeoftheEpochR.DuringEpochTanynodeinthehexagonwillingtobroadcastitsownmessagewillbroadcast.Ifthereisnosuchnodeinthehexagon,thenanySuppliernodewillbroadcastamessagewhichithasreceivedfromitsProviderinadifferenthexagon. Lemma9. Eventuallyeverynodereceivesmessagegeneratedbyalltheothernodes. Proof. AsweassumethatthegraphgeneratedbythebidirectionallinksintheWSNisconnected,therefore,thereisatleastasinglepathbetweenanytwonodes.Let'sassumethatthemessagegeneratedbyanodeviisnotreceivedbynodevjatkhopdistanceonpath(vi,vi+1,...,vi+(k)]TJ /F7 7.97 Tf 6.59 0 Td[(1),vj).Now,thewaytheprotocolworks,themessagemigeneratedbyviwillbebroadcastedinitshexagonduringanEpochassignedtoitshexagon.Ifnodevi+1isinthesamehexagonitwillreceivemiinthesameEpoch,elseitwillreceivemiinsomelaterEpoch.Similarly,themessagemiwillbetransferredfromvi+1tovi+2.Asthe 69 PAGE 70 path(vi,vi+1,...,vi+(k)]TJ /F7 7.97 Tf 6.59 0 Td[(1),vj)connectsvitovj,itiscertainthatvjwillreceivethemessagewithinnitenumberofEpochs,whichisacontradiction. 4.3DistributedAllToOneDataAggregationSchedulingAlgorithm AlltoonedataaggregationisanimportantoperationinWSN.Periodicallyitisrequiredthatthesensedinformationfromallthesensornodesbeaggregatedatthesinknodevsforfurtherprocessingandforwarding.Inthissection,weintroduceadistributedprotocoltogenerateaninterferenceawareschedulefordataaggregationfromallthenodesv2(Vnvs)atthesinknodevs.Weassumethat,usingthedistributedBFSalgorithm[ 56 ]orthedistancevectoralgorithm,everynodeknowsitsclosestdistanceintermsofhopcountstovsanditsonehopneighborontheclosestpathtovs,suchaneighboristermedastheCollector.LettheradiusofthegraphG=(V,E)withrespecttovsisRandnodesinVaredividedintosubsetsS1,S2,...,SR,suchthatSiisthesubsetofnodeswhichareihopsawayfromthevs.WeobservethatallnodesinSiwillhavetheirCollectornodesinSi)]TJ /F7 7.97 Tf 6.59 0 Td[(1. Weassumethe2DplanecoveredbytheWSNnodesispartitionedintoregularhexagonswithdiameterrTminandiscoloredusingAlgorithm 7 ,consideringdistanced=(+1)rTmax.AllthenodesinahexagonelectsaTransmitternodeamongthemselves,whichhasminimumhopdistancetothesink(tiesarebrokenonthebasisofsmallerid).ThetimeisdividedintoEpochsandanyhexagonwithcolorciisassignedtheTthEpochs,suchthatciTmodjk2j.AnEpochisdividedintotwopartsEpochRandEpochT.Inalltoonedataaggregationprotocol,theEpochRisusedbyanodeinahexagontotransmitamessagetoitsrespectiveTransmitternodeandduringEpochRtheTransmitternodeforwardsthatmessagetoitsCollectornode.Hence,inasingleEpoch,amessagefromanodeinahexagonisforwardedatleastonehopclosertothesinkwithoutanyinterference. Eachnodev2VmaintainsaForwardqueuewhichisinitializedbyinsertingthemessagegeneratedbyv.TheForwardqueueexpandswhen:1)vactsasaCollectorin 70 PAGE 71 somesetSiandreceivesmessagesfromsomeTransmitternodeinsetSi+1,or2)whenvactsaTransmitternodeandcollectsmessagesfromothernodesinitshexagon.TheForwardqueueshrinks:1)whenvforwardsmessagestoitsrespectiveTransmitternodeor2)whenvactsasaTransmitternodeandforwardsmessagetoitsCollector. DuringtheEpochRoftheallocatedEpochs,nodesinallhexagonsattempttotransferonemessagefromtheirForwardqueuetotheForwardqueueoftheirTransmitternodeusingRoundRobinschedulingbasedonincreasingorderoftheirids.TheTransmitternodethenduringtheEpochTforwardsamessagefromitsForwardqueuetoitsCollector,whichisonehopclosertovs.Inthismannerthedatamessagesareaggregatedfromallnodestothesinknodevsonmultihoppathswithoutinterference. Lemma10. TwoTransmitternodesintwodifferenthexagonswiththesamecolorcannothavethesameCollector. Proof. AssumethattwoTransmitternodesvt1andvt2intwodifferenthexagonsofsamecolorhavesameCollectornodevc.Forthisvchastobeintransmissionrangeofvt1andvt2.Accordingtothetriangularinequality,theEuclideandistanced(vt1,vt2)betweenvt1andvt2willbelessthanorequaltod(vt1,vc)+d(vt2,vc)2rTmax,thisisacontradiction,asthed(vt1,vt2)(+1)rTmax,where>1. Lemma11. Thedataaggregationfromallthenodestothesinkisinterferencefree. Proof. TheTransmitternodeindifferenthexagonsarescheduledtoreceiveandforwardmessagesbasedonhexagoncoloring.Asaresultofwhichtheysatisfythesufcientconditionsforinterferenceawareness.Therefore,interhexagoninterferencecannotexist.Further,onlyasinglenodecantransmittoitsTransmitternodeduringtheEpochRoftheEpochallocatedtoitshexagon.Hence,therecannotbeintrahexagoninterfere. Consequently,thereisnointerferencewhileaggregatingdatafromallthenodestothesinknodevs. Lemma12. Messagesfromallnodesareeventuallyaggregatedatthesinkvs. 71 PAGE 72 Proof. ForanynodevbelongingtothesetSi,duringtheEpochallocatedtoitshexagonitsmessagemvisforwardedtoanodeinSi)]TJ /F7 7.97 Tf 6.59 0 Td[(1,fromwhereitisfurtherforwardedtoanodeinSi)]TJ /F7 7.97 Tf 6.59 0 Td[(2insomelaterEpochandsoontillthemessagereachesthesink.Thisappliestoallthenodesinthenetwork.Hence,themessagesfromallnodesinthenetworkareaggregatedatthesinknodevs. Lemma13. Thelatencyofdataaggregationfromallthenodestothesinkisboundedby2jV)]TJ /F4 11.955 Tf 11.95 0 Td[(1jl(+1) p 3=2+1m2. Proof. Duetothepropertyofhexagoncoloring,theTransmitternodeslocatedindifferenthexagonsofthesamecolorinconsecutivesetsSiandSi+1satisfythesufcientconditionsforinterferenceawarenessmentionedinLemma 1 .Thus,theycanbescheduledtoreceiveortransmitduringthesameEpoch.Hence,duringl(+1) p 3=2+1m2EpochsallthesetsS1,S2,...,SRcanbescheduledbasedonthecolorofthehexagontheirnodesbelongsto. ThenumberofEpochsrequiredbythenodesinSRtoforwardtheirmessagestonodesinSR)]TJ /F7 7.97 Tf 6.59 0 Td[(1isboundedbyjSRjl(+1) p 3=2+1m2.DuringtheseEpochsallthesetsS1,S2,...,SR)]TJ /F7 7.97 Tf 6.59 0 Td[(1musthaveindividuallyforwardedatmostjSRjl(+1) p 3=2+1m2messagestoonesetclosertothesinknodevs. NowinatmostnextjSR)]TJ /F7 7.97 Tf 6.59 0 Td[(1jl(+1) p 3=2+1m2Epochs,thesetSR)]TJ /F7 7.97 Tf 6.59 0 Td[(1willbeabletocompletelyforwardallitsremainingmessagesalongwiththemessagesitreceivedfromSR.AndbythistimeS1,S2,...,SR)]TJ /F7 7.97 Tf 6.59 0 Td[(2musthaveindividuallyforwardedatmost(jSR)]TJ /F7 7.97 Tf 6.59 0 Td[(1j+jSRj)l(+1) p 3=2+1m2messagestoonesetclosertothesinknodevs. EventuallyafteratmostjSRjl(+1) p 3=2+1m2+jSR)]TJ /F7 7.97 Tf 6.58 0 Td[(1jl(+1) p 3=2+1m2+...+jS2jl(+1) p 3=2+1m2Epochs,thesinknodevswillreceivethemessagesofallthenodesindifferentset. AndaseachEpochhastwotimeslots,hence,thelatencyisboundedby: 2jSRjl(+1) p 3=2+1m2+2jSR)]TJ /F7 7.97 Tf 6.59 0 Td[(1jl(+1) p 3=2+1m2+...+2jS2jl(+1) p 3=2+1m2 72 PAGE 73 =2(jS1j+jS2j+...+jSRj)l(+1) p 3=2+1m2=2jV)]TJ /F4 11.955 Tf 11.96 0 Td[(1jl(+1) p 3=2+1m2timeslots. Theorem4.1. Distributedalltoonedataaggregationschedulingalgorithmhasanapproximationguaranteeof2l(+1) p 3=2+1m2. Proof. ThetrivialtheoreticallowerboundforalltoonedataaggregationisjV)]TJ /F4 11.955 Tf 11.96 0 Td[(1j.And,accordingtoLemma 13 ,thelatencyofalltoonedataaggregationofthedistributedprotocolis2jV)]TJ /F4 11.955 Tf 11.95 0 Td[(1jl(+1) p 3=2+1m2,hence,theapproximationratiois2l(+1) p 3=2+1m2. 4.4DistributedAllToAllBroadcastSchedulingAlgorithm Thedistributedprotocolforalltoallbroadcastschedulingworksintwophases.Intherstphase,thedatemessagesfromallthenodesareaggregatedatthesinknodevs.Inthesecondphase,vsdistributesallthemessagesitreceivedintherstphasetoallthenodesinWSN.Fortherstphasethedistributedschedulingprotocolforalltoonedataaggregationcanbeused.Afterallthemessagesarecollectedintherstphase,inthesecondphasetheschedulingofdistributionofthedatamessagesreceivedfromallnodesatthesinknodesvsisperformedasfollows: Whenthesinknodevs2S1receivesallthejV)]TJ /F4 11.955 Tf 11.95 0 Td[(1jmessages,theForwardqueuesofalltheTransmitternodesareemptyinallthehexagonsandarereadytoreceivemessagesfromtheirrespectivecollectorstobroadcastthemtonodesintheirhexagonduringtheallocatedEpochs.NowthesinknodeinS1startsbroadcastingonemessageineveryEpochallocatedtoitshexagon.Asaresultofthisineveryk2EpochsonemessageisreceivedbyallnodesinS2.TheTransmitternodesinS3afterk2EpochswillstartschedulingthemselvestoreceiveanewbroadcastmessagefromtheirCollectorinS2duringtheEpochRandbroadcastittoallthenodesintheirhexagonduringtheEpochToftheallocatedEpoch.Similarly,theTransmitternodesinS3receiveandbroadcastthemessagesfromtheirCollectorsinS2andsoon.ThispipeliningisfollowedtillallthenodesinthenetworkreceiveallthejV)]TJ /F4 11.955 Tf 11.96 0 Td[(1jmessages. 73 PAGE 74 Lemma14. Thedistributedalltoallbroadcastisinterferencefree. Proof. TheproofissimilartoLemma 11 Lemma15. Thelatencytodisseminatetheaggregateddatafromsinkvstoalltheothernodesis 2jVjl(+1) p 3=2+1m2+2Rl(+1) p 3=2+1m2 Proof. In2k2=2l(+1) p 3=2+1m2timeslotsatleastonemessageisreceivedbyallnodesinS2fromthesinknodeinS1.So,inatmost2jVjl(+1) p 3=2+1m2timeslots,allthejVjmessageswillbereceivedbyallthenodesinS2fromthesinknodeinS1.DuringthistimeatleastjVj)]TJ /F4 11.955 Tf 18.07 0 Td[(1messagesmustbereceivedbyallnodesinS3fromthenodesinS2,similarlynodesinS4musthavereceivedjVj)]TJ /F4 11.955 Tf 18.43 0 Td[(2messagesfromthenodesinS3andsoon.Finallythelastmessagewilltakeatmost2(R)]TJ /F4 11.955 Tf 12.37 0 Td[(1)l(+1) p 3=2+1m2timeslotstoreachtoallthenodesinSR.Hence,thetotallatencyfordisseminatingthedataofallthenodesfromsinktoallthenodesis2jVjl(+1) p 3=2+1m2+2Rl(+1) p 3=2+1m2. Lemma16. [ 51 ]ThelowerboundofalltoallbroadcastisjVj+R)]TJ /F4 11.955 Tf 11.95 0 Td[(1. Theorem4.2. Theapproximationratioofthedistributedprotocolforalltoallbroadcastis4l(+1) p 3=2+1m2. Proof. FromLemma 13 and 15 ,wehavethelatencyofalltoallbroadcastschedulingis4jVjl(+1) p 3=2+1m2+2Rl(+1) p 3=2+1m2,andcomparedtothelowerbound,wehavetheapproximationratio4l(+1) p 3=2+1m2. 4.5ExperimentalEvaluation Inthissection,wepresenttheexperimentalevaluationofourproposedalgorithmsthroughsimulations.Weranouralgorithmsonrandomlygeneratednetworktopologiesandevaluatedthemintermsofexperimentalapproximationratio(whichistheratiooftheexperimentallatencytothetheoreticallowerbound).Westudiedthebehaviorofour 74 PAGE 75 Figure41. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. algorithmsbasedonthreeimportantparameters:1)numberofsensornodesintheWSN,2)and3). 4.5.1ResultsforVaryingtheNumberofSensorNodes Inthissetofexperiments,weplacedthesensornodesinasquareareaofsides500m.Weconsidered=2,rTmin=100mandrTmax=200m(i.e.=2).WevariedthenumberofsensornodesjVjfrom10to500,withanincrementof10.ForeveryvalueofjVjweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 41 showstheeffectofnumberofsensornodesintheWSNonalltoalldatabroadcasting.Weobservethattheperformanceofthelocalizedalltoallbroadcastalgorithmisalwaysbetterthanthedistributedone.Themainreasonforthisisthatincaseofdistributedalltoallbroadcastalgorithmallthemessagesarerstaggregatedatthesinknodevs.Andthenfromtheretheyarefurtherdisseminatedtoallothersensornodes.Thismayresultinbottlenecksonthepathsfromvarioussensornodestovs,causinghigherlatency.WeobservethatasthenumberofnodesinWSNincreases,thecurvesforboththealgorithmtendstobecomeconstant.Thiscanbeexplainedas,afterincreasingnumberofnodestoacertainextent,thediameteroftheWSNstartsdecreasingandbecomesalmostconstantaftercertainnumberofnodes.Thisresultsinalmostsamenumberofhopsamessageneedstotravelthedistancebetweenthemostdistantnode. 75 PAGE 76 Figure42. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. Figure43. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. Thus,thelatencyincreasesonlybecauseoftheincreaseinnumberofnodesandnotbecauseofincreaseinthediameterofgraph.Therefore,theexperimentalapproximationratioismaintained. Figure 42 showstheeffectofnumberofnodesforalltoonedataaggregationalgorithm.Theplotissimilartothatofalltoalldatabroadcastandcanbeexplainedinthesamemanner.Theexperimentalapproximationratiobecomesalmostconstant,aftercertainnumberofnodesbecauseofnonvaryingnetworkdiameter. Figure 43 showstheeffectofnumberofnodesforonetoalldatabroadcasting.Theplotissimilartothealltoallandalltoone.Thisisbecause,apparentlythelatencyof 76 PAGE 77 Figure44. EffectofonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. thebroadcastisdrivenbytheradiusofthegraph.Whichtendstobecomeconstantaftercertainnumberofnodesinthenetwork. 4.5.2ResultsforVarying Inthissetofexperimentsweplaced300nodesinasquareareaofsides500m.Wexed=2andrTmin=100m.Wevariedfrom1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreachvalueofweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 44 showstheplotsoflocalizedalltoalldatabroadcastinganddistributedalltoalldatabroadcastingonvarying.Weobservethereisalittleriseintheexperimentalapproximationratiosforboththeplotswhenchangesfrom1to1.2afterwhichtheexperimentalapproximationratiostendstobeconstant.Thiscanbeexplainedbythefactthatwhenincreases,thenumberofcolorsusedtocolortheWSNalsoincreases.Withthisthenumberoftimeslotsanodeneedtowaittotransmitthemessagealsoincreases.Thisdirectlyaffectsthelatency,resultinginincreaseintheexperimentalapproximationratio.But,whenisfurtherincreasedthesizeoftheneighborhoodofanodealsoincreasesanditstransmissioninformsmorenumberofnodes.Apartfromthisthediameterofthenetworkalsodecreaseswithincreasein.Hence,furtherincreasingdoesnoteffectstheexperimentalapproximationratio. 77 PAGE 78 Figure45. EffectofonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. Figure46. EffectofonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. InFigure 45 andFigure 46 ,theplotsfordistributedalltoonedataaggregationandonetoalldatabroadcastingonvaryingaregiven.Weobservethattheexperimentalapproximationrationinboththeplotsminutelyuctuatearoundacertainpointanddoesnotshowmuchincrease.Thiscanagainbeexplainedbythefactthatincreasingdecreasestheradiusofthegraph,asnodespossiblyhavelargerneighborhoodwhenislarge. atouralgorithmshowsamuchbetterperformance,incomparisontotheirproposedtheoreticalapproximationguarantees. 78 PAGE 79 Figure47. EffectofonAverageExperimentalApproximationRatioofAlltoAlldatabroadcastingAlgorithms. 4.5.3ResultsforVarying Inthissetofexperiments,weplaced300nodesinasquareareaofsides500m.Weconsidered,rTmin=100,rTmax=200(i.e.=2)andvariedfrom1.0to3.0withincrementof0.1tocloselymonitoritseffect.Foreachvalueofweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 47 showstheplotsoflocalizedalltoalldatabroadcastanddistributedalltoalldatabroadcast.Weobservethatboththeplotsdonotshowmuchvariationonincreasing.Thiscanbeexplainedbythefactthatincreasingdoesnotaffectsthediameterofthegraph,whichremainsconstantforsamenumberofnodes.Hence,theexperimentalapproximationratioremainsthesame.Figure 48 and 49 showstheplotsofalltoonedataaggregationandonetoalldatabroadcastingonvarying.Theplotsaresimilartotheplotsoflocalizedanddistributedalltoallbroadcastandcanbeexplainedinthesimilarmanner. Inourexperimentalevaluation,weobservedthatthefactorssuchasnumberofnodesinthenetworkand,thatdirectlyaffectsthediameterofthenetwork,havereasonableimpactonthelatencyofdatabroadcastingandaggregationinWSNs.Further,weobservedthatouralgorithmshowsamuchbetterperformanceincomparisontotheirproposedtheoreticalbounds. 79 PAGE 80 Figure48. EffectofonAverageExperimentalApproximationRatioofAlltoOnedatabroadcastingAlgorithms. Figure49. EffectofonAverageExperimentalApproximationRatioofOnetoAlldatabroadcastingAlgorithms. 4.6Conclusion Inthischapter,westudiedlocalizedbroadcastschedulinginaninterferenceenvironmentmodeledbyprotocolinterferencemodel.Westudiedtwoproblems:1)Minimumlatencyalltooneaggregationschedulingand2)Minimumlatencyalltoallbroadcastscheduling.Forminimumlatencyalltoallbroadcastscheduling,weproposedtherstlocalizedalgorithmandtherstdistributedapproximationwithapproximationguaranteeof4l(2(+1) p 3+1m2.Further,forminimumlatencyalltooneaggregationschedulingweproposedtherstdistributedalgorithmwithanapproximationguaranteeofl2(+1) p 3+1m2. 80 PAGE 81 CHAPTER5DETECTIONANDTRACKINGOFPHENOMENACLOUD:NEWLOCALIZEDAPPROACHESANDAPPLICATIONS 5.1Introduction Contemporarywirelesssensornetworkresearchdoneintheareaofdetectionandtrackinghasprimarilyconcentratedonobservingmotionofobjectswhoseshapeandsizeareinvariant[ 41 43 ].However,manyreallifeeventssuchasoilspills,gasclouds,randomwalkingmotionofpeople,ormovementofagroupofpeople,henceforthcalledPhenomenaClouds,arecharacterizedbynondeterministic,dynamictemporalvariationsofcloudshape,sizeanddirectionofmotionalongmultipleaxes.Theseeventscannotbemodeledinwelldenedterms.Thus,itisdifculttoapplyexistingmechanismsinsuchsituationduetothefactthatcurrentcloudbasedtrackingtechniquesareorientedtowardsmonitoringthemotionofwelldenedobjectsalongasingleaxisataparticulartime.Theyarenotequippedformonitoringtheshape,sizeandmotionofphenomenacloudswhosebehaviorcannotbereadilymodeledusingclassicaltheory. Moreover,theutilityofphenomenaclouddetectionandtrackingisnotrestrictedonlytoapplicationdomainsinvolvinggascloudsoroilspills.Infact,theycanalsobeutilizedinsituationswherethequalityofdataoriginatingfromindividualsensorscannotbetrustedinisolation.Insuchcases,therawsensordataoriginatingfromthesystemistypicallyextremelynoisywhichmakesitverydifculttodistinguishactualeventsfromrandomstimuli.Hence,aquorumofmultiplesensorswhicharelocatedincloseproximitytoeachotherisrequiredtoreducetheprobabilityoffalsepositives.Throughourcollectiveresearchandsystemsexperienceovertheyearsinacompletelydifferentdeploymentdomain(SmartSpaces,alsoknownasAmbientIntelligence),wehavediscoveredagreatutilityinapplyingthephenomenacloudconceptforefcientlyandaccuratelymonitoringvariouseventsinthespace,suchasdetectionofbarefootwalking,whichisanimportantapplicationfordiabetespatients. 