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Broadcast Scheduling and Detection of Dynamic Phenomena in Wireless Sensor Networks

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Title:
Broadcast Scheduling and Detection of Dynamic Phenomena in Wireless Sensor Networks
Creator:
Tiwari, Ravi
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (151 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Computer Engineering
Computer and Information Science and Engineering
Committee Chair:
Thai, My Tra
Committee Members:
Chow, Yuan-Chieh R.
Chen, Shigang
Kahveci, Tamer
Pardalos, Panagote M.
Graduation Date:
8/7/2010

Subjects

Subjects / Keywords:
Aggregation ( jstor )
Algorithms ( jstor )
Approximation ( jstor )
Broadcasting ( jstor )
Broadcasting industry ( jstor )
Hexagons ( jstor )
Octahedrons ( jstor )
Scheduling ( jstor )
Sensors ( jstor )
Tessellations ( jstor )
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
approximation, broadcast, centralized, combinatorial, interference, localized, optimization, phenomena, scheduling
Genre:
Electronic Thesis or Dissertation
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
Computer Engineering thesis, Ph.D.

Notes

Abstract:
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 NP-hard. 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 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 non-deterministic 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 all-to-one data aggregation