81 PAGE 82 Withanewapplicationandabroaderconceptofphenomenaclouds,earlystudiesonboundarydetectionandtrackingofwelldenedshapesarenolongersufcient[ 12 13 19 44 45 ].Onlyoneworkrecentlystudiedonsimilarapplications,calledNilePDT(astreambasedmechanism)maybeapplicable[ 46 ].However,thiscentralizedapproachdoesnottakeintoaccountthecostofacquiringandtransmittingsensorreadingsandtypicallyrequiresparticipationfromallsensorsinthenetwork.Unfortunately,sensorsamplingcostsandnetworkingandprocessingoverheadscanhaveacriticaleffectonthepracticalviabilityoftheentiresmartspace Thisraisesaneedforadistributedinnetworkdetectionmechanism,wherethedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofaphenomenonatanygiventimeanddoesnotrequireallthesensornodestoremainunnecessarilyactive.Alongthisdirection,weintroduceamathematicalmodelandinnetworkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergyefcientanddistributedalgorithm,calledFullDensityAlgorithm(FDA)forrealtimedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained.Plus,theproposedalgorithmcanbeusedinanewapplicationdomain,i.e,detectionawalkingmotion. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizetheenergyconsumptionduringthephenomenaclouddetectionandtrackingprocess.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 82 PAGE 83 4.Providinganovellocalizedalgorithm,calledOptimizedDensityAlgorithm(ODA)whichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinarealworldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 6.Validatingourapproachesusingbothrealworldapplicationsandsimulationstoanalyzetheirperformancesascomparedtostreambasedapproaches[ 46 ]. Theremainderofthispaperisstructuredasfollows.Section 5.2 describesthephenomenaclouds,theircharacteristicsalongwiththecriticalchallengesandanalyzestheirstructuresusingthesetofproposedparameters.Ourrstinnetworkdetectionandtrackingalgorithm,includingitsfaulttolerancemechanism,isproposedinSection 5.3 .InSection 5.4 ,weoptimizethepowerconsumptionandresourceutilization,onwhichweformulateanintegerprogramfordetectionandtrackingofaphenomenacloudandproposealocalizedprotocolbasedonthehexagontilingtechnique.Section 5.5 presentsaninterestingpracticalrealworldapplicationofourphenomenadetectionandtrackingalgorithminthesmartspace.Section 5.6 providesevaluationandanalysisoftheperformanceofourapproachesthroughreallifeexperimentsandsimulations.Section 5.7 providestheoverviewoftheexistingliterature.Finally,Section??concludesthepaperwithsomefuturework. 5.2PhenomenaCloud:ChallengesandRepresentation Aphenomenoncloudcanbedenedasamanifestationofanumberofsimultaneouseventsreachingcriticalmassandspanningacontiguousspace.Assuchaphenomenonexpands,shrinks,ortranslatesrandomlyinanondeterministicfashionoverthetime,itsshape,sizeanddirectionofmovementeithercannotbeanticipatedaccuratelyorhavemodelswhichareusuallytoocomplexforrealtimecomputing 83 PAGE 84 bysensornetworks,whichlargelyconsistoflowendnodeswithlimitedprocessingcapabilities.Examplesofphenomenacloudsincludegasclouds,oods,oilspills,wildforestresorevenmovementoftouristsinamuseum. 5.2.1MajorChallenges Themajorchallengesthatarefacedduringdetectionandtrackingofphenomenacloudsareasfollows: 1.Initialdetectionofphenomenon.Initialoccurrencesofthephenomenonmightbescatteredthroughoutthespace.Detectionthereforemustbeattemptedatmultiplelocations. 2.Avoidingfalsepositives.Theprobabilityofasinglesensoroutputtingaccuratereadingsataspecicpointintimeisverylow.Itisquitepossibleforasensortotemporarilymalfunctionorbesubjecttoenvironmentalconditionswhichmightcauseittooutputvalueswhichincorrectlyindicatetheoccurrenceofaphenomenon.Thusdetectionmustrequireinputsfrommultiplesensorslocatedcloselytoeachother. 3.Trackingaphenomenoninrealtime.Aphenomenoncansuddenlygroworshrinkinsizeandalsomoveinmultipledirectionssimultaneously.Therefore,trackingitinrealtimecanbecomeamassivelycomplextask.Toenablecosteffectiverealtimetracking,therateofstatusupdatesfromthesensornetworktotheuserneedstobekeptataminimumtoreducenetworkcostandprocessingoverhead.4.Operatingunderharshconditionsresultingindisconnectedoperation:Hostilephenomenalikerescanleadtodisruptionofcommunicationsbetweenthesensornetworkandthebasestation.Therefore,thedetectionandtrackingprocessshouldbeabletooperateinanautonomousmannerwithoutrequiringremotesupervision. 5.2.2Representation Inthissection,weproposeasetofparameterstoformallydescribethestructureofphenomenaclouds.Werepresentaphenomenoncloudasa5tuple,P=ha,b,pT,m,ni.Thelowerandupperboundsoftherangeofsensorvalueswhich 84 PAGE 85 Figure51. DissectionofthePhenomenaCloud constituteaphenomenonaredenotedbyaandbrespectively.Forexample,ahydrogengascloudcanhavea=20%volumeandb=100%volume.pTisthethresholdprobability,mistheobservationcountandnistheminimumquorum. Asensor'sreadingissaidsatisfyingtheProbabilityCondition,iffitislyingintherange[a,b]withprobabilitygreaterthanpTduringthelastmobservations(thatis,inaslidingwindowofsizem).Asensorissaidtoparticipateinaphenomenoncloud(orsatisfythePhenomenonCondition)P=ha,b,pT,m,ni,iffitandatleastnneighborsensorssatisfytheProbabilityCondition.Thiscriterionensuresthatasensormusthaveasufcientnumberofneighborsinagreementwithitbeforeitcanclaimtheexistenceofaphenomenoncloud,therebyreducingtheoccurrenceoffalsepositives.WedenePhenomenonSettobethesetofsensorssatisfyingthePhenomenonCondition. WeconsideraphenomenoncloudiscomposedofmultipleregionsasshowninFigure 51 .Theinnermostregion,calledtheCoreregionofthecloudiswherethephenomenonismoststronglyobserved.Clearly,thesensorslyinginthecoreregionsatisfythePhenomenonConditionandhence,aremembersofthePhenomenonSet.TheMiddleregionistheouterborderofthephenomenacloudwheretheProbabilityConditionissatisedbutthePhenomenonConditionisnotyetsatised.TheOuterregiondenotesthefringeswhereuncertaintyregardingtheoccurrenceofthephenomenonishighest,hence,theouterfringeistheregionwherethephenomenaissparseandisnotdetected.Section 5.3.1 describestherolesassignedtothesensors 85 PAGE 86 basedonwhichregiontheyfallinataparticulartimeandhowtheyareutilizedtoperformlocalizedinnetworkdetectionandtracking. 5.3ProposedSolutionforDetectionandTracking Inthissection,wepresentourproposedapproachforthephenomenonclouddetectionandtracking,calledFullDensityAlgorithm(FDA).Webeginwithclassifyingsensorsintodifferentcategoriesasdiscussedaboveaccordingtotheirrolesinthedetectionandtrackingprocess.Wethendescribevariousresponsibilitiesofanysensornodewithrespecttocategoriesofitsneighborsandlistasetofruleswhichgovernthetransitionofsensorsfromonecategorytoanotherwhichformthemainpartofourdetectionandtrackingstrategy.Therestofthissectioncoversthedifferentstagesofdetectionandtrackingprocessinchronologicalorder.Italsodescribesmechanismsforhandlingnodefailuresandhowapplicationscanutilizetherealtimetrackingdataproducedbythesensornetwork.Figure 53 pictoriallydepictsanexamplefordetectionandtrackingprocessofasinglephenomenoncloud. Figure52. ClassicationoftheParticipatingSensors 5.3.1ClassicationofSensors Figure 62 showsthephenomenonclouddepictedinFigure 51 superimposedoveragroupofsensors.Sensorsareclassiedaccordingtotheregionwheretheyarelocated,whichdeterminestheirroleindetectionandtrackingofphenomenacloud.Thedifferentcategoriesareasfollows: 86 PAGE 87 1.CandidateSensor:AsensorwhichsatisestheProbabilityConditioniscalledacandidatesensor.Ithastheresponsibilityofactivelysensingandnotifyingitsneighborsaboutitsstate.ItalsoreceivesnoticationsfromitsneighborsinordertoidentifywhetheritsatisesthePhenomenaConditiontobecomeapartofthePhenomenonSet.Asensorbecomesacandidatesensorwhenittransitionsfromthepotentialcandidatestageduringtheexpansionofthephenomena,orwhenittransitionsfromthetrackingstageduringtheshrinkingofthephenomena. 2.PotentialCandidateSensor:AsensorwhichisactivelysensingthephenomenonbutdoesnotsatisfytheProbabilityConditioniscalledapotentialcandidatesensor.Thesesensorskeepmonitoringtheirreadingtoenableaneighborcandidatesensorstocheckthevalidityoftheirobservations.Asensorbecomesapotentialcandidateifeither1)ithasbeenselectedbythecentralizedqueryprocessoraspartoftheinitialdetectionphase(describedinSection 5.3.4 ),or2)oneofitsneighborsbecomesacandidatesensorduringtheexpansionofthephenomena,or3)whenacandidatesensortransitionsfromcandidatestagetopotentialcandidatestageduringtheshrinkingofthephenomena.TheresponsibilityofthepotentialcandidateistonotifyitsneighboringcandidatesensorswheneveritsreadingsatisestheProbabilityCondition.Potentialcandidatesensorsformthefringesofdetectionandmakeuptheouterregionofthephenomenoncloud.Essentially,thesetofpotentialcandidatesensorsformsaphenomenonfrontwhichgrowsandshrinksdynamically. 3.TrackingSensor:Asensorwhichhasalreadydetectedaphenomenoneventandisnowactivelyengagedinthetrackingprocessiscalledatrackingsensor.AcandidatesensorbecomesatrackingsensorafteritsatisesthePhenomenonCondition(denedinSection 5.2.2 ).Trackingsensorscoversthecoreregionofthephenomenacloud.ThePhenomenonSetisthecollectionofalltrackingsensors,hence,eachcloudconsistsofsubsetsoftrackingsensorsfromthePhenomenonSet. 87 PAGE 88 4.IdleSensor:Allsensorswhichdonotbelongtoanyoftheabovethreecategoriesarecalledidlesensors.Thesesensorsarenotengagedinphenomenondetectionortrackinganddonotperformanymonitoringwhatsoever.Typically,mostsensorsinthespacewillfallinthiscategorysinceonlyselectedclustersofsensorswillbeactivelyengagedinthedetectionandtrackingofphenomenacloudsatanygiventime.Thisensuresthatthedetectionandtrackingprocessisexecutedinalocalizedmannerwithminimalexpenditureofenergy. Figure53. DetectionandTrackingofaPhenomenaCloud Remarks.Wehavemodiedthedenitionsofcandidateandpotentialcandidatesensorsascomparedtoourinitialdenitionsinthepreliminarywork[ 57 ].Morespecically,in[ 57 ],wedenedthatacandidatesensorisnotrequiredtosatisfytheProbabilityConditionandapotentialcandidatesensorcannothaveatrackingsensor,butonlycandidatesensorasitsneighbors.Consequently,evenifacandidatesensordoesnotsatisfytheProbabilityCondition,itunnecessarilyinvokesallitsidle 88 PAGE 89 Figure54. ActionTakenbyaSensorNodewithrespecttoitsNeighborswhicharenotidle neighborsaspotentialcandidates,therebycausingexcessiveresourceusage.Incontrast,inthispaper,acandidatesensormustsatisfytheProbabilityConditionandapotentialcandidatesensorcanhasatleasteitheronetrackingorcandidatesensorinitsneighborhood.Therefore,onlythoseidlesensorsareinvokedaspotentialcandidateswhichhavephenomenaoccurringintheirvicinity.Thisslightlymodicationhaveanimpactontheperformanceintermsofenergyandresourceconsumptionswhichweshowlaterinsection 6.5 5.3.2KeepingTabsontheNeighborhood Eachsensornodekeepstrackofthecategoryofitsneighbors.Thisisdoneinapeertopeerfashion,whereasensortransitioningfromonecategorytoanothernotiesitsneighborsviaa1hopbroadcastwithoutinvolvingthecentralizedqueryprocessor.WeusedZigBeecommunicationprotocolinoursystem,whichnativelysupports1hopbroadcasting.Thecategoryofasensoranditsneighborsdeterminestheirmutualresponsibilitiestowardseachother.Forexample,acandidatesensornodeAhas 89 PAGE 90 twoneighborsBandCwhereBisapotentialcandidateandCisatrackingsensor.Inthiscase,BwillalertAwheneveritsreadingssatisfytheProbabilityCondition.AndwheneverA'sreadingisnolongersatisedtheProbabilityCondition,AwillonlyalertCbutnotB.Therefore,asinglesensornodeplaysdifferentroleswithrespecttodifferentcategoriesofitsneighbors.Figure 54 liststheactionsasensornoderequiredtoperformwithrespecttothecategoriesofitsneighbors.ThecellsmarkedNotApplicableimplythatsuchcombinationsarenotpossibleaccordingtotransitionrulesgiveninnextsubsection. 5.3.3TransitionRules Wenowreadytopresentasetofrulesthatgovernthetransitionofasensorfromonecategorytoanother.Theserulesareexecutedinnetworkandcontroltheentiredetectionandtrackingprocess. 1.R1:Candidate!Tracking:IfasensorsatisesthePhenomenonConditionthenittransitionsintothetrackingcategory.Onceasensorisinthetrackingcategory,itbecomesamemberofthePhenomenonSet. 2.R2:PotentialCandidate!Candidate:ApotentialcandidatesensorwilltransitiontoacandidatesensorifitsatisestheProbabilityCondition.Thisrulecorrespondstothefactthatwheneveraphenomenoncloudmovesorexpands,anewsetofsensorssensesthephenomenaandsatisestheProbabilityCondition,resultinginthemovementorexpansionofthephenomenonfront. 3.R3:Idle!PotentialCandidate:Anidlesensortransitionsintoapotentialcandidateifanyofitsneighborsbecomesacandidatesensor. 4.R4:Tracking!Candidate:AtrackingsensorwilltransitiondowntothecandidatecategoryifitisunabletosatisfythePhenomenonCondition.Insuchacase,thesensorwillceasetobeamemberofthePhenomenonSet. 5.R5:Candidate!PotentialCandidate:AcandidatesensorwilltransitiontoapotentialcandidatesensorifitdoesnotsatisfytheProbabilityConditionanymore. 90 PAGE 91 6.R6:PotentialCandidate!Idle:Apotentialcandidatetransitionsintoanidlesensorifallofitsneighborsareeitherpotentialcandidatesoridle,thatis,noneofitsneighborsisinthecandidatecategoryortrackingcategory. 5.3.4InitialSelectionofPotentialCandidateSensors Themaingoalofthisstageistodetectinitialoccurrencesofphenomenaclouds.Aphenomenoncloudcanmanifestitselfinmultiplelocationssimultaneously,hence,monitoringoneparticularlocationisnotadequate.However,intheinterestofconservingnetworkresourcesandpowerfortheentiresensorgrid,wecannotrequireeachandeverynodetomonitoritsreadings.Acompromisebetweenthetwoapproachescanbefollowedwherespecicsensorsaredirectlychosentobepotentialcandidatesbythecentralizedqueryprocessor.Thecriterionforsuchaselectioncanbebasedonthelocationofnodesorpasthistoryoftheirreadings.Forexample,ifweareplanningtodetectgasleaksinapipeline,itmightbeusefultochoosethesensorslocatedatthevalvesandjointstobetheinitialsetofpotentialcandidatesensorssincetheprobabilityofaleakgettingstartedatthoselocationsishigher.WeusedthiscriterionintheSmartFloorapplicationdescribedinSection 5.5 ,wheresensorslocatedneardoorwaysareselectedasinitialpotentialcandidatessothatwheneverapersonenterstheroom,thesystemisimmediatelyabletopickuptheirpresenceandcommencethedetectionandtrackingprocesstomonitortheirmovement.Anothercriterioncanbetheofflineuseofanavailablemathematicalmodelofthephenomenoncloudtodeterminelocationswheretheprobabilityofoccurrenceisthehighest.Incasesuchacriterionishardtoformulate,alternativelythesystemcanrandomlyselectsensorsasinitialpotentialcandidatessuchthattheyareuniformlydistributedoverthesensorspace.Thesesensorsandtheirrespectiveneighborhoodscanbeviewedasautonomousclustersofearlywarningsystemsfordetectingthesuddenmanifestationofpossiblymultiplephenomenaclouds.Sincesensordeploymentpatternstendtobehighlyapplicationandphenomenonspecic,wedonotgointodetailsoftheirdeployment.Forpurposesof 91 PAGE 92 discussionfortherestofthispaper,weassumethatsensornodesaredeployedinsuchamannerthateachsensorhasasufcientnumberofneighborstopotentiallyavoidfalsepositives. 5.3.5MonitoringforInitialOccurrences Thequeryprocessorpushesthephenomenoncloudparametersontoeachoftheselectedinitialpotentialcandidatesensornodesinthenetwork.Atthebeginningofeveryepoch,eachpotentialcandidatenodemonitorsitsreadingsandsendsa1hopbroadcastmessageifitsatisestheProbabilityConditionandtransitionsintoacandidatesensornode.Inordertoenablesensornodestosendorreceivealertbroadcaststoandfrommultipleneighborssimultaneouslyduringthesameepoch,aslottedapproachisusedtoensurecollisionavoidancesimilartowhatisdescribedin[ 58 ].Eachepochissubdividedintomultiplesubepochsandeachnodeonlybroadcastsalertsduringitsassignedsubepoch.ThecandidatesensornodeaggregatesalertsreceivedviabroadcastsfromitsneighborsanddeterminesifitsatisesthePhenomenonCondition.AcandidatesensorsatisesthePhenomenonConditionifitsreadingssatisfytheProbabilityConditionanditalsoreceivesbroadcastalertsfromatleastnneighborswhichalsosatisfytheProbabilityConditioninthesameepoch. 5.3.6NoticationofInitialOccurrence IfaninitialpotentialcandidatenodehassatisedtheProbabilityCondition,ittransitionstoacandidatesensornode.Furthermore,whenacandidatesensornodesatisesthePhenomenonCondition,itnotiesthequeryprocessorresidinginthebasestationthatithasdetectedpresenceofaphenomenoncloud.ThequeryprocessoraddsthecandidatenodetothePhenomenonSetandthecandidatesensortransitionstoatrackingsensornodeusingruleR1giveninSection 5.3.3 92 PAGE 93 5.3.7GrowthofPhenomenonCloud WhenapotentialcandidatesensorsatisestheProbabilityCondition,itgetstransitionedintoacandidatesensorusingruleR2.Itnotiesallitsneighborsaboutthistransitionbybroadcastinganalertmessage.EachoftheneighborsensoronreceivingthealertmessagetransitionsintoapotentialcandidateiforiginallytheywereidlesensorsusingruleR3.Inthismanner,thedetectionmechanismgetsdistributedandpropagatedinnetwork,withoutinvolvementofthecentralizedqueryprocessor,asthephenomenoncloudgrowswithtime.Eachsensornodekeepstrackofitsneighborhoodviathebroadcastalertsthatitreceivesanddeterminestheactionstobeundertakenwithrespecttoaspecicneighborbasedonwhichcategoryeachneighborfallsin,asdescribedinFigure 54 Figure55. RatioofTotalActiveSensorstoCloudSizeinaRectangularSensorGrid TheplotinFigure 55 depictsanexampletoshowtheeffectagrowingphenomenoncloudhasonthenumberofactivesensors(tracking,candidatesandpotentialcandidatesensors)involvedinitsdetectionandtracking.Weobservethatinourdistributedinnetworkapproach,thenumberofactivesensorsrequiredatanygiventimeisonlyslightlymorethanthenumberofsensorsactuallyneededtoparticipateindetectionandtrackingthephenomenoncloudandtheratioofactivesensorsversusphenomenacloudsizedecreaseswithincreaseincloudsize.Thisisduetothefactthatthe 93 PAGE 94 detectionandtrackingprocessisexecutedinnetworkinalocalizedmannertoensuremaximumefciency.Onlythosesensornodeswhichareintheimmediatevicinityofaphenomenoncloudorarelyingwithinthecloudareactivelyinvolvedinthedetectionandtrackingprocess.ThepropagationofthisprocessinthenetworkisgovernedsolelybythebehaviorofthephenomenoncloudandhandledbythesensornodesinadistributedbutcooperativemannerusingtherulesspeciedinSection 5.3.3 ,withoutneedinganyassistancefromthecentralizedqueryprocessor. 5.3.8ShrinkingofPhenomenonCloud ThephenomenoncloudissaidtobeshrinkingwhenthesensorsfallinginthetrackingregionidentiesthattheynolongersatisfythePhenomenaCondition.AccordingtoFigure 54 ,afterasensortransitionsintotracking,itsneighborswillonlysendalertsiftheirreadingsfailtosatisfytheProbabilityCondition.AtrackingsensorisnolongerparticipatinginthetrackingofthephenomenoncloudifitdeterminesthatlessthannofitsneighborscurrentlysatisfytheProbabilityCondition.Insuchacase,thetrackingsensornodenotiesthequeryprocessorwhichremovesthetrackingsensorfromthePhenomenonSet,therebysignifyingthatthephenomenoncloudhasshrunk.ThetrackingsensornodethentransitionsintoacandidatesensorusingruleR4.WhenthephenomenacloudfurthershrinksandthecandidatesensordoesnotevensatisfytheProbabilityCondition,ittransformsintoapotentialcandidatesensorusingtransitionruleR5ifithasatleastonecandidateortrackingsensornodeinitsneighborhood.AndallofthepotentialcandidateneighborsofthissensornodetransitionsintoidlesensorsusingtransitionruleR6iftheydonothaveanyothercandidateortrackingnodeintheirneighborhood.WemakeanotethatifallthephenomenacloudsdisappearcompletelythenafterallthetransitionsareappliedasperrulesgiveninSection 5.3.3 ,thesensorspacewillrevertbacktothesetupdescribedinSection 5.3.4 ,whereonlytheinitialsetofpotentialcandidatesensorswillremainactive. 94 PAGE 95 5.3.9RealTimeMonitoringbyApplications ThecentralizedqueryprocessorcontinuouslymaintainsthePhenomenonSetatanygiventime.Thequeryprocessorisabletotrackphenomenoncloudsinrealtime,withminimumprocessingandnetworkingoverheadofreceivingupdatesfromthesensornodes.ThePhenomenonSetisonlyupdatedwheneverasensortransitionstoorfromthetrackingcategory.Hence,thequeryprocessoronlyrequiresminimalupdatestocontinuouslytrackphenomenaclouds.WeevaluatethenetworkandprocessingcostsforthisupdateschemeinSection 5.6.2 Sincethelocationofeachsensornodeisknownbeforehand,anapplicationsuchasaGUIbasedphenomenoncloudvisualizationtoolcaneasilyreconstructaviewofthevariousphenomenoncloudsinrealtimeusinginformationfromthePhenomenonSetinconjunctionwithsensorlocationinformation.BylookingatwhichsensorsenterorleavethePhenomenonSet,themotionofmultiplephenomenoncloudscanalsobetrackedovertimeandmoresophisticatedanalysisandpredictionperformedatacentralizedlevel.Thisisextremelyusefulforapplicationssuchas[ 59 ]whichcandeterminesafepassagesforrescueworkersthroughmultipleoccurrencesofphenomenoncloudssuchasgasleaksandwildres. Inaddition,thecardinalityofthePhenomenonSettogetherwithsensorlocationcangiveapplicationssomeinformationaboutthesizeofvariousphenomenaclouds.Thesizeofaphenomenoncloudcanhavedifferentimpactsdependingontheapplicationcontext.Forexample,ifanapplicationisconcernedwithdetectionofphosphatedustclouds,aPhenomenonSetoflowcardinalitymaynothavemuchsignicance.However,ifanapplicationistaskedwiththedetectionofhydrogencyanide(HCN)leakage,thenthedetectionofevenasmallcloudindicatesseriousconsequences. 5.4OptimizingEnergyConsumptionandResourceUtilization Wenowturnourattentiontooptimizingtheenergyconsumptionandresourceutilizationofourproposedmechanism.Inordertominimizethenumberofactive 95 PAGE 96 sensorsrequiredfordetectionandtracking,rstweproposeamathematicalmodelbasedonIntegerProgram(IP)whichusesaminimumnumberofactivesensors(candidate,potentialcandidate,andtrackingsensors)fordetectionandtracking.Thismodelcanbeusedasanexcellentbenchmarktoevaluateourproposedmechanism.Next,weproposealocalizedalgorithm,calledOptimizedDensityAlgorithmtofurtherreducetheresourceutilizationbasedonournoveltechnique,calledHexagontiling. 5.4.1TheIntegerProgramFormulation TheIPisdividedintotwoparts.Intherstpart,allthesensornodesarecategorizedintoPotentialCandidates,Candidates,Tracking,andIdlesensors.Inthesecondpart,anoptimizationisperformedtominimizethenumberofactivetrackingsensornodes. LetVdenoteasetofallsensornodeswherejVj=NandN(i)denoteasetofneighborsofsensornodei.Foreachi2V,weassociatethreevariablesdenedasfollows: xpi=8><>:1ifsensoriisapotentialcandidate0otherwise (5) xci=8><>:1ifsensoriisacandidate0otherwise (5) xti=8><>:1ifsensoriisatracking0otherwise (5) WenowformulatetherstIPofwhichsolutionsdeterminethestatusofeachsensornodei: minPNi=1(xpi+xci+xti) 96 PAGE 97 subjecttoxpi+xci+xti18i2V (5) (xci+xti))]TJ /F4 11.955 Tf 11.96 0 Td[((Pi)]TJ /F3 11.955 Tf 11.96 0 Td[(PT)>08i2V (5) Xj2N(i)(xcj+xtj))222(jN(i)j(xpi+xci+xti)08i2V (5) Xj2N(i)(xcj+xtj))222(jN(i)jxti PAGE 98 WenowintroducethesecondIPasfollows: minPjTji=1xisubjecttoxin+Xj2N(i)xj)]TJ /F3 11.955 Tf 11.96 0 Td[(n08i2T (5) xin)]TJ /F10 11.955 Tf 15.68 11.36 Td[(Xj2N(i)xj08i2T (5) xi2f0,1g8i2T (5) ThesecondIPminimizesthenumberofactivecoretrackingnodesinordertooptimizethepowerconsumptionfordetectingandtrackingthephenomenacloud.Constraint 5 and 5 ensurethatacoretrackingnodecangotothesleepmodeifitsatisestheminimumquorumconditionalongwithallofitsneighbors. 5.4.2OptimizedDensityAlgorithm InlightoftheaboveIP,wenowpresentalocalizedprotocol,calledOptimizedDensityAlgorithm(ODA)tofurtherenhancetheresourceutilizationofourproposedFDAdiscussedinSection 5.3 .AsshownintheIP,weproposetoidentifyasetofcoretrackingnodes,andthenswitchthesenodesbackandforthbetweenthesleepandactivemodesfollowingsomecertainrules.Rememberthatacoretrackingnodecangotothesleepmodeifitsatisestheminimumquorumconditionalongwithallofitsneighbors. Beforedescribingourprotocol,werstdiscusssomepreliminarieswhichleadtotheformationoftheprotocol. Themainideaoflocallydecidingasleep/activemodeofacoretrackingnodeisbasedonanefcientclusteringofthesensornodesinthenetwork.Wepartitionthenetworkintoclustersinsuchawaythatthenodesinadjacentclustersareneighborsofeachother.ThuswerstproposeanideatolocallyperforminnetworkclusteringwithmessagecomplexityO(1).Ourideaisbasedonageographicallybutlocally 98 PAGE 99 partitioningtheplaneintoregularidenticalpartitions,suchthatallnodeslocatedwithinthesamepartitionformsacluster.Thesizeofeachpartitionwillbedenedbythetransmissionrangerofasensornode,andweconsiderallthesensornodeshavethesametransmissionrange.Oncetheclusteringisperformed,thenodeswithinapartitionelectstheclusterheads.Atanypointintime,theclusterheadswillremainactiveandtherestofcoretrackingnodeswillsleepaslongaseachclusterheadhasatleastnactiveneighbors. Letusconsiderhowtoperformsuchpartitionbasedonthetilingtechnique.Whatistheoptimalshapeoftheregularunitpartitionsothatwecanpartitiontheplaneintotheminimumnumberofclusterssuchthatallnodesinadjacentclustersareneighborsofeachother?Suchapartitionwillminimizethetotalnumberofactivecoretrackingnodes. Therearefourpossibleplanetilingpolygons:1)square,2)rhombus,3)equilateraltriangle,and4)regularhexagon.Asweneedthenodesintwoadjacentpartitionsmustbeneighborsofeachother,consequently,themaximumdistancebetweentwopointslocatedintwoadjacentpartitionsmustber.Figure 56 57 58 and 59 ,showsthefourpossiblepartitioningusingdifferentplanetilingpolygons.Itiseasytoseethattilingaplaneusingtheregularhexagonscoversthemaximumarea,thuslessernumberofclustersforagivenarea.Therefore,weuseregularhexagonasapartitionshapeforourtilingtechniqueandnextpresenthowtolocallyperformthistiling. 5.4.2.1Clusteringmethod Wepartitionthe2DplanecoveredbytheWSNintoregularhexagonsofsidelengthr p 13toformahexagonaltilingasshowinFigure 510 .Allthesensorslocatedwithinthesamehexagonformacluster.Noticethattheirexistsacoordinatesysteminwhichtheaxisareinclinedat60o,suchthatallthehexagoncenterslieontheintegralcoordinatesofthisnewcoordinatesystem. 99 PAGE 100 Figure56. Partitionshapeassquare. Figure57. Partitionshapeasrhombus. Figure58. PartitionshapeasEquilateralTriangle. Figure59. PartitionshapeasRegularHexagon. WeassumethatallthesensorsareequippedwithalocationidenticationdevicesuchasaGPSorusedsomelocalizationmethods[ 54 55 60 ].Further,weassumethatallthesensorsareawareoftheEuclideanlocationofthebasestation.Thiscanbedonebyonebroadcastfromthebasestation.Wenowshowthatifanodevknowsitscoordinates(xv,yv)andthecoordinatesofthebasestation(xb,yb)intheCartesiansystem,thenwithouthavingtheglobalviewofthehexagontiling,itcanlocallycomputeitscoordinates(xhv,yhv)inthenewcoordinatesystem.Furthermore,nodevcanidentifytheintegralcoordinatesofthehexagoninwhichitislocated. Figure510. TheHexagonLattice 100 PAGE 101 Let(0,0)bethecoordinateofthebasestationinthenewcoordinatesystem.Nodevcancomputeitsnewcoordinates(xhv,yhv)asfollows: xhv=f(xv)]TJ /F3 11.955 Tf 11.95 0 Td[(xb))]TJ /F4 11.955 Tf 13.15 8.09 Td[((yv)]TJ /F3 11.955 Tf 11.95 0 Td[(yb) tan60og=rp 3 2p 13 (5) yhv=(yv)]TJ /F3 11.955 Tf 11.96 0 Td[(yb)sin60o=rp 3 2p 13 (5) Thecoordinatesofthehexagonh(i,j)inwhichnodevislocatedisgivenas: xhv=f(xv)]TJ /F3 11.955 Tf 11.95 0 Td[(xb))]TJ /F4 11.955 Tf 13.15 8.09 Td[((yv)]TJ /F3 11.955 Tf 11.95 0 Td[(yb) tan60og=rp 3 2p 13 (5) yhv=(yv)]TJ /F3 11.955 Tf 11.96 0 Td[(yb)sin60o=rp 3 2p 13 (5) Allthesensornodesaftercomputingthecoordinatesoftheirrespectivehexagonsexchangethisinformationwiththeirneighborsandidentifyalltheothernodesintheircluster.Allthenodeshavingthesameh(i,j)willbelongstothesamecluster.Notethatthiscommunicationisonly1hopasthehexagonhasthelength(hexagondiameter)of2r p 13andtheclusteringpartitioncanbedoneonlyonetimeduringthedeploymentandsetupofaWSN. 5.4.2.2Localizedprotocol WearenowreadytointroduceourlocalizedprotocolforoptimizingenergyconsumptionandresourceutilizationofthedetectionandtrackingprocessdescribedinSection 5.3 .Noticethatthepartitionallowsallnodesinonehexagonandthatofsixadjacenthexagonsbeneighborsofeachother.AsshowninFigure 511 ,nodesinclusterC1willhaveallnodesinclustersC2,C3,C4,C5,C6,C7intheirneighborhood. Nowasthephenomenacloudwillexpandandthecoretrackingregionwillenlarge,therewillbealargenumberofcoretrackingnodesinthenetwork.Thecoretrackingnodeswillrunthefollowingprotocolinonlinemannertoschedulethemselvesintoactiveandsleepmode: 101 PAGE 102 Figure511. Clusteringonthebasisofhexagonlattice 1.Allthecoretrackingnodesinaclusterselectaclusterhead,thiscanbeselectedonthebasisofmaximumenergyleftoronanyotherarbitraryfactor[ 61 ]. 2.Eachelectedclusterheadperformsaonehopbroadcasttoinformitspresence.Consequently,allnodesintheneighborclustersareinformedaboutthepresenceofthisclusterhead. 3.Atthisstep,eachnodeinaclustercanhaveatmostsevenclusterheadsinitsneighborhood.Nowallthecoretrackingnodessendbacktotheclusterheadstheextrarequirednumberofclusterheadstheyneedtosatisfytheminimumquorumcondition. 4.Ifanyofthecoretrackingnodesinaclusterdoesnotsatisfytheminimumquorumcondition,thenthelastclusterheadintheclusteragaininvokestheclusterheadelectionprotocolwithintheclustertogenerateanextraclusterhead.Thisisrepeateduntilallthenodesinaclustersatisfytheminimumquorumcondition. 5.Finally,alltheclusterheadsinaclusterarescheduledtobeactive,whereasalltheothercoretrackingnodesintheclusterarescheduledtosleepinordertoconservetheenergy. 6.Ifanyactiveclusterheadfailsorgoesdownbecauseofgettingdepletedofenergy,thenanewclusterheadiselectedtoreplaceit. 102 PAGE 103 Figure512. GatorTechSmartHouse Figure513. SmartFloorTilewithforcesensorsandAtlasPlatformNode 5.5APracticalApplicationofPhenomenaDetectionandTracking Wefeltthatitwouldbeinterestingtodescribeanewrealworldapplicationofphenomenadetectionandtrackingwhichisradicallydifferentfromthegascloudandoilslicksimulationsthatareusuallypresented.TheapplicationthatwedescribeinvolvestheSmartFloor[ 62 ]intheGatorTechSmartHouse(Figure 512 )[ 63 ].Inaddition,weusethisapplicationtoevaluatetheperformanceofourapproachesasdescribedlaterinsection 6.5 TheSmartFloordeployedin2005,consistsofagridofpiezoelectricforcesensorsdeployedundertheraisedoortilesofthehouse.EachtilehasasinglesensorconnectedtoanAtlasPlatform[ 64 ]ZigBeenodeplacedbelowitscenter(Figure 513 ),whichallowsastepanywhereonthetiletobedetected.TheSmartFloorcovers 103 PAGE 104 theentireresidentialareaofthe2500sq.ft.houseandallowsittomonitoritsresidents'movementandlocationwithoutencumberingthemwithtagsorothertrackingdevices. WhiledesigningtheSmartFloorapplication,anaiveexpectationwasthatwhenapersonstepsonatile,onlythesensorunderneaththattileoutputsareadingofsignicantmagnitude.Unfortunately,basedonourexperienceovertheyears,wefoundthatthiswasclearlynotthecase.Duetovariousreasonsincludingseeminglyrandomvibrations,individualsensorssometimesoutputlargereadingsevenwhennobodyissteppingonthem.Thisresultsinaverynoisysensoryenvironmentwhereonecannotdistinguishbetweenagenuinestepandrandomspikesbyrelyingonindividualsensorsalone. Figure514. RippleEffectofaFootStepontheSmartFloor Figure515. WalkingmotionasaPhenomena 104 PAGE 105 Wealsoobservedthatwhenapersonstepsonatilenotonlydoesthisresultinthattile'ssensorregisteringastrongreadingbutsomeofitsneighboringtilesalsooutputsignicantlylargereadings.Hence,thesteppingactionofafootonaoortilecausesarippleeffectintheimmediateneighborhoodofthetile.Figure 514 showsanactualscreenshotofthisphenomenonoccurringintheSmartFloorwherereddotsindicatetilesregisteringreadingsofhighermagnitudeandgreenindicatestileswithloweryetsignicantmagnitude.Weusedthisobservationtodescribewalkingasaphenomenonbydeningastepintermsofaphenomenoncloud(asshowninFigure 515 ),inordertoreducethenumberoffalsepositivesandprovideaccuratelocationinformationaboutthehome'sresident.Moreover,sinceourapproachtophenomenondetectionandtrackingdoesnotrelyonmathematicalmodelingtotrackthedirectionofmovementofaphenomenon,hence,thismakesitextremelysuitableforobservingphenomenasuchaswalkingwhereitisextremelydifculttoaccuratelymodelthepaththatapersonwillfollowatanygiventime. AstepcanbedescribedasaphenomenoncloudS=ha,b,pT,m,ni,whereaandbdenotethelowerandupperboundsofaforcesensorreadingindicatingthatafoothassteppedonatileorinitsimmediatevicinity.Thisvaluedependsontheparticularsensorbeingused.Forexample,basedonempiricalstudy,wefoundthatfortheInterlinkforcesensorsusedintheSmartFloor(havinganoutputrangeof[0,1023],a=150andb=600foranindividualweighingbetween110to240pounds.Theoptimalvaluesoftheotherparametersweredeterminedviaexperimentationandaredescribedinthefollowingsection.MoredetailsaboututilizingphenomenondetectionandtrackingtomonitorresidentlocationandobservewalkingcharacteristicssuchasgaitvelocityandstridelengthintheGatorTechSmartHousecanbefoundin[ 65 ]. 5.6PerformanceEvaluation Inthissection,weevaluatevariousaspectsofthedistributedphenomenondetectionandtrackingapproachesdescribedinthispaper.Therstsetofexperiments 105 PAGE 106 evaluatestheeffectivenessofourdetectionstrategyinarealworldsensordeploymentandanalyzestheeffectofvaryingphenomenaparametersdescribedinSection 5.2.2 .Thesecondsetofexperimentsusessimulationtoevaluatetheresourceusageandpowerconsumptionofourapproachescomparedwiththestreambasedmethod.Wereliedonsimulationinthiscasebecausewewantedtomeasureresourceusageandpowerconsumptioninlargesensornetworksofvaryingsizes.Anditwasnotpracticallyfeasibleforustophysicallydeploysensorsinsuchlargenumbersforthepurposeofexperimentation. 5.6.1EffectivenessofDetectionStrategy Inthisrstsetofexperiments,westudytheeffectivenessofourphenomenondetectionandtrackingmechanisminarealworldsensordeploymentinsidetheGatorTechSmartHouse. 5.6.1.1Experimentalsetup WechosetoevaluateeffectivenessbyperformingexperimentsusingtheSmartFloor(previouslydescribedinSection 5.5 )wherehumanfootstepsarerepresentedasphenomenacloudsandphenomenondetectionandtrackingisusedtomonitorthelocationofaresidentinthehouse.Weobservedtheeffectofphenomenondenitionparameters(pT,mandn,denedinSection 5.2.2 )onthedetectionefciencyofourtechnique.Wevariedthevaluesofeachoftheseparametersandstudiedtheireffectbyloggingthenumberoffalsepositives,falsenegatives/missesandcorrectdetectionsofahumanstep.Inordertoaidourevaluation,werestrictedmovementtoa100sq.ft.areainthelivingroomofthesmarthouseandhadtestsubjectswalkalongaclearlymarkedpathontheoor.Thisallowedustologtheactualstepsthatapersonwastakingandcollectstatisticsoncorrectdetectionsanddetectionerrors. 5.6.1.2Resultsandanalysis Theexperimentalresultsarepresentedas3graphsshowninFigures 516 517 and 518 .Figure 516 showstheeffectofvaryingparameternwhichdetermines 106 PAGE 107 Figure516. EffectofvaryingnwithpT=0.4andm=150 theminimumquorumofneighboringsensorsrequiredtoconclusivelydeterminetheoccurrenceofaphenomenon.SincetheSmartFloorisdeployedasarectangulargridofsensors,thevalueofnvariesfrom0to8.Weobservethatforn=0(whichcorrespondstothenaivecase)thenumberoffalsepositivesisextremelyhighsincethesystemisentirelyrelyingonoutputsfromsinglesensorstodeterminetheoccurrenceofafootstepevent.Therefore,eventhoughtherearenomisses/falsenegativesandalltheactualfootstepsaredetected,theiroccurrenceislostinthenoiseofhavinganextremelylargenumberoffalsealerts.Asweincreasethevalueofn,thenumberoffalsepositivescomesdownsharplysincenowmultipleneighboringsensorsneedtoagreeontheoccurrenceofaphenomenon.Wealsonoticethatasnincreases,thenumberofmissesalsoincrease,therebyreducingthenumberofcorrectdetections.Thisisduetothefactthatwalkingisessentiallyatransienteventwhereafootstephastobedetectedbyaspecicsensorwithinaverysmalltimewindow.Hence,eventhoughwepostulatedthattheactionofsteppingonatilecausesarippleeffectamongstneighboringtiles,itisnotnecessarythatthenumberofneighborsexperiencingthiseffectwillalwaysmeettheminimumquorumrequirement(n)withinthetimewindow.Forlargevaluesofn,thenumberofmissesisveryhighandconsequently,thenumberofcorrectdetectionsbecomesverylow,sincethequorumrequirementsbecometoostringentandcannot 107 PAGE 108 besatisedinmostorallcases.WefoundthatfortheGatorTechSmartHouseSmartFloor,settingnequalto2or3ensuresareasonablygoodlevelofperformance,wherethenumberoffalsepositivesiscomparativelylowascomparedtothenumberofcorrectdetectionsandapproximately77%ofallfootstepsaresuccessfullydetected. Figure517. EffectofvaryingpTwithn=3andm=150 Figure 517 showstheeffectofvaryingthethresholdprobabilitypT.Weobservethatasthresholdprobabilityincreases,thenumberoffalsepositivesdecreasessinceitltersoutrandomspikes.Randomspikestypicallyresultinonlyafewreadingsofsignicantmagnitudewithinaxedsizeslidingwindow,hence,thereisasharpdropinthenumberoffalsepositivesevenwhenweonlyincreasepTfrom0.1to0.2.Howevermakingtheprobabilityrequirementmorestringentalsoresultsinanincreaseinthenumberoffalsenegatives/misses.Thisisduetothefactthatsinceweareusingaslidingwindowofxedsize,asthenumberofreadingsinthewindowthatarerequiredtoliewithinthephenomenadenedbounds[a,b]inordertosatisfytheProbabilityCondition(denedinSection 5.2 )increases,thechanceoftheProbabilityConditiongettingsatiseddecreases.FortheSmartFloorwefoundthatsettingpT=0.4resultsinareasonablygooddetectionratewithalownumberoffalsepositivesandmisses. Figure 518 showstheeffectofvaryingtheslidingwindowsizem.Weobservethatiftheslidingwindowsizeistoolow,thisresultsinalargenumberoffalsepositives 108 PAGE 109 Figure518. Effectofvaryingmwithn=3andPT=0.4 despitehavingahighprobabilitythreshold.Thisisduetothefactthatincaseofsensorswhichhaveahighsamplingrateevenrandomspikescanresultinafairlylargecontiguoussetofsignicantreadings.Sincethesystemessentiallyusesthethresholdfrequency(pTm)toevaluatewhetherasensorsatisestheProbabilityCondition,forsmallwindowsizesthecorrespondingthresholdfrequencyisalsolowevenifthresholdprobabilitypTiskepthigh.Hence,thereisahighprobabilitythatrandomspikesgetmistakenforactualfootsteps.Increasingtheslidingwindowsizeontheotherhand,raisesthethresholdfrequencywhichaswecanobserveresultsinamoderateincreaseinthenumberofmisses.WefoundthatfortheSmartFloor,settingtheslidingwindowsizem=150resultsinreasonablygooddetectionperformancewithouttaxingmemoryresourcesofindividualsensornodes. 5.6.2ResourceandPowerConsumption Inthissection,westudytheeffectivenessandefciencyofourproposedapproachesintermsofenergyconsumptionandresourceutilization.Wesimulatedthephenomenacloudbyspawningitsmultipleoccurrencesatdifferentlocationsfollowedbytheirrandommovementandexpansionoverarectangulargridofsensors.Weapplieddifferentapproachesfordetectingandtrackingthephenomenacloudandperformedacomparativeanalysis.Wesimulatedthefollowingalgorithms: 109 PAGE 110 1.StreamPDT[ 46 ]:AcentralizedstreambasedalgorithmwherephenomenadetectionandtrackingisperformedbyaCentralizedQueryProcessor(CQP).WesimulatedNilePDT[ 46 ],awellknowndetectionsystemdevelopedatPurdueUniversity,whichutilizedStreamPDTstrategy. 2.DistPDT:Adistributedphenomenadetectionandtrackingalgorithmwhichweproposedinourpreliminarywork[ 57 ]. 3.FullDensityAlgorithm(FDA):ThephenomenadetectionandtrackingmechanismdescribedinSection 5.3 ,inwhichwehavemodiedthedenitionsofcandidateandpotentialcandidatesensors(fromDistPDT)toreducethenumberofunnecessaryactivesensors. 4.OptimizedDensityAlgorithm(ODA):ThephenomenadetectionandtrackingmechanismdescribedinSection 5.4.2 afterapplyingthelocalizedprotocoltooptimizetheresourceutilization. WealsorantheIPformulationintroducedinSection 5.4.1 onsmallsizednetworkstoverifyhowfaroursolutionisfromtheoptimalsolution. Figure519. PowerConsumptionSpecicationsforAtlas 5.6.2.1Experimentalsetup Weperformedsimulationsinthefollowingfourdifferentsetups: 1.Intherstsetofsimulations,wesimulatedtherandommovementandexpansionofphenomenacloudfor50epochsonarectangularsensorgridofsize121121deployedoveranareaof1200m1200m. 110 PAGE 111 2.Inthesecondsetofsimulations,wevariedthesizeofthesensorgridfrom101101to301301andsimulatedtherandommovementandexpansionofphenomenacloudfor25epochsinordertoshowthescalabilityofourproposedalgorithms. 3.Inthethirdsetofsimulations,wesimulatedtherandommovementandexpansionofphenomenacloudfor5epochsonasmallrectangularsensorgridofsize1010tocomparetheperformanceofouralgorithmswiththeoptimalsolutiongeneratedbytheIntegerProgramintroducedinSection 5.4.1 4.Finally,thefourthsetofsimulationsistoverifythefunctioningandperformanceofeachofabovementionedalgorithmspictoriallythroughsnapshotstakenduringtheirexecutions.Wesimulatedtherandomexpansionofphenomenacloudfor20epochsonamediumsizedrectangulargridof5151sensorsdeployedoveranareaof500m500m.Wealsodiscussthepacketlosttoleranceofourproposedalgorithmsinthissetofsimulations. WeconnectedeachsensortoanAtlasZigBeenode,whosehardwareisbasedonAtmelZlinkRCBdesign.Atthebeginningofeachsimulation,werandomlyspawnedphenomenacloudindifferentareasonthesensorgrid.Duringeachepoch,thevariationofphenomenacloudmotionandsizeweresimulatedbyrandomlychangingshape,sizeanddirectionofmotionofitsboundary.Hence,thesimulationcanbeviewedasarandomwalkofphenomenoncloudoverasensorgrid.Oursimulationsintroduceahighdegreeofuncertaintyregardingphenomenoncloudmovementandtesttheperformanceofdetectionandtrackingalgorithmstothefullestextent.Duringeachepoch,weloggedfourstatisticswhichare1)thenumberofactivesensorsinvolved,2)thenumberofnetworkmessagesexchangedbetweensensorsfortheinnetworkimplementationofproposedalgorithms,3)thenumberofupdatessenttotheCentralizedQueryProcessor(CQP),and4)energyconsumption.Wecalculatedtheenergyconsumptionofnodesasafunctionofprocessingcosts(includingsamplingsensors)andnetworkcosts(incurred 111 PAGE 112 Figure520. Epochwisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. Figure521. EpochwisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) Figure522. Epochwisecomparisonbasedonnumberofmessagesexchangedbetweenonehopneighborstoimplementthealgorithms. Figure523. EpochwisecomparisonbasedontheEnergyConsumption. inreceivingandtransmittingdataovertheradio),whicharebasedontheAtlasZigBeenodehardwarespecicationslistedinFigure 610 5.6.2.2Resultsandanalysis SimulationresultsfortherstsetofexperimentsarepresentedinFigures 520 524 whichcompareperformancesofStreamPDT,DistPDT,FDAandODA.Ofwhich,Figures 520 521 522 ,and 523 provideepochwisecomparison,whereasFigure 524 providescomparisonbasedonanoverall50epochs. 112 PAGE 113 Figure524. Comparisonbasedonoverall50Epochs Figure 520 evaluatestheperformancesofthefouralgorithmsintermsofthenumberofactivenodesinvolvedinthedetectionandtrackingprocess.Ascanbeseen,ODAshowsthebestperformanceandStreamPDThastheworstperformance.PoorperformanceofStreamPDTisduetothefactthatitusescentralizedprocessing,inopposetotheinnetworkprocessingusedbyourproposedalgorithms.Consequently,StreamPDTrequiresallsensornodestoremainactiveatallthetime.Incontrast,DistPDTonlyneedsasetofpotentialcandidate,candidateandtrackingnodestoremainactive,whichresultsincomparativelyabetterperformance.FDAperformsslightlybetterthanDistPDTasitstringentlyactivatesthecandidatesandpotentialcandidates,resultinginmoreefcientresourceusage.ODAshowsthebestperformance,asitfurtheroptimizestheresourceusageofFDAbyreducingcoverageredundanciesinthecoretrackingregion.Morespecically,FDAneeds75%lessactivenodesincomparisontoStreamPDTand6%lessactivenodesincomparisontoDistPDTovertheperiodof50epochs,asshowninFigure 524 .Likewise,Figure 524 alsorevealsthatODAneeds84%lessactivenodesincomparisontoStreamPDTand40%lessactivenodesincomparisontoDistPDTovertheperiodof50epochs.ODAshowsaperformanceenhancementof36%overFDAduetotheoptimizationstep. Figure 521 showstheepochwisecomparisonofthefouralgorithmsbasedonthenumberofupdatemessagessendtotheCQP.Asthenumberofupdatemessages 113 PAGE 114 directlydependsuponthenumberofactivetrackingnodesinthecoreregion,thenumberofupdatemessagesisequalforbothDistPDTandFDA.Duetothelocalizedoptimizationprotocol,ODAgeneratestheminimumnumberofupdatemessageswithoutdegradingtheperformanceofdetectionandtracking.AsincaseofStreamPDT,allsensorsneedtoreporttotheCQPthroughupdatemessages;hence,itgeneratesthemaximumnumberofupdatemessages.Indetails,ascanbeseeninFigure 524 ,ODAgenerates86%and39%lessernetworktrafcintermsofupdatemessagescomparingtoStreamPDTandDistPDT(FDA)respectively. Figure 522 illustratestheepochwisecomparisonbasedonthenumberofprotocolmessagescollectivelyexchangedbyalltheactivenodeswiththeironehopneighbors.StreamPDTisastraightforwardalgorithminwhichallsensornodesperformonehopbroadcastoftheirsensedinformation.Consequently,thenumberofprotocolmessagesexchangedinanepochisequaltothenumberofnodesinthenetwork.However,fortheotherthreealgorithms,onlyactivesensornodesbroadcasttheexchangedmessagebasedontheirrespectivecategories.ODAperformsthebestandgeneratesminimumnumberofexchangedmessages,whereasFDAcomparativelyperformsbetterthanDistPDT.Figure 524 showsthatFDAgenerates77%and6.41%lesserexchangedmessagesincomparisontoStreamPDTandDistPDTrepsectively.Furthermore,itshowsthatODAgenerates86%and42.5%lesserexchangedmessagesincomparisontoStreamPDTandDistPDTrespectively.ODAimprovesFDAbygenerating38.54%lessexchangedmessagesandithasahugesignicantimprovementoverStreamPDT. TheepochwisecomparisonofthefouralgorithmsbasedontheenergyconsumptionisshowninFigure 523 .Asexpected,StreamPDTrequiresallsensornodestoalwaysactivelysense,thusitconsumesenergythemost.ODAperformsthebest,whereasFDAisbetterthanDistPDT.Figure 524 showsthatFDAconsumes74.52%lesserenergyincomparisontoStreamPDTand5.86%incomparisontoDistPDT.Similarly,ODAconsumes83.15%lesserenergyincomparisontoStreamPDT 114 PAGE 115 and37.76%incomparisontoDistPDT.ODAimprovestheenergyconsumptionofFDAby34%,reectingthatapplyingtheoptimizationstepmakesasignicanthelp. Insummary,fortherstsetofexperiments,ODAperformsthebestandStreamPDTperformstheworstinallterms:thenumberofactivenodes,thenumberofexchangemessages,thenumberofupdatemessages,andenergyconsumption.AlsonoticethatthegraphforStreamPDTisaconstantlinewhenthephenomenacloudsareenlargingbecauseallsensornodesinthegridremainactiveatalltimeregardlessofthecloud'ssize.Fortheotherthreealgorithms,whenthephenomenaexpand,thegraphsareincreasing,butnotlinearly. Figure525. Comparisonbasedondifferentgridsize. Inthesecondsetofsimulations,wevariedthegridsizeasshowninFigure 525 .ItcanbeobservedthatDistPDT,FDA,andODAdonotshowmuchvariationinallfourcomparisonparameterswithrespecttoincreaseinthegridsize.Thisisderivedfromthefactthatforthesealgorithms,thedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofphenomenacloudatanygiventimeanddoesnotrequireallsensornodestoremainunnecessarilyactive.Incontrast,StreamPDTrequiresallnodesinthenetworktoremainactiveandsendupdatemessagesabouttheirdetectingstatustotheCQP.Therefore,asthegridsizeincreases,themoreactivenodesandthelargernetworktrafc.Consequently,theperformanceofStreamPDTdegrades.ThesimulationresultsshowthatDistPDT,FDA,andODAarescalabletothesizeofgrids 115 PAGE 116 Figure526. Epochwisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. Figure527. EpochwisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) Figure528. Epochwisecomparisonbasedonnumberofmessagesexchangedbetweenonehopneighborstoimplementthealgorithms. Figure529. EpochwisecomparisonbasedontheEnergyConsumption. andODAperformsthebestintermsofallthecomparisonparameters.TheperformanceofStreamPDTistheworstandnotscalable. Figures 526 530 presentsimulationresultsforthethirdsetofexperiments,ofwhichwecomparethesolutionsofthefouralgorithmswiththeoptimalsolutiongeneratedbytheIPdescribedinSection 5.4.1 .NotethatsincesolvingIPisactuallyNPhard,weonlysimulatedthissetofexperimentsonthesmallsizegridof1010during5epochsofrandommovementandexpansionofphenomenaclouds.Figures 116 PAGE 117 Figure530. Comparisonbasedonoverall5Epochs Figure531. SnapshotsofexpandingphenomenacloudduringEpochst10,t15,t20. Figure532. ActiveSensorsduringEpocht10,forDistPDT. 526 529 provideanepochwisecomparisonwhereasFigure 530 summarizestheresultsoverallthe5epochs. Ascanbeseen,StreamPDTuses62.5%moreactivenodesincomparisontotheIPsolution.DistPDTimprovestheresultbyusing35.74%moreactivesensorscomparedtotheIPsolution.FDAfurtherimprovesthesolutionbyusingonly17.62%moreactivenodescomparedtotheIPsolution.Andasexpected,ODAshowsthebestperformanceandonlyuses13.82%moreactivenodesincomparisontotheoptimalsolution. IntermsofthenumberofupdatemessagessenttotheCQP,StreamPDTshowstheworstperformancebygenerating88.2%moreupdatemessagesthantheIPsolution.DistPDTshowsconsiderableimprovementbygenerating40%moreupdatemessages 117 PAGE 118 Figure533. ActiveSensorsduringEpocht10,forFDA. Figure534. ActiveSensorsduringEpocht10,forODA. Figure535. ActiveSensorsduringEpocht15,forDistPDT. Figure536. ActiveSensorsduringEpocht15,forFDA. Figure537. ActiveSensorsduringEpocht15,forODA. Figure538. ActiveSensorsduringEpocht20,forDistPDT. thantheIPsolution.AsthesetoftrackingnodesisthesameforDistPDTandFDA,thenumberofupdatemessagesthereforemustbethesame.ODAshowsaslightlyimprovementandgenerates33.33%moreupdatemessagesthantheIPsolution.TheprotocolmessagesexchangedbetweentheonehopneighborsinStreamPDTis85.8% 118 PAGE 119 Figure539. ActiveSensorsduringEpocht20,forFDA. Figure540. ActiveSensorsduringEpocht20,forODA. morethantheIPsolution.DistPDTandFDArespectivelygenerates63.59%and36.04%moreprotocolmessagescomparedtotheIPsolution.ODAgenerates29.70%moreprotocolmessagesthantheIPsolution.NotethatODAusesonly13.82%moreactivenodesthanthatoftheIP,however,theimplementaionoftheoptimizationstepaddsanextramessageoverhead,thusitdoesnotsavemuchofexchangedmessagesasexpected. Theenergyconsumptionismainlycontributedbyactivelysensingsensors.Again,astheStreamPDTneedsupdatesfromallsensors,ithastheworstperformanceintermsofenergyconsumption.Itconsumes62.32%moreenergythantheIPsolutionovertheperiodof5epochs.DistPDT,FDA,andODAconsumes36%,18.05%,and15.09%moreenergythantheIPsolution,repectively. Inordertohaveabetterviewofhowtheproposedalgorithmsfunctionduringthemovementofthephenomenacloud,weperformedthefourthsetofsimulationstopictoriallyillustratethefunctioningandperformanceofDistPDT,FDA,andODA.Figure 61 showssnapshotsoftheexpandingphenomenacloudatepochst10,t15,andt20.Figures 532 533 ,and 534 aretherespectivesnapshotsshowingtheactivenodesforDistPDT,FDA,andODAduringepocht10.Likewise,theresultofepocht15isshowninFigures 535 536 ,and 537 andthatofepocht20ispresentedinFigures 538 539 ,and 540 .Ascanbeseen,whenthephenomenonexpands,thenumberofactivenodes 119 PAGE 120 expandsmoothlyaswelltofullycoverandtrackthephenomenon'smovement.Also,attheborderofthephenomenon,theDistPDThasathickergreenlinethanthatofFDA,showingthatDistPDTrequiresmorecandidatenodesduetoourpreviousrelaxeddenition.Inaddition,attheinnerareaofthephenomenon,whilealltrackingnodesareactiveforDistPDTandFDA,ODAhassomeinactivetrackingnodes.Thisisduetotheoptimizationsteptocovertheentireareaandsatisfythequorumbutstillminimizetheenergyconsumption.Duringtheoverall20epochs,FDAinvolved10.84%lesseractivenodescomparedtoDistPDT.ODAfurtherimprovestheperformancebyusing36.54%lessactivenodescomparedtoDistPDT. Figure541. Percentageofholesgeneratedwrtpercentageofupdatemessageslost Toevaluatethedegreeoffaulttoleranceofourproposedalgorithms,wefurtherranthesimulationsallowingthelossofupdatemessageinthenetworkandsummarizetheresultsinFigure 541 .Inaddition,Figures 542 547 pictoriallyshowtheholesgeneratedforFDAandODAwhiledetectingphenomenacloud,whenpercentagesofupdatemessageslostare5%,10%and15%respectivelyduringtheepocht20.AholeisrepresentedasaredballandisgeneratedwhenthedetectionstatusofatrackingsensorcannotbedeterminedattheCQPbasedontheupdatemessagesreceived. Weobservedthatouralgorithmsshowedareasonableperformancewhenthenetworkisvulnerableofmessagelosses.Figure 541 showsthepercentageofholesgeneratedbyFDAandODAwithrespecttothepercentageofupdatemessageslost.Ascanbeseen,theholesgeneratesbyFDAisverynegligible,evenonly0.275%attherateof15%ofupdatemessagelost.Asexpected,ODAgeneratesmoreholes.Thisisclearly 120 PAGE 121 atradeoffbetweentheenergyconsumptionandfaulttolerance.Inordertoreducetheenergyconsumptionandmessagecomplexity,ODAleavesenoughactivecoretrackingsensorstosastiedtherequiredquorumwhereasalltrackingsensornodesinFDAareactive.WecanslighlymodifyODAtobemorefaulttolerancebyallowingmorecoretrackingsensorstobeactive.Morespecically,atstep(4)insection 5.4.2.2 ,insteadofrepeatinguntiltheminimumquorumnissatised,wecanrepeattheprocessuntilallactivenodesinaclustersatisfynquorumconditionwhere1.Thebiggeris,themoreactivenodesare,thelesserholesgenerated. Letusfurtherlookintothesnapshots(Figure 542 547 )toseethelocationoftheseholes.Theholesweremostlycreatedintheinnerpartofthecoretrackingregion.Thisispartiallybecauseweonlyallowsomecoretrackingnodes(whichlocateintheinnerregion)tobeinactive.Whenupdatemessagesofsomeactivecoretrackingnodesgetlost,itresultsinlackofinformationabouttheseactivecoretrackingnodesandthesleepingcoretrackingnodeswhichtheywerecovering.Asonlyafewholesaregeneratedattheboundaryofthecoretrackingregion,consequently,theregionwherethephenomenacloudiscurrentlylocatedcaneasilybeidentiedattheCQPevenif15%ofupdatemessagesarelost,asshowninFigure 547 5.7RelatedWork InanearlystageofthephenomenadetectionandtrackingusingWSNs,thephenomenonisstaticandconnedtoasetofpointsorwithinacertainarea,oftenknownasthecoverageproblem(see[ 23 66 ]andreferencestherein).Towardsnowadays,asthephenomenaaredynamic,haveirregularshapes,andinvariantmovements,therehasbeenrecentlyanongoingresearchondetectionandtrackingofphenomenacloud[ 12 13 19 42 44 46 67 68 ]. ThemostcloselyrelatedworkisNilePDT[ 46 ],whichisaPhenomenaDetectionandTracking(PDT)frameworkrunningontopofcentralizedNiledatastreammanagementsystem,developedbyIndianaCenterforDatabaseSystems(ICDS)at 121 PAGE 122 PurdueUniversity.NilePDTisdesignedfordetectingandtrackingphenomenoncloudssuchasgasclouds,oilspillsandchemicalwastespillage.NilePDTusestwocustomdatabaseoperators,namely,SNScanandSNJointoperformphenomenondetectionandtracking.TheSNScanoperatorscansallthesensorsinthenetworkandchoosescandidatesensorswhichhaveahighprobabilityofdetectingthephenomenon.TheSNJoinoperatorthenevaluateseachofthesecandidatesensorsandchecksiftheyjoinwithothercandidatesacertainnumberoftimesandhencedetectaphenomenonevent.NilePDTusesfeedbackcontroltocontinuouslytunetheSNScanandSNJoinparameterstomaximizeefciencyofthedetectionprocess.ThemaindrawbackoftheNilePDTapproachisthatittakesastreamingdatabaseviewoftheprocess.Itdoesnotconsideranymechanismsforcontrollingtheowofdataatthesourcesensorsthemselvesoraddresspowerconsumptionandnetworkbandwidthissuesinsidethesensornetwork.Furthermore,itrequiresallsensorstopumpreadingstotheSNScanoperatortoallowittochoosephenomenoncandidates,whichcanleadtopotentiallymassivescalabilityissues.Inthispaper,wehavecomparedouralgorithmstothiswork,referredatStreamPDT. Omotayoetal.[ 67 ]describeadataharvestingframeworkfortracingphenomena.Theyproposealgorithmsformaintainingadatafarmonthenodesbymaximizingtheutilizationoftheironboardnonvolatilestorage,forenablingbacktrackingtodeterminethecauseofaphenomenon.McErleanet.al.[ 42 ]proposeadistributedeventdetectionandtrackingalgorithmformovingobjectsusingWSNs.However,thissystemassumestheprioravailabilityofoptimaladhocroutingmechanismsandisprimarilydesignedfordetectingindividualdiscreteobjectswithwelldenedshapeandsize,asopposedtophenomenoncloudswhoseshapeandsizetypicallycannotbedenedinexactterms. Therearealsosomeworkstudyingtheboundaryofthephenomenacloudsinsteadofdetectingandtrackingtheentirearea[ 12 19 22 68 71 ].Asthesestudiesarenotinthescopeofthispaper(wedetectandtracktheentirearea),weonlybrieymention 122 PAGE 123 themhere.ChintalapudiandGovindanin[ 68 ]describedalgorithmsfordetectingsensorslyingclosesttotheedgesofaphenomenoncloud.However,theirapproachnotonlyrequiresassumptionsregardingtheshapeoftheedges(suchaswhetheritisalineoranellipse),butcanalsoleadtoahighnumberoffalsepositives,sincetheextremefringesofaphenomenonaremoresusceptibletosensorerrorsandrapiductuations.Fromtheirdescription,itappearsthattheiredgesensorscorrespondtotheOuterregionofthephenomenoncloud(denedinSection 5.3.1 ).Ourmechanisms,ontheotherhand,avoidfalsepositivesbyonlyreportingthosesensorswhichlieintheCoreregionnamely,trackingsensors.Moreover,ourapproachdoesnotmakeanysimplifyingassumptionsregardingtheshapeofthecloudedges. In[ 19 21 ],theauthorsproposedadistributedmethodtostatisticallyestimatetheboundaryofthephenomena,buttheyconsideronlystaticphenomena.In[ 69 71 ],algorithmsconsideringmobilesensornodesareproposedtoapproximatetheboundaryofaphenomenacloud.In[ 45 ],Chenget.al.proposedamethodforcontinuouslymonitoringtheboundaryofthephenomenacloud,buttheyrequireallthesensorsinWSNsactivelysenseallthetimeandtheyonlyconcentratedonreducingthecommunicationoverhead.In[ 12 ],adynamicclusterstructureforobjectdetectionandtrackingwhichrequiresallsensornodestobeactiveisproposed.Theirproposedclusterformationhashighcommunicationoverhead,thusitisdifculttohandlefastchangesofphenomenacloudstate.In[ 13 ],Kimet.al.proposedanotheralgorithmfortrackingthephenomenaboundarybutitrequiresallthesensornodestobeactiveperiodically. 5.8Conclusion Inthispaper,weproposeseveraldistributedalgorithmstodetectandtrackseveraltypesofphenomenaclouds,regardlessoftheirshapesandmovementdirection.Thephenomenacloudscanhavevariantshapes,sizeanddirectionofmotionalongmultipleaxes.Werstproposeadistributedalgorithmforinsitudetectionandtracking 123 PAGE 124 ofphenomenacloudsinthesensorspace.Wenextprovideamathematicalmodeltooptimizetheenergyconsumption,onwhichwefurtherproposealocalizedalgorithmtominimizetheresourceutilization.Ourproposedapproachesnotonlyensurelowprocessingandnetworkingoverheadatthecentralizedqueryprocessorbutalsominimizethenumberofsensorswhichareactivelyinvolvedinthedetectionandtrackingprocessesatanygiventime.Wevalidateourapproachusingbothreallifesmarthomeapplicationsaswellassimulationexperiments,whichanalyzetheeffectivenessandefciencyofourproposedalgorithms.Wealsoshowthatouralgorithmsresultinsignicantreductioninresourceusageandpowerconsumptionascomparedtothecontemporarystreambasedapproaches. Aspartofourfuturework,wearelookingforamodelassisteddetectionandtracking,wheredistributionofdetectiontaskswillbestreamlinedbasedonpredictionsregardingthedirectionofmovementofthephenomenacloud.Wearealsosearchingforreallifedatasetsfromdifferentapplicationdomainsforfurthervalidatingandnetuningourapproaches. 124 PAGE 125 Figure542. DetectionandTrackingwith5%updatemessagelostforFDA. Figure543. DetectionandTrackingwith5%updatemessagelostforODA. Figure544. DetectionandTrackingwith10%updatemessagelostforFDA. Figure545. DetectionandTrackingwith10%updatemessagelostforODA. Figure546. DetectionandTrackingwith15%updatemessagelostforFDA. Figure547. DetectionandTrackingwith15%updatemessagelostforODA. 125 PAGE 126 CHAPTER6LOCALIZEDENERGYEFFICIENTDETECTIONANDTRACKINGOFDYNAMICPHENOMENABOUNDARY 6.1Introduction MostoftheexistingresearchinphenomenadetectionandtrackingusingWirelessSensorNetworks(WSNs)assumesthephenomenaisinvariantinshape,sizeandmotion[ 19 23 ].However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgasesthatarecharacterizedbynondeterministicvariationsinshape,sizeanddirectionofmotion.Duetotheabsenceofanywelldenedmodeltorepresentdynamicphenomena,theirdetectionandtrackingthroughWSNsisverychallenging. Sincesensornodeshavelimitedenergyandprocessingpower,thedetectionandtrackingofdynamicphenomenabecomesevenmorechallenging.Inapplicationsinvolvingdynamicphenomenasuchasoilspills,gasleakage,etc,itisdesirabletoidentifyandtracktheareaaffectedbythephenomena.Therefore,itismoresensibletodetectandtrackonlythephenomenaboundaryengulngtheaffectedareainsteadoftrackingtheentirephenomena.Existingworksondetectionandtrackingofphenomenaboundarymostlyconsiderstaticphenomena[ 19 23 ]onlyfewstudydynamicphenomena[ 12 13 ].Duetothenatureoftheirsolutions,theworksforstaticphenomenaboundarycannotbeextendedtodynamicphenomena. Recently,Kimet.al[ 13 ]haveproposedaprotocolnamedTOCOB,whichhasthebestperformanceintheliterature.TOCOBneedsallthesensornodestoperiodicallysensephenomenaandcomparetheircurrentdetectionstatuswiththepreviousone.Ifthedetectionstatusofasensornodeischanged,itiscalledaChangedValueNode(CVN).ACVNbroadcastsaCompareOneZero(COZ)messagetoitsneighbors.AnodereceivingatleastoneCOZmessageofdifferentstatusthanitsowniscalledaBoundaryNode(BN).Further,someRepresentativeNodes(RNs)areselectedamongtheBNswhichreportthedetectionstatusofasingleCVNintheirneighborhoodtotheCQP.Thereare 126 PAGE 127 somedrawbacksofTOCOB.Firstly,itneedsallthesensornodestoparticipateinthedetectionandtrackingprocess,whichisnotenergyefcient.Secondly,itprovidesverysparseboundaryinformationtotheCQP,whichlimitsthequalityofphenomenaboundaryestimation.Thirdly,themethodforidentifyingtheRNsisnotefcientandcouldsuppressalargeamountofboundaryinformationfromsendingtotheCQP,furtherdegradingthedetectionandtrackingofphenomenaboundary. Inthischapter,weproposeanenergyefcientlocalizedprotocolfordetectionandtrackingofdynamicphenomenaboundaryofanyirregularshape.Inourproposedprotocol,thedetectionandtrackingprocessislocalizedtothenodesintheimmediateneighborhoodofthephenomenaboundary.Thisresultsinonlynecessarynodesactivelyparticipatinginsensingthephenomenaboundary,whilerestofthenodesremaininactiveuntiltheyarerequired.Inordertoreducethetrafcgeneratedbyupdatemessages,weproposeanefcient,robustlocalizedclusteringalgorithmbasedonhexagontilingofthe2DplanecoveredbytheWSN.Theproposedclusteringalgorithmdoesnotrequirereclusteringwhenthephenomenaboundarydynamicallyvaries. Furthermore,weproposeadataaggregationtechniquetoaggregatetheboundaryinformationattheclusterheads.Ourdataaggregationtechniqueconsiderablyreducesthesizeofupdatemessagessenttothecentralizedqueryprocessorwithoutcompromisingontheamountofinformationtobereported.ThesimulationresultsshowthatourprotocolperformsremarkablybetterthanTOCOB[ 13 ]intermsofenergyconsumptionandresourceusage. Therestofthechapterisorganizedasfollows:InSection 6.2 ,wepresentthenetworkmodelalongwithsomepreliminarydenitions.WeprovidedetaileddescriptionofthedetectionandtrackingprotocolfordynamicphenomenaboundaryinSection 6.3 .ThelocalizedclusteringmethodanddataaggregationschemeisdescribedinSection 6.4 .InSection 6.5 ,weevaluatetheproposedprotocolthroughextensivesimulations.Finally,Section 6.6 concludesthepaper. 127 PAGE 128 6.2SystemModel NetworkModel:AsetofinsitusensornodesVdeployedona2DplanealongwithasetofcommunicationlinksEformtheWSN.Eachsensornodev2Visequippedwitharadiotransceiverwithcommunicationranger.ThesetofnodeswithinthecommunicationrangeofvformsitsneighborhoodN(v).Furthermore,thereexistsaCentralizedQueryProcessor(CQP),wherethesensedinformationfromtheWSNiscollectedforfurtherprocessing. Asensornodeisactiveifitssensingfunctionalityison,otherwiseitisinactive. Anactivesensornodeisreferredasdetectpositiveifitdetectsthephenomenonisexisting,whereasifitdetectsthephenomenaisnotexistingitisreferredasdetectnegative. DynamicPhenomena:Adynamicphenomenarepresentstheoccurrenceofanyeventthatshowsdynamicvariationsinshape,sizeanddirectionofmotion.Themostsuitableexamplesofdynamicphenomenaareoilspills,mudow,diffusionorleakageofgases,etc. PhenomenaBoundary:Thephenomenaboundaryisdenedasacurvethatinscribestheareaaffectedbythephenomena.Itdelineatestheareaunderconsiderationintotheregionwherethephenomenaexistsandtheregionwherethephenomenahasnotyetreached.Basedonthephenomenaboundary,wepresenttheclassicationofthesensornodesdescribedinFigures 61 & 62 6.3DetectingandTrackingofDynamicPhenomenaBoundary Inthissection,wepresentourprotocolfordetectionandtrackingthedynamicphenomenaboundary.Figure 65 showsthestatetransitiondiagramforasensornode.Thestatesrepresentpossiblesensorclassesandtheedgesrepresentconditionsfortherespectivetransitions.Figure 63 showsvarioustypesofmessagesthatsensornodesmaygenerateandexchangetoimplementthedetectionandtrackingprotocol.Figure 64 showsthesetoftransitionrulesgoverningthetransitionofasensornodefromonestate 128 PAGE 129 Figure61. ClassicationofSensorNodesintheWSN Figure62. TypesofNodesintheWSN toanother.TheserulesareexecutedlocallytocontroltheentiredetectionandtrackingprocesswithouttheinterventionoftheCQP.Therestofthissectioncoversdifferentstagesofdetectionandtrackingprocessinchronologicalorder. A.Initialselectionofsensornodes:Themainpurposeofthisstageistodetecttheinitialoccurrenceofthephenomena.Thephenomenacanoccuratmultiplelocations, 129 PAGE 130 Figure63. TypesofmessagesintheWSN Figure64. TheTransitionRules hence,itisnotsufcienttomonitoronespeciclocation.However,monitoringtheentireareawithouttheoccurrenceofphenomenawouldbeextravagant.Therefore,wecanapplyatradeoffbetweenthetwoapproachesbyselectingthesensorsdeployedatvulnerablelocationsasOBnodesandkeepthemactive.Wecanselectthesevulnerablelocationsonthebasisofthetypeoflocationorthepasthistory.Forinstance,todetect 130 PAGE 131 Figure65. StateTransitionDiagramforaSensornode Figure66. Expansionofthephenomenacloud gasleakageinthepipeline,itmightbeusefultochoosethesensorslocatedatvalvesandjointsasOBnodesandkeepthemactive. B.Monitoringofinitialoccurrenceofphenomena:WeassumethattimeisdividedintodiscretetimeslotscalledEpochs.AtthebeginningofeveryEpoch,theinitiallyactiveOBnodeswillcollecttheirreadingstocheckiftheyaredetectpositive.Ifanyofthem 131 PAGE 132 aredetectpositive,theywillbroadcastanINVKmessagetotheirimmediateinactiveOneighborsandtransitionintoBnodes,basedonruleR2.AfterreceivingtheINVK,theinactiveOneighborswilltransitionintoOBnodesandbecomeactive,basedonruleR1.IfanactivenodeinanEpochisdetectpositive,itbroadcastsa+ivePHSTmessagetoitsneighbors,otherwise,itbroadcastsaivePHSTmessage. C.Growthofphenomena:WhenthephenomenagrowssomeoftheOBnodesbecomedetectpositive.TheseOBnodesbroadcastINVKmessagestotheirinactiveOneighborsandtransitionintoBnodes,basedonruleR1.TheinactiveOnodesonreceivingtheINVKmessages,transitionintoOBnodes,basedonruleR2.Further,duringthegrowthofphenomena,someBnodes,onreceiving+ivePHSTmessages,maynoticethatalltheirneighborsaredetectpositive.Additionally,iftheyhaveatleastoneBnodeintheirneighborhood,theytransitionintoIBnodes,basedonruleR3,elsetheytransitionintoInodes,basedonruleR4andbecomeinactive.Eventually,thephenomenaisalwayscoveredbythesetofcurrentlyactivenodesandtheinformationaboutthelocationofthephenomenaboundarycanbecollectedfromthesetofBnodes. D.Shrinkingofphenomena:Whenthephenomenashrinks,someofthecurrentBnodesbecomedetectnegative.IfanyoftheseBnodeshaveatleastonedetectpositiveBnodeintheirneighborhood,theytransitionintoOBnodes,basedonruleR7.Otherwise,theytransitionintoOnodesandbecomeinactive,basedonruleR8.Further,duringtheshrinkingphase,ifanIBnodeonreceivingaivePHSTnoticesthatithasanOBnodeinitsneighborhood,ittransitionsintoaBnode,basedonruleR6andbroadcastsanIVNKmessagetoinvokeitsinactiveIneighbors.TheseInodes,onreceivingtheINVKmessages,activateandtransitionintoIBnodes,basedonruleR5.ThiswaytheinformationaboutthelocationofthephenomenaboundaryisalwayscontainedinthecurrentsetofBnodes. E.AggregationandReportingUpdatemessagestoCQP:Whenthereisanyvariationinthephenomenaboundary,itshouldbereportedtotheCQPthrough 132 PAGE 133 Figure67. Shrinkingofthephenomenacloud updatemessages.InthefollowingsectionwedescribeanefcientclusteringanddataaggregationmechanismforeffectivelyreducingthetrafcgeneratedbytheupdatemessagesdestinedtoCQPwithoutcompromisingtheamountofinformationtobereported.SinceweassumetheCQPisawareofthelocationofeachsensornode,aGUIbasedphenomenaboundaryvisualizationapplicationcanbedeveloped.Thisapplicationwilltaketheonlineinformationaboutthecurrentsetofboundarynodesandwillestimateanddisplaythemapoftheareaaffectedbythephenomena.Further,themapwilldynamicallyevolvebasedonthevariationsinthesetofboundarynodesB. F.Handlingfailures:ThefailureofsensornodesinWSNsisunavoidable.ThismayaffectthedetectionandtrackingprocessassomeOnodesmaynotactivateduetothefailureofsomeOBnodesduringthegrowthofthephenomena.Inaddition,itisalsopossiblethatduringtheshrinkingphasesomeIBnodesmayfailandwouldnotinvoketheInodestocovertheshrinkingofthephenomena.Insuchcases,ifinsomeEpoch,anOnodeoranInodedoesnotreceiveaivePHSTor+ivePHSTfromtheirrespectiveOBorIBneighbors,thentheymustassumesomefailurehasoccurredandbecomeactivebytransitionintoOBandIBnodesrespectively.Thiswillascertainthatthefailuredoes 133 PAGE 134 notaffectthedetectionandtrackingprocessandphenomenaboundarywillalwaysbecoveredbythecurrentsetofactivenodes. Figure68. Xh)]TJ /F3 11.955 Tf 11.95 0 Td[(YhcoordinateSystemforHexagontilingH 6.4LocalizedClusteringandDataAggregation Inthissection,werstdescribealocalizedmethodforgeographicallyclusteringtheWSN.Wethendiscussadataaggregationmethodtoaggregatethephenomenaboundaryinformationattheclusterheadstoformupdatemessages. A.Localizednetworkclustering: WelocallygenerateageographicalclusteringoftheWSN.Thegeneratedclustersaredisjointandrespectivelylocatedwithinnonoverlappingregularhexagonsofsidesr 2formingahexagontilingoftheareacoveredbytheWSN,asshowninFigure 68 .Onthebasisofthehexagoncenters,anewXh)]TJ /F3 11.955 Tf 12.72 0 Td[(Yhcoordinatesystemcanbegeneratedwithaxisinclinedat60o.Thisnewcoordinatesystemhastwounitvectors!i(p 3 2r,0)and!j(p 3 4r,3 4r).Asensornodeneedstondthehexagoninwhichitislocatedtoidentifyitscluster.Thelocationofeachnodev2Vi.e(xv,yv)on2Disidentiedusingsomeadhocpositioningmethod[ 54 55 ]orsensornodesmaybeequippedwithGPSfunctionality.EachnodeisawareoftheCQP'slocation(xb,yb)onthe2Dplane.TheCQP'slocationon 134 PAGE 135 Xh)]TJ /F3 11.955 Tf 10.38 0 Td[(Yhcoordinatesystemis(0,0).Basedonthis,anodev2Videntiesitscoordinates(xhv,yhv)andtheintegralcoordinatesh(i,j)ofitshexagoninXh)]TJ /F3 11.955 Tf 12.3 0 Td[(Yhcoordinatesystemasfollows: xhv=fxv)]TJ /F3 11.955 Tf 27.73 8.09 Td[(yv tan60og=rp 3 2 (6) yhv=yvsin60o=rp 3 2 (6) Thecoordinatesofthehexagonh(i,j)inwhichnodevislocatedisgivenas: i=$fxv)]TJ /F3 11.955 Tf 27.74 8.08 Td[(yv tan60og=rp 3 2+1 2% (6) j=$yvsin60o=rp 3 2+1 2% (6) DuringtheinceptionoftheWSN,eachsensornodev2Videntiesitslocation(xv,yv)andhexagonh(i,j)andexchangesthisinformationwithitsneighbors.Thenodeslocatedwithinthesamehexagonformacluster.Onthebasisoffactorssuchasthemaximumenergycontained,aclusterheadcanbeelected(smallestidisusedtobreaktheties).Basedonthenodeids,theclusterheadformsasortedlistofnodesintheclusteralongwiththeirrespectivelocations.TheclusterheadthensendsamessagecontainingthislistalongwiththehexagoncoordinatesoftheclustertotheCQP.TheCQPformsahashmapindexedonthebasisofhexagoncoordinatesandstoresinitthesortedlistofnodesinthehexagon. B.DataAggregationandReporting:TheclusterheadgeneratesabitarraycalledReportarray.TheReportarraycontainsabitforeachnodeinthehexagon,arrangedinsortedorderoftheirids.IfaclusterheadhasBnodesinitshexagon,asshowninFigure 69 ,itreceivesBINFOmessagesfromthemandgeneratestheReportarray,settingthebitscorrespondingtotheBnodesinthehexagon.ItthensendsthisReportarraytotheCQPalongwithitshexagoncoordinatesinaPINFOmessage.The 135 PAGE 136 CQPonreceivingthePINFOmessage,basedonthehexagoncoordinatesaccessesthehashmap.ItthenidentiestheboundarynodesinthehexagonusingtheReportarrayandstoresthisinformationinthehashmap.Theinformationabouttheboundarynodes,storedinthehashmapcaneasilybeusedasaninputtotheGUIbasedphenomenaboundaryvisualizationapplicationtogenerateanddisplaythemapoftheareaaffectedbythephenomena. Figure69. Dataaggregationbasedonclusteringgeneratedbythehexagonaltiling Figure610. Powerconsumptionspecicationsforasensornode 6.5PerformanceEvaluation Inthissection,weevaluatetheeffectivenessandefciencyofourproposedprotocolintermsofresourceutilizationandenergyconsumptionthroughsimulations.WeconsideredaWSNhaving2000sensornodesdeployedonasquareareaofsides600m.Nodes 136 PAGE 137 Figure611. Comparisonbasedonnumberofboundarynodes. Figure612. Comparisonbasedonnumberofupdatemessages. Figure613. Comparisonbasedonenergyconsumption. Figure614. Comparisonbasedonmessagesexchanged. intheWSNcommunicatebasedonZigbeeprotocol(IEEE802.15.4).Eachnodehasasingleradiointerfacewithtransmissionrange10m.ThepowerconsumptionspecicationsforthesensornodesareprovidedinFigure 610 .WecomparedourproposedprotocolwiththeTOCOBprotocolproposedbyKimet.al[ 13 ].Thecomparisonwasbasedonthreeimportantfactors:1)BoundarynodesandupdatemessagessendtotheCQP,2)Energyconsumptionand3)Protocolmessagesexchangedbythenodestoimplementtheprotocol. Simulationswereperformedintwodifferentsetups.Intherstsetup,weperformanEpochwisecomparisonoftwoprotocols.Wesimulatedthedynamicphenomenabyspawningitsthreeoccurrencesatlocations(200,200),(400,200)and(400,300), 137 PAGE 138 Figure615. Comparisonbasedonnumberofupdatemessagesatdifferentphenomenaexpansionspeed. Figure616. Comparisonbasedonenergyconsumptionatdifferentphenomenaexpansionspeed. Figure617. Comparisonbasedonmessagesexchangedatdifferentphenomenaexpansionspeed. followedbytheirrandommotionandexpansionoverthesquarearea.Foreachfactor,weran100iterationsandaveragedtheresults.Eachiterationranfor60Epochs.Inthesecondsetup,weperformthecomparisonoftwoprotocolsbasedonexpansionspeedofthephenomena.Wesimulatedthephenomenabyspawningitsoccurrenceatlocation(300,300)followedbyitsexpansionatvariousspeeds.Foreachofthethreefactors,weran100iterationsandaveragedtheresults.Eachiterationranfor30Epochs. 138 PAGE 139 Figure618. SnapshotofphenomenainWSN. Figure619. Estimatedboundarywith0%messageloss. Figure620. Estimatedboundarywith15%messageloss. Figure621. Estimatedboundarywith30%messageloss. Figure622. Estimatedboundarywith45%messageloss. A.BoundaryNodesandupdatemessages:Figure 611 & 612 showthecomparisonoftwoprotocolsbasedonnumberofboundarynodesandupdatemessagesrespectively.ThetwogurestogetherreecttheefciencyofourproposedlocalizedclusteringanddataaggregationprotocolinreducingthenumberofupdatemessagesdestinedtoCQPwithoutleavingbehindtheinformationgeneratedbyanyboundarynode.Ourprotocolgenerates22%lesserboundarynodesand65%lesserupdatemessagesin 139 PAGE 140 comparisontoTOCOB,whichreectsbetterresourceusageandlessernetworktrafcdestinedtotheCQPcontainingtheinformationfromalltheboundarynodes. Figure 615 showstheeffectofphenomenaspeedontheupdatemessagesgeneratedforeachprotocol.Itcanbeobservedthatthenumberofupdatemessagesisproportionaltothephenomenaspeed.Thisisbecausewhenthephenomenonexpandswithhigherspeed,therearelargerchangesinthephenomenaboundary,whichresultsinlargerupdatemessages.ItcanbeseeninFigure 615 thatourprotocolhandlesthehigherphenomenaspeedmuchmoreefcientlyincomparisontoTOCOB. Furthermore,anupdatemessagegeneratedbyarepresentativenodeinTOCOBhasapayloadsizeof3bytesandcarriestheinformationofonlyasingleCVN,whereasinourcaseweobservethatanupdatemessage(PINFO)generatedbyaclusterheadhasapayloadsizeof3to4bytesandcontainsReportarraywhichcarriestheinformationofalltheboundarynodesinthecluster. B.EnergyConsumption:Figure 613 showstheEpochwiseenergyconsumptionofboththeprotocols.InTOCOB,asallthesensornodesactivateduringeachsamplingperiodtotakereadings,hence,itisnotveryenergyefcient.However,inourprotocolonlyIB,BandOBnodesactivatetocollectthereadingsduringeachsamplingperiod.Weobservethatourprotocolconsume90%lesserenergythanTOCOB. Figure 616 showsthatenergyconsumptionisproportionaltothespeedofthephenomena.OurprotocolshowsmuchbetterresultsincomparisontoTOCOBwhenthephenomenamovesathigherspeeds. C.Messagesexchangedforprotocolimplementation:Figure 614 and 617 showcomparisonofthenumberofmessagesneededtobeexchangedamongtheneighboringsensornodestoimplementthetwoprotocolinWSN.ItcanbeobservedthatTOCOBneedslesserprotocolmessagestocommunicate.Themainreasonforthisisthatourprotocolneedsthenodesclosetothephenomenaboundarytoremainactiveandthey 140 PAGE 141 needtocommunicatetheirstatustotheirneighbors,whichresultsinanincreaseintheexchangedmessageoverhead. D.EffectofmessagelossesonestimationofphenomenaboundaryatCQP:Ourprotocolworksfordetectingandtrackingphenomenaofanyirregularshape,butforeaseofimplementationweconsiderthephenomenashapetobeacirculardisk.Figure 618 showsasnapshotofadynamicallyspreadingphenomena.Figure 619 620 621 and 622 showtheestimatedphenomenaboundaryatCQPforthesnapshotinFigure 618 ,whenthemessagelossesintheWSNare0%,15%,30%and45%respectively.ItcanbeobservedthatourproposedprotocolisrobustagainstthenetworkmessagelossesandproduceareasonablygoodestimationofthephenomenaboundaryattheCQPevenif45%ofthenetworkmessagesarelost. 6.6Conclusion Inthispaper,weproposedanovelprotocolfordetectionandtrackingofdynamicphenomenaofanyirregularshapethroughWSN,withanobjectiveofminimizingtheresourceusageandenergyconsumption.Wealsoproposedarobustlocalizedclusteringanddataaggregationmethod,whichhelpsinreducingthenetworktrafcgeneratedbytheinformationpacketdestinedtotheCQP.Theexperimentalresultsshowsthatourproposedprotocolconsumed90%lesserenergyandgenerates65%lessernetworktrafcdestinedtotheCQP,incomparisontotheexistingwork.Furthermore,ourproposedprotocolisrobustagainstthenetworkmessagelossesandproducereasonablygoodboundaryestimationattheCQPevenif45%ofthenetworkmessagesarelost. 141 PAGE 142 CHAPTER7CONCLUSION ThisdissertationmainlyfocusesonfollowingtwoimperativeoptimizationproblemsinWSNs: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena(phenomenacloud). InChapter 2 ,weformulatedatabroadcastinginWSNsasInterferenceawarebroadcastscheduling(IABS)problemwithanobjectivetominimizethebroadcastlatency.WemodelWSNin2Dasadiskgraphandin3DasaBallGraph.Weconsideramorerealisticnetworkmodelwherethenodesmayhavedifferenttransmissionranges,whiletheirinterferencerangeistimesoftheirtransmissionrange,where>1.WeproposeO(1)centralizedapproximationalgorithmsforIABSproblemin2Dand3DWSNsrespectively.Theseapproximationalgorithmshavethestateoftheartapproximationratioforthenetworkmodelweconsidered. Further,inChapter 3 ,basedonthenetworkandinterferencemodelintroducedinChapter 2 ,westudylocalizeddatabroadcastingandproposealocalizedapproximationalgorithmfordatabroadcast.Ouralgorithmhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2.ThisistherstlocalizedapproximationratiofordatabroadcastinginWSNs.Wealsoextendedourlocalizedalgorithmfor3DWSNs. Furthermore,inChapter 4 ,westudythealltoalldatabroadcastingandalltoonedataaggregationandpropose: 1.AO(1)distributedapproximationalgorithmforalltoonedataaggregation. 2.AO(1)distributedapproximationalgorithmforalltoalldatabroadcast. 3.ALocalizedalgorithmforalltoalldatabroadcast. AlltoonedataaggregationisafundamentaloperationinWSNs,inwhichthedatafromallthenodesisaggregatedinasinknodeforfurtherprocessingandforwarding.Ourdistributedalgorithmforalltoonedataaggregationistherstinliteratureandhas 142 PAGE 143 aconstantapproximationguaranteeof2l2(+1) p 3+1m2.Ourdistributedalgorithmforalltoalldatabroadcastingisalsotherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. InChapter 5 ,weintroduceamathematicalmodelandinnetworkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergyefcient,localized,innetworkalgorithmforrealtimedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizingtheenergyconsumptionofthephenomenacloudsdetectionandtracking.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 4.Providinganovellocalizedalgorithmwhichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinarealworldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 6.Validatingourapproachesusingbothrealworldapplicationsandsimulationstoanalyzeitsperformanceandresourcerequirementsaswellascomparingitwiththatofstreambasedapproaches. 143 PAGE 144 Furthermore,inChapter 6 ,weprovideanenergyefcientlocalizedinnetworkdetectionandtrackingprotocolfortrackingtheboundaryofthephenomenacloud.Thisprotocolismorerelevantforscenariossuchasoilspills,gasleakage,etc,whereitismoresensibletodetectandtrackonlythephenomenaboundaryengulngtheaffectedareainsteadoftrackingtheentirephenomena.Simulationresultsareprovidedtoshowthattheproposedprotocolismoreefcientthantheexistingworks. 144 PAGE 145 REFERENCES [1] S.H.Huang,P.J.Wan,J.Deng,andY.Han,Broadcastschedulingininterferenceenvironment,inIEEETransactiononMobileComputing,2008,vol.7. [2] E.BiagioniandK.Bridges,Theapplicationofremotesensortechnologytoassisttherecoveryofrareandendangeredspecies,InSpecialissueonDistributedSensorNetworksfortheInternationalJournalofHighPerformanceComputingApplications,August2002. [3] E.BiagioniandG.Sasaki,Wirelesssensorplacementforreliableandefcientdatacollection,inInProceedingsoftheHawaiiiInternationalConferenceonSystemsSciences,January2003. [4] A.Cerpa,J.Elson,D.Estrin,L.Girod,M.Hamilton,andJ.Zhao,Habitatmonitoring:Applicationdriverforwirelesscommunicationstechnology,inInProceedingsofthe2001ACMSIGCOMMWorkshoponDataCommunicationsinLatinAmericaandtheCaribbean,April2001. [5] A.Mainwaring,J.Polastre,R.Szewczyk,D.Culler,andJ.Anderson,Wirelesssensornetworksforhabitatmonitoring,inInACMInternationalWorkshoponWirelessSensorNetworksandApplications(WSNA'02),Atlanta,GA,September2002. [6] D.C.Steere,A.Baptista,D.McNamee,C.Pu,andJ.Walpole,Researchchallengesinenvironmentalobservationandforecastingsystems,inInProceedingsofthesixthannualinternationalconferenceonMobilecomputingandnetworking.2000,ACMPress. [7] H.Wang,J.Elson,L.Girod,D.Estrin,andK.Yao,Targetclassicationandlocalizationinhabitatmonitoring,inInProceedingsoftheIEEEICASSP2003,HongKong,April2003. [8] R.Szewczyk,E.Osterweil,J.Polastre,M.Hamilton,A.Mainwaring,andD.Estrin,Habitatmonitoringwithsensornetworks,Commun.ACM,vol.47,no.6,pp.34,2004. [9] S.Kim,S.Pakzad,D.Culler,J.Demmel,G.Fenves,S.Glaser,andM.Turon,Wirelesssensornetworksforstructuralhealthmonitoring,inSenSys'06:Proceedingsofthe4thinternationalconferenceonEmbeddednetworkedsensorsystems,NewYork,NY,USA,2006,pp.427,ACM. [10] S.Kim,P.S.,C.D.,D.J.,F.G.,G.S.,andM.Turon,Healthmonitoringofcivilinfrastructuresusingwirelesssensornetworks,inInformationProcessinginSensorNetworks,2007.IPSN2007.6thInternationalSymposiumon,April2007,pp.254. 145 PAGE 146 [11] S.RostandH.Balakrishnan,Memento:AHealthMonitoringSystemforWirelessSensorNetworks,inIEEESECON,Reston,VA,September2006. [12] X.ji,H.Zha,M.J.J.,andK.G.,Dynamicclusterstructureforobjectdetectionandtrackinginwirelessadhocsensornetworks,IEEEICCC'04,2004. [13] J.H.Kim,K.B.Kim,C.S.Hussain,M.W.Cui,M.S.Park,M.W.Cui,andM.S.Park,Energyefcienttrackingofcontinuousobjectsinwirelesssensornetworks,UIC'08,2008. [14] N.Kurata,B.F.Spencer,andM.Sandoval,Efcientbroadcastinginmultiradiomultichannel,andmultihopwirelessnetworkbasedonselfpruning,inHPCC'07,2007. [15] R.Gandhi,S.Parthasarthy,andA.Mishra,Minimizingbroadcastlatencyandredundancyinadhocnetworks,inMobihoc'03,2003,pp.222. [16] C.Ho,O.Katia,T.Gene,andV.Kumar,Floodingforreliablemulticastinmultihopadhocnetworks,inDIALM'99:Proceedingsofthe3rdinternationalworkshoponDiscretealgorithmsandmethodsformobilecomputingandcommunications,NewYork,NY,USA,1999,pp.64,ACM. [17] K.Obraczka,K.Viswanath,andG.Tsudik,Floodingforreliablemulticastinmultihopadhocnetworks,Wirel.Netw.,vol.7,no.6,pp.627,2001. [18] S.Y.Ni,Y.C.Tseng,Y.S.Chen,andJ.P.Sheu,Thebroadcaststormprobleminwirelessadhocnetwork,inMobiCom'99,1999,pp.151. [19] S.Duttagupta,K.Ramamritham,andP.Ramanathan,Distributedboundarytrackingusingsensornetworks,inThe3rdIEEEIntl.ConferenceonMobileAdhocandSensorSystems,Vancouver,Canada,October2006. [20] K.Ren,K.Zeng,andW.Lou,Secureandfaulttoleranteventboundarydetectioninwirelesssensornetworks,WirelessCommunications,IEEETransactionson,January2008. [21] C.Zhang,Y.Zhang,andY.Fang,Distributededgedetectionwithcompositehypothesistestinwirelesssensornetworks,WirelessNetworks,January2009. [22] P.K.Liao,M.K.Chang,andC.C.Kuo,Distributededgedetectionwithcompositehypothesistestinwirelesssensornetworks,GLOBECOM'04,2004. [23] M.T.Thai,F.Wang,D.H.Du,andX.Jia,Coverageproblemsinwirelesssensornetworks:designsandanalysis,IJSNET,2008. [24] I.ChlamtacandS.Kutten,Onbroadcastinginradionetworksproblemsanalysisandprotocoldesign,IEEETransactionsonCommunications,vol.33,pp.1240,1985. 146 PAGE 147 [25] M.ElkinandG.Kortsarz,Animprovedalgorithmforradionetworks,SymposiumOnDiscreteAlgorithms(SODA),2005. [26] I.GaberandY.Mansour,Centralizedbroadcastonmultihopradionetworks,JournalofAlgorithms,vol.46,no.1,pp.1,2003. [27] E.KushilevitzandY.Mansour,An!(dlog(n=d))lowerboundforbroadcastinradionetworks,inSIAMjournalonComputing,1998,vol.27,pp.702. [28] D.R.KowalskiandA.Pelc,Centralizeddeterministicbroadcastinginundirectedmultihopradionetwork,inAPPROXRANDOM'04,2004. [29] I.ChlamtacandO.Weinstein,Thewaveexpansionapproachtobroadcastingprobleminmultihopradionetwork,IEEETransactionsonCommunications,vol.39,pp.426,1991. [30] M.ElkinandG.Kortsarz,Logarithmicinapproximabilityoftheradiobroadcastproblem,JournalofAlgorithms,vol.52,pp.8,2004. [31] M.ElkinandG.Kortsarz,Polylogarithmicadditiveinapproximabilityoftheradiobroadcastproblem,InAPPROXRANDOM'04:Proc.of7thInternationalworkshoponApproximationAlgorithmsforCombinatorialOptimizationProblems,2004. [32] S.H.Huang,P.J.Wan,X.Jia,H.Du,andW.Shang,Minimumlatencybroadcastschedulinginwirelessadhocnetworks,inINFOCOM'07,2007,pp.733. [33] L.Gasieniec,D.Peleg,andQ.Xin.,Fastercommunicationinknowntopologyradionetwork,inPODC'05:Proceedingof24thannualsymposiumonPrinciplesofdistributedcomputing,2005,pp.129. [34] X.G.Viennot,Astrahlerbijectionbetweendyckpathsandplanartrees,inDiscreteMath,2002. [35] Z.Chen,C.Qiao,J.Xu,andT.Lee,Aconstantapproximationalgorithmforinterferenceawarebroadcastinwirelessnetworks,inINFOCOM'07,2007,pp.740. [36] R.Mahjourian,F.Chen,R.Tiwari,M.T.Thai,H.Zhai,andY.Fang,Anapproximationalgorithmforconictawarebroadcastschedulinginwirelessadhocnetworks,inMobiHoc'08,2008,pp.331. [37] X.Chen,X.Hu,andJ.Zhu,Minimumdataaggregationtimeprobleminwirelesssensornetworks,inInMSN2005,2005,pp.133. [38] S.H.Huang,P.J.Wan,T.Chinh,Y.S.li,andF.Yao,Nearlyconstantapproximationfordataaggregationtimeprobleminwirelesssensornetworks,inInIEEEINFOCOM2007,2007. 147 PAGE 148 [39] X.Xu,S.Wang,X.Mao,S.Tang,andX.Li,Animprovedapproximationalgorithmfordataaggregationinmultihopwirelesssensornetworks,inInACMMobihoc2009,2009. [40] P.J.Wan,S.H.Huang,L.Wang,Z.Wan,andX.Jia,Minimumlatencyaggregationschedulinginmulyihopwirelesssensornetworks,inInACMMobihoc2009,2009. [41] P.Juang,H.Oki,Y.Wang,M.Martonosi,L.Peh,andD.Rubenstein,Energyefcientcomputingforwildlifetracking:designtradeoffsandearlyexperienceswithzebranet,SIGARCHComput.Archit.News,vol.30,no.5,pp.96,2002. [42] D.McErleanandS.Narayanan,Distributeddetectionandtrackinginsensornetworks,inProc.36thAsilomarConferenceonSignals,SystemsandComputers,2002. [43] Palm,The29palmsexperiment:Trackingvehicleswithauavdeliveredsensornetwork:http://tinyos.millennium.berkeley.edu/29palms.htm.,2000. [44] S.Duttagupta,K.Ramamritham,andP.Kulkarni,Trackingdynamicboundaryfrontsusingrangesensors,inThefthEuropeanConferenceonWirelessSensorNetworks,January2008. [45] C.ZhongandM.Worboys,Energyefcientcontinuousboundarymonitoringinsensornetworks,inTechnicalReport,http://www.spatial.maine.edu/czhong/boundary monitoring.pdf,2007. [46] M.Ali,M.Mokbel,W.Aref,andI.Kamel,Detectionandtrackingofdiscretephenomenainsensornetworkdatabases,inSSDBM'2005:Proceedingsofthe17thinternationalconferenceonScienticandstatisticaldatabasemanagement,Berkeley,CA,US,2005,pp.163,LawrenceBerkeleyLaboratory. [47] R.Kremens,J.Faulring,A.Gallagher,A.Seema,andA.Vodacek,Autonomouselddeployablewildlandresensors,inInternationalJournalofWildlandFire,2003,vol.12,pp.237. [48] J.Heidemann,Y.Li,A.Syed,J.Wills,andW.Ye,Underwatersensornetworking:Researchchallengesandpotentialapplications,inUSC/ISITechnicalReportISITR2005603,2005. [49] J.Cassels,Anintroductiontothegeometryofnumbers,inBerlin:SpringerVerlag,1971. [50] W.MathWorld,Spacellingpolyhedron, http://mathworld.wolfram.com/SpaceFillingPolyhedron.html [51] S.H.Huang,H.Du,andE.K.Park,Minimumlatencygossipinginmultihopwirelessnetwork,inInProceedingsofMobihoc2008,2008,pp.733. 148 PAGE 149 [52] R.Tiwari,T.Dinh,andM.T.Thai,Onapproximationalgorithmsforinterferenceawarebroadcastschedulingin2dand3dwirelesssensornetworks,inInproceedingsofInternationalconferenceonWirelessAlgorithms,SystemsandApplications,WASA'09,2009. [53] P.GuptaandP.Kumar,Thecapacityofwirelessnetworks,inIEEETransactiononInformationTheory,March2000. [54] B.Niculescu,Adhocpositioningsystem(aps)usingaoa,inINFOCOM'03,2003. [55] B.Niculescu,Adhocpositioningsystem(aps),inInGLOBECOM'01,November2001. [56] B.AwerbuchandR.Gallager,Anewdistributedalgorithmtondbreadthrstsearchtree,inIEEETransactiononInformationTheory,May1987. [57] R.BoseandA.Helal,Localizedinnetworkdetectionandtrackingofphenomenacloudsusingwirelesssensornetworks,inProceedingsoftheInternationalConferenceonIntelligentEnvironments(IE),2009. [58] S.Madden,M.Franklin,J.Hellerstein,andW.Hong,Tag:atinyaggregationserviceforadhocsensornetworks,inProc.of5thAnnualSymposiumonOperatingSystemsDesignandImplementation,2002. [59] S.Bhattacharya,N.Atay,G.Alankus,C.Lu,O.B.Bayazit,andG.Roman,Roadmapqueryforsensornetworkassistednavigationindynamicenvironments,inInternationalConferenceonDistributedComputinginSensorSystems(DCOSS06),2006. [60] N.Bulusu,J.Heidemann,andD.Estrin,Gpslesslowcostoutdoorlocationferverysmalldevices,inIEEEPers.Commun.(SpecialIssueonSmartSpaceandEnvironments),2000,vol.7,pp.28. [61] A.AbbasiandM.Younis,Asurveyonclusteringalgorithmsforwirelesssensornetworks,inComput.Commun.,Oct2007,vol.30,pp.2826. [62] R.Bose,J.King,H.ElZabadani,S.Pickles,andA.Helal,Buildingplugandplaysmarthomesusingtheatlasplatform,inProceedingsofthe4thInternationalConferenceonSmartHomesandHealthTelematics,June2006. [63] A.Helal,W.Mann,H.ElZabadani,J.King,Y.Kaddoura,andE.Jansen,Gatortechsmarthouse:Aprogrammablepervasivespace,inIEEEComputer,March2005. [64] J.King,R.Bose,S.Pickles,A.Helal,andH.Yang,Atlasaserviceorientedsensorplatform,inProceedingof1stIEEEInternationalWorkshoponPracticalIssuesinBuildingSensorNetworkApplications,2006. 149 PAGE 150 [65] R.BoseandA.Helal,Observingwalkingbehaviorofhumansusingdistributedphenomenondetectionandtrackingmechanisms,inProceedingsof2ndInternationalWorkshoponPracticalApplicationsofSensorNetworks,heldinconjunctionwiththeInternationalSymposiumonApplicationsandtheInternet(SAINT),Turku(Finland),2008. [66] M.Cardei,M.T.Thai,Y.Li,andW.Wu,Energyeffcienttargetcoverageinwirelesssensornetworks,inProceedingsofthe24thconferenceoftheIEEECommunicationsSociety(INFOCOM),2005. [67] A.Omotayo,M.Hammad,andK.Barker,Efcientdataharvestingfortracingphenomenainsensornetworks,inProc.18thInternationalConferenceonScienticandStatisticalDatabaseManagement(SSDBM),2006. [68] K.K.ChintalapudiandR.Govindan,Localizededgedetectioninsensorelds,inAdHocNetworksJournal,2003. [69] D.MarthalerandA.L.Bertozzi,Collectivemotionalgorithmsfordeterminingenvironmentalboundaries,inSIAMConferenceonApplicationsofDynamicalSystems,2003. [70] Z.JinandA.L.Bertozzi,Environmentalboundarytrackingandestimationusingmultipleautonomousvehicles,inDecisionandControl,200746thIEEEConferenceon,Dec2007,pp.4918. [71] A.Savvides,J.Fang,andD.Lymberopoulos,Usingmobilesensingnodesfordynamicboundaryestimation,inMobiSys2004WorkshoponApplicationsofMobileEmbeddedSystems(WAMES2004),June2004. 150 PAGE 151 BIOGRAPHICALSKETCH RaviTiwariwasbornin1978,inthehistoriccitynamedAgra,locatedinnorthcentralIndia.HereceivedhisBachelorofEngineeringdegreeincomputerscienceandengineeringintheyear2001fromDr.BhimRaoAmbedkarUniversity(FormallyAgraUniversity),Agra,India.In2004,hereceivedhisMasterofEngineeringdegreewithspecializationincommunication,controlsandnetworkingfromRajeevGandhiTechnicalUniversity,Bhopal,India. 151 1. StreamPDT [46]: A centralized streambased algorithm where phenomena detection and tracking is performed by a Centralized Query Processor (CQP). We simulated NilePDT [46], a wellknown detection system developed at Purdue University, which utilized StreamPDT strategy. 2. DistPDT: A distributed phenomena detection and tracking algorithm which we proposed in our preliminary work [57]. 3. Full Density Algorithm (FDA): The phenomena detection and tracking mechanism described in Section 5.3, in which we have modified the definitions of candidate and potential candidate sensors (from DistPDT) to reduce the number of unnecessary active sensors. 4. Optimized Density Algorithm (ODA): The phenomena detection and tracking mechanism described in Section 5.4.2 after applying the localized protocol to optimize the resource utilization. We also ran the IP formulation introduced in Section 5.4.1 on small sized networks to verify how far our solution is from the optimal solution. Operation Current(mA) Duration(secs) Sampling Sensor. Proce sing or A.0 2.0 Listening tor Messages Reccih in Mcessages ,,' 256kbps 1 5.0 0.002 Transmitting Messages 4f, 256kbps I 5.0 0.002 Figure 519. Power Consumption Specifications for Atlas 5.6.2.1 Experimental setup We performed simulations in the following four different setups: 1. In the first set of simulations, we simulated the random movement and expansion of phenomena cloud for 50 epochs on a rectangular sensor grid of size 121 x 121 deployed over an area of 1200m x 1200m. 110 Similarly, nodes v2 and v3 will be responsible to receive and forward from neighboring hexagons with colors {12, 13, 16, 17, 21, 22, 25} and {1, 2, 3, 6, 7, 8} respectively. Lemma 7. If any two Suppliers nodes sl and s2 in a hexagon have their respective possible providers pi e PPs, and p2 E PPs2 of the same color, pi, p2 belong to the same hexagon. Proof. Let pi and p2 belong to different hexagons hi and h2 respectively of the same color. Based on Algorithm 7, closest distance between h, and h2 must be at least (a )r,~x. But if pi is the neighbor of si and p2 is the neighbor of s2, then the maximum possible distance between hi and h2 will be rTx, which is a contradiction. D Algorithm 7 Hexagon Coloring Algorithm (H, a, /3) 1: k (+l(a3 +] 2: for All h(i,j) E H do 3: if (i < 0) then 4: i' = (k 1) (i mod k) 5: else 6: i' = (i mod k) 7: end if 8: if (j < O) then 9: j = (k 1) (jo mod k) 10: else 11: = (j mod k) 12: end if 13: Color(h(i,j)) = j'k + i'k + 1 14: end for 3.2.2 Broadcast Scheduling of Broadcast Message In this section, we describe the protocol for broadcasting a message m from the source node v,, to all other nodes. We assume that time is divided into sufficiently large discrete time slots called Epochs. All hexagons with color ci are assigned Tth Epochs, such that c, T mod k2, where k2 is the number of colors use by Algorithm 7 to color the hexagon tiling. During comparison to TOCOB, which reflects better resource usage and lesser network traffic destined to the CQP containing the information from all the boundary nodes. Figure 615 shows the effect of phenomena speed on the update messages generated for each protocol. It can be observed that the number of update messages is proportional to the phenomena speed. This is because when the phenomenon expands with higher speed, there are larger changes in the phenomena boundary, which results in larger update messages. It can be seen in Figure 615 that our protocol handles the higher phenomena speed much more efficiently in comparison to TOCOB. Furthermore, an update message generated by a representative node in TOCOB has a payload size of 3 bytes and carries the information of only a single CVN, whereas in our case we observe that an update message (PINFO) generated by a cluster head has a payload size of 3 to 4 bytes and contains Report array which carries the information of all the boundary nodes in the cluster. B. Energy Consumption: Figure 613 shows the Epochwise energy consumption of both the protocols. In TOCOB, as all the sensor nodes activate during each sampling period to take readings, hence, it is not very energy efficient. However, in our protocol only IB, B and OB nodes activate to collect the readings during each sampling period. We observe that our protocol consume 90% lesser energy than TOCOB. Figure 616 shows that energy consumption is proportional to the speed of the phenomena. Our protocol shows much better results in comparison to TOCOB when the phenomena moves at higher speeds. C. Messages exchanged for protocol implementation: Figure 614 and 617 show comparison of the number of messages needed to be exchanged among the neighboring sensor nodes to implement the two protocol in WSN. It can be observed that TOCOB needs lesser protocol messages to communicate. The main reason for this is that our protocol needs the nodes close to the phenomena boundary to remain active and they 140 detection and tracking process is executed innetwork in a localized manner to ensure maximum efficiency. Only those sensor nodes which are in the immediate vicinity of a phenomenon cloud or are lying within the cloud are actively involved in the detection and tracking process. The propagation of this process in the network is governed solely by the behavior of the phenomenon cloud and handled by the sensor nodes in a distributed but cooperative manner using the rules specified in Section 5.3.3, without needing any assistance from the centralized query processor. 5.3.8 Shrinking of Phenomenon Cloud The phenomenon cloud is said to be shrinking when the sensors falling in the tracking region identifies that they no longer satisfy the Phenomena Condition. According to Figure 54, after a sensor transitions into tracking, its neighbors will only send alerts if their readings fail to satisfy the Probability Condition. A tracking sensor is no longer participating in the tracking of the phenomenon cloud if it determines that less than n of its neighbors currently satisfy the Probability Condition. In such a case, the tracking sensor node notifies the query processor which removes the tracking sensor from the Phenomenon Set, thereby signifying that the phenomenon cloud has shrunk. The tracking sensor node then transitions into a candidate sensor using rule R4. When the phenomena cloud further shrinks and the candidate sensor does not even satisfy the Probability Condition, it transforms into a potential candidate sensor using transition rule R5 if it has at least one candidate or tracking sensor node in its neighborhood. And all of the potential candidate neighbors of this sensor node transitions into idle sensors using transition rule R6 if they do not have any other candidate or tracking node in their neighborhood. We make a note that if all the phenomena clouds disappear completely then after all the transitions are applied as per rules given in Section 5.3.3, the sensor space will revert back to the set up described in Section 5.3.4, where only the initial set of potential candidate sensors will remain active. Effect of / on Average Latency .................. Effect of a on Average Latency .................. Comparison of various heuristics algorithms . . . . . . 41 Effect of No. of Nodes on Average E data broadcasting Algorithms..... 42 Effect of No. of Nodes on Average E data broadcasting Algorithms..... 43 Effect of No. of Nodes on Average E data broadcasting Algorithms ..... experimental Approximation experimental Approximation experimental Approximation experimental Approximation 310 311 312 44 Effect of / on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 45 Effect of 3 on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 46 Effect of 3 on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 47 Effect of a on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 48 Effect of a on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 49 Effect of a on Average Experimental Approximation Ratio of broadcasting Algorithms .................. 51 52 53 54 55 56 57 58 59 510 AlltoAll data AlltoOne data OnetoAll data AlltoAll data AlltoOne data OnetoAll data . . . . . . Dissection of the Phenomena Cloud . . . . . . . . . . . . Classification of the Participating Sensors . . . . . . . . . . . Detection and Tracking of a Phenomena Cloud . . . . . . . . . Action Taken by a Sensor Node with respect to its Neighbors which are not idle Ratio of Total Active Sensors to Cloud Size in a Rectangular Sensor Grid .. Partition shape as square .. . . . . . . . . . . . . . . . Partition shape as rhombus ................... .......... Partition shape as Equilateral Triangle. . . . . . . . .. . . ... Partition shape as Regular Hexagon. . . . . . . . ... . . ... The Hexagon Lattice . . . . . . . . . . . . . . . . . . . . . . 63 . . . . . 65 . . . . 66 Ratio of AlltoAll . . . . . 75 Ratio of AlltoOne . . . . . 76 Ratio of OnetoAll . . . . 76 77 78 78 79 80 80 85 86 88 89 93 100 100 100 100 100 The broadcasting structure is a subgraph Gb = (Vb, Eb), which spreads over all hexagons in which WSN nodes are located. It has two kinds of nodes; Supplier nodes and Provider nodes, which are connected through Provider edges (refer Figure 31). Responsible for receiving message m from their Provider Nodes in neighboring hexagons, and supply it to nodes in their hexagon. Responsible for providing message m, if they have already received, to a requesting Supplier Node in the neighboring hexagon. A bidirectional edge connecting a Supplier Node and a Provider Nodes Figure 31. Elements of the Broadcasting Structure. All nodes v c V identify their locations (xv, y,) on 2D plane using some localization method [54, 55] or they may be equipped with GPS devices for this. They also know the location of the base station (xb, Yb) in 2D plane, which is located at (0, 0) in the Xh Yh coordinate system. Each v e V locally computes the integral coordinates of the hexagon h(i,j) in which it is located in Xh Yh coordinate system as follows: = (X Xb) (Y / Tin V2 (31) tan 60 2 2 j= (y, yb) sin 600/r, i (32) After identifying h(i,j), node v identifies the color of h(i,j) using Algorithm 7, which colors the hexagon tiling using k2 (= 3 + 1 colors and guarantees that any two hexagons at closest distance d < (a + 1)rx have different colors. Figure 32 shows an example of hexagon coloring generated by Algorithm 7. Node v broadcast its id, hexagon coordinates h(i,j) and color to its onehop neighbors and based on similar information it receives from its onehop neighbors, it generates: 1. A set HN(v) c N(v), which is a set of nodes located in the same hexagon in which v is located. When a node v is a Supplier node, it broadcasts a Provider Request message to all its neighbors in PPv. The nodes vj e PPv respond with a Provider Response message and become Provider nodes for v and edges connecting them to v become Provider edges. The set of Supplier nodes, Provider nodes and Provider edges form the broadcast structure Gb = (Vb, Eb) for the WSN. 23 24 25 21 22 21 20 117 V0 0 14 1  o Cli o 12 0 O 1o 6 .8 5 1 2 4 Figure 33. An Example showing the functioning of a part of the broadcast structure. Figure 33 shows a portion of the broadcast structure with respect to a single hexagon whose color is 11. Black nodes depict Supplier nodes, gray nodes depict Provider nodes and white nodes are rest of nodes in the hexagon. The edges shown are Provider edges. The Supplier node v, is be responsible to receive and forward the broadcast message in its hexagon, if any one of its Provider in neighboring hexagons with colors {10, 14,15, 20, 21, 24} who has already received the broadcast message. ON BROADCAST SCHEDULING AND DYNAMIC PHENOMENA DETECTION IN WIRELESS SENSOR NETWORKS By RAVI TIWARI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 Figure 26. CoColor Hexagons of h(O, 0) for / = 2 andj = 3. The index of sublattice Rh in H i.e. Idet(A, B) = i2 +j2 + = 19. Theorem 2.1. The coloring generated by the above method is an optimal solution to the Distanced Hexagon Center Coloring problem. Proof. According to Lemma 2, Algorithm 1 optimally identifies cocolor hexagons which forms a rhombic lattice Rh with unit vectors A = i + j and B = j/ (i + j). The number of sublattices similar to Rh in H is given as Idet(A, B) = i2 + j2 + i [49]. Therefore, the minimum number of colors needed to color H are i2 +j2 + ij. If we use i 2 ij 1 colors then at least two rhombic sublattices will be assigned same color. As the distance between the hexagons in different rhombic sublattices is not guaranteed to be at least d, it will not be the solution for Distanced hexagon coloring problem. Therefore, the optimal number of colors needed will be i2 +j2 + i, hence, the provided solution is optimal. D a constant approximation guarantee of 2 2(a/3 + l]. Our distributed algorithm for alltoall data broadcasting is also the first in literature and has a constant approximation guarantee of 4 (2(, +1 2. In Chapter 5, we introduce a mathematical model and innetwork distributed mechanisms with the following specific contributions: 1. Analyzing the structure of phenomena clouds and proposing a set of parameters to comprehensively describe them without requiring complex models. 2. Presenting an energyefficient, localized, innetwork algorithm for realtime detection and tracking of phenomena clouds, which do not require customization of the network routing layers. The proposed algorithm works in an autonomous manner without requiring intervention from the centralized query processor residing in the base station and hence, is suitable for disconnected mode of operation, when continuous communication with the base station cannot be maintained. 3. Introducing a mathematical model based on Integer Program (IP) to further optimizing the energy consumption of the phenomena clouds detection and tracking. This model provides an excellent benchmark for evaluating the performance of the proposed algorithms. 4. Providing a novel localized algorithm which can further enhance the resource utilization based on a new technique, called hexagon tiling. This new algorithm locally allows sensor nodes to be in active or sleeping modes without compromising on the quality of detection and tracking. 5. Presenting a practical application which has been deployed in a realworld smart space and utilizes the phenomena detection and tracking mechanism described in this paper, to solve critical challenges faced during its deployment. 6. Validating our approaches using both realworld applications and simulations to analyze its performance and resource requirements as well as comparing it with that of streambased approaches. 143 a b 1  // 3 1 1,)  II //T \ , c d Figure 23. Comparison of different plane tiling polygon. Figures a, b, c and d respectively show a square, a rhombus, a triangle and a hexagon, having maximum distance within them equal to 1. tiling regular polygons: 1) Square, 2) Rhombus, 3) Equilateral Triangle and 4) Regular Hexagon, as the unit partition shape and compare their areas, as shown in Figure 23. We observe that a regular hexagon of sides 1 has the maximum area. Consequently, we select it as the unit partition shape. Figure 24 shows the regular hexagon tiling of 2D plane. We formally define the regular hexagon tiling and coloring of 2D plane as Distanced Hexagon coloring problem: Distanced Hexagon Coloring problem: Given a regular hexagon tiling H of 2D plane and a distance d e R+, find the minimum number of colors needed to color H, such that two hexagons hl, h, E H having the same color must have the Euclidean distance distance(hl, h2) > d. The distance distance(hl, h2) is measured between two closest points pi and p2, where, p, lies within h, and P2 lies within h2. for assigning ranks to the nodes of BFS tree. In [35], Chen et.al studied this problem in a more realistic model, they considered transmission range is smaller than interference range. They proposed an 0(a2) approximation ratio, where a is the ratio of interference range and transmission range, with a > 1. In [36] Reza et. al studied this problem, considering a > 1 proposed an 0(a2) approximation with a better analysis. Apart from the interference and transmission range they also considered the carrier sensing range. Using a 2Disk model, Scott et. al. studied the broadcast scheduling problem and proposed an approximation algorithm with ratio 6 ( + 2)] [1]. They considered a > 1 and each node has the same transmission range rT and their interference range ri = arT. Unfortunately, almost all above mentioned works considered the same transmission range for all nodes. Only [15] considered a disk graph model, but they considered transmission range and interference range to be same, which is not a practical assumption, as interference range is always greater than the transmission range. Furthermore, all existing works studying broadcast scheduling in wireless networks model the network as a 2D planar graph in which the nodes exists in 2D plane. However, this is not appropriate in all cases, as most of the time the nodes acquire locations in 3D. Furthermore, all existing works in broadcast scheduling provide centralized solutions with some approximation guarantees. There is no localized approximation algorithm in the existing literature. In the existing literature, alltoone aggregation scheduling is mostly studied in UDG with interference range equal to the transmission range. In [37], Chen et. al. proposed a (A 1)approximation algorithm, where A is the maximum node degree. Based on maximal independent set, Huang et. al. [38] proposed an algorithm with latency bound of 23R + A 18, which was improved to 16R + A 14 by Xu et. al. [39]. In [40], Wan et. al. considered that for any node, the interference range is greater than the transmission range and proposed an algorithm with latency /Pp+(15R + A 4), where p is the ratio of [52] R. Tiwari, T. Dinh, and M. T. Thai, "On approximation algorithms for interferenceaware broadcast scheduling in 2d and 3d wireless sensor networks," in In proceedings of International conference on Wireless Algorithms, Systems and Applications, WASA '09, 2009. [53] P. Gupta and P. Kumar, "The capacity of wireless networks," in IEEE Transaction on Information Theory, March 2000. [54] B. Niculescu, "Ad hoc positioning system (aps) using aoa," in INFOCOM '03, 2003. [55] B. Niculescu, "Ad hoc positioning system (aps)," in In GLOBECOM '01, November 2001. [56] B. Awerbuch and R. Gallager, "A new distributed algorithm to find breadth first search tree," in IEEE Transaction on Information Theory, May 1987. [57] R. Bose and A. Helal, "Localized innetwork detection and tracking of phenomena clouds using wireless sensor networks," in Proceedings of the International Conference on Intelligent Environments (IE), 2009. [58] S. Madden, M. Franklin, J. Hellerstein, and W. Hong, "Tag: a tiny aggregation service for ad hoc sensor networks," in Proc. of 5th Annual Symposium on Operating Systems Design and Implementation, 2002. [59] S. Bhattacharya, N. Atay, G. Alankus, C. Lu, O. B. Bayazit, and G. Roman, "Roadmap query for sensor network assisted navigation in dynamic environments," in International Conference on Distributed Computing in Sensor Systems (DCOSS06), 2006. [60] N. Bulusu, J. Heidemann, and D. Estrin, "Gpsless low cost outdoor location fer very small devices," in IEEE Pers. Commun. (Special Issue on Smart Space and Environments), 2000, vol. 7, pp. 2834. [61] A. Abbasi and M. Younis, "A survey on clustering algorithms for wireless sensor networks," in Comput. Commun., Oct 2007, vol. 30, pp. 28262841. [62] R. Bose, J. King, H. EIZabadani, S. Pickles, and A. Helal, "Building plugandplay smart homes using the atlas platform," in Proceedings of the 4th International Conference on Smart Homes and Health Telematics, June 2006. [63] A. Helal, W. Mann, H. EIZabadani, J. King, Y Kaddoura, and E. Jansen, "Gator tech smart house: A programmable pervasive space," in IEEE Computer, March 2005. [64] J. King, R. Bose, S. Pickles, A. Helal, and H. Yang, "Atlas a serviceoriented sensor platform," in Proceeding of 1st IEEE International Workshop on Practical Issues in Building Sensor Network Applications, 2006. 149 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ON BROADCAST SCHEDULING AND DYNAMIC PHENOMENA DETECTION IN WIRELESS SENSOR NETWORKS By Ravi Tiwari August 2010 Chair: My T Thai Major: Computer Engineering Majority of network applications designed on top of Wireless Sensor Networks (WSNs) involve detection and tracking of some physical phenomena. Additionally, they utilize some primitive services such as broadcasting and aggregation for disseminating and collecting information. Broadcasting is an operation to promulgate some information from a source node to all other nodes in the network. In contrast, aggregation is an operation to collect the sensed information from all nodes in the network at a specific sink node. Sensor nodes in WSNs communicate via radio transmissions. Due to Wireless Broadcast Advantage (WBA) of radio transmissions, performing efficient data broadcasting or data aggregation with minimum latency is nontrivial and proved to be NPhard. Flooding is a straightforward approach which can be used. Unfortunately, it generates redundant transmissions, contentions and collisions, which aggravates the network throughput and results in a broadcast storm. Broadcast scheduling and aggregation scheduling are more intelligent and effective mechanisms to perform efficient broadcasting and aggregation respectively. These are based on scheduling the interfering transmissions, which avoids broadcast storm and improves network throughput. Existing researches on broadcast scheduling and aggregation scheduling provide centralized solutions, which cannot be implemented locally. Additionally, they consider very elementary network and interference models, in which, either all sensor nodes have efficient centralized heuristic for broadcast scheduling. Finally, Section 2.7 concludes the chapter. 2.2 Network Model and Problem Definition 2.2.1 Network Model We assume that each sensor node vi has transmission range r,T e [rTn, r,Tx] and interference range r/i = arT (a > 1), where rT, and rTax are the minimum and maximum transmission ranges in the WSN respectively and r=3 > 1. The 2D Network Model: In 2D, the WSN is represented by a directed disk graph G = (V, E), where V is a set of sensor nodes deployed on the 2D plane and E is the set of directed communication links. Each node vi e V is associated with two open disks, the transmission disk DiT and the interference disk D, centered at vi, with radius ri and r/ respectively. If a node vj is located within DiT, there exists a directed link (vi, vj) E E. Additionally, if v, is also located within DT then (vj, vi) E E and there exists a bidirectional link between vi and vj. The 3D Network Model: Similar to 2D, in 3D, the WSN is represented by a directed ball graph G = (V, E). A transmission ball BT and an interference ball Bi are associated with every sensor node vi e V centered at vi with radius r, and r/ respectively. If a node vj is located within Bi', there exists a directed link (vi, vj) e E. Further, if v, is also located within BT then (v,, v,) c E and there exists a bidirectional link between vi and vj. Based on the above network model, we define the interference model as follows: 1. If the Euclidean distance between a transmitter vt, and a receiver vr, i.e. d(vt,, Vr) < rtT, the energy level of the transmitted signal from vt, is sufficient at vr to interpret the transmitted data. 2. If rtT < d(vt,, vr) < r,, the transmitted signal from vt, cannot be correctly interpreted by vr, still it can be perceived. However, if d(vt, v,) > r,, the transmitted signal from vt, is beyond the perception of vr. c A . p Sr Figure 56. Partition shape as square. Figure 57. Partition shape as rhombus. Figure 58. Partition shape as Equilateral Triangle. Figure 59. Partition shape as Regular Hexagon. We assume that all the sensors are equipped with a location identification device such as a GPS or used some localization methods [54, 55, 60]. Further, we assume that all the sensors are aware of the Euclidean location of the base station. This can be done by one broadcast from the base station. We now show that if a node v knows its coordinates (xv, yv) and the coordinates of the base station (xb, yb) in the Cartesian system, then without having the global view of the hexagon tiling, it can locally compute its coordinates (xv, yvh) in the new coordinate system. Furthermore, node v can identify the integral coordinates of the hexagon in which it is located. Figure 510. The Hexagon Lattice 100 r' 5.3.7 Growth of Phenomenon Cloud When a potential candidate sensor satisfies the Probability Condition, it gets transitioned into a candidate sensor using rule R2. It notifies all its neighbors about this transition by broadcasting an alert message. Each of the neighbor sensor on receiving the alert message transitions into a potential candidate if originally they were idle sensors using rule R3. In this manner, the detection mechanism gets distributed and propagated innetwork, without involvement of the centralized query processor, as the phenomenon cloud grows with time. Each sensor node keeps track of its neighborhood via the broadcast alerts that it receives and determines the actions to be undertaken with respect to a specific neighbor based on which category each neighbor falls in, as described in Figure 54. 25 20 0 15 46E 10 0 S00 1000 150 2000 2500 3000 3500 Phenomena Cloud Size Figure 55. Ratio of Total Active Sensors to Cloud Size in a Rectangular Sensor Grid The plot in Figure 55 depicts an example to show the effect a growing phenomenon cloud has on the number of active sensors (tracking, candidates and potential candidate sensors) involved in its detection and tracking. We observe that in our distributed innetwork approach, the number of active sensors required at any given time is only slightly more than the number of sensors actually needed to participate in detection and tracking the phenomenon cloud and the ratio of active sensors versus phenomena cloud size decreases with increase in cloud size. This is due to the fact that the on the practical viability of the entire smart space. This raises a need for a distributed innetwork detection mechanism, where the detection and tracking process is localized to the immediate neighborhood of a phenomenon at any given time and does not require all the sensor nodes to remain unnecessarily active. Along this direction, in Chapter 5, we introduce a mathematical model and innetwork distributed mechanisms with the following specific contributions: 1. Analyzing the structure of phenomena clouds and proposing a set of parameters to comprehensively describe them without requiring complex models. 2. Presenting an energyefficient, localized, innetwork algorithm for realtime detection and tracking of phenomena clouds, which do not require customization of the network routing layers. The proposed algorithm works in an autonomous manner without requiring intervention from the centralized query processor residing in the base station and hence, is suitable for disconnected mode of operation, when continuous communication with the base station cannot be maintained. 3. Introducing a mathematical model based on Integer Program (IP) to further optimizing the energy consumption of the phenomena clouds detection and tracking. This model provides an excellent benchmark for evaluating the performance of the proposed algorithms. 4. Providing a novel localized algorithm which can further enhance the resource utilization based on a new technique, called hexagon tiling. This new algorithm locally allows sensor nodes to be in active or sleeping modes without compromising on the quality of detection and tracking. 5. Presenting a practical application which has been deployed in a realworld smart space and utilizes the phenomena detection and tracking mechanism described in this paper, to solve critical challenges faced during its deployment. a broadcast storm [18]. A more intelligent approach to perform efficient data broadcast or data aggregation is to schedule the interfering transmission. This avoids broadcast storm and considerably improves network throughput and latency. In the existing literature on WSNs, broadcast scheduling and aggregation scheduling are formulated as two important optimization problems with objective to minimize latency. Most of the existing research on phenomena detection and tracking using WSNs assume the phenomena is invariant in shape, size and motion [1923]. However, in real life there exist dynamic phenomena such as oil spills, mud flow, diffusion or leakage of gases that are characterized by nondeterministic variations in shape, size and direction of motion. These dynamic phenomena are termed as phenomena cloud. Due to the absence of any well defined model for phenomena clouds, their detection and tracking through WSNs is extremely challenging. Since sensor nodes have limited energy and processing power, the efficient detection and tracking of phenomena cloud with an objective to maximize network life time is a challenging optimization problem. The inherently distributed nature of sensor nodes introduces many intriguing and challenging optimization problems which have enormous research potential. Efficiently solving these problems is pivotal for resourcefully designing critical applications for WSNs. The focus of this dissertation is mainly on following two imperative optimization problems in WSNs: 1. Efficient data broadcasting and aggregation. 2. Efficient detection and tracking of dynamic phenomena (phenomena cloud). In the rest of this chapter, we provide a detailed introduction and background for these two problems. 1.1 Efficient Data Broadcasting and Aggregation Data broadcasting and data aggregation are two most primitive operations in multihop WSNs. The purpose of data broadcasting is to convey a message from a source to all other nodes. Its latency directly governs the performance of various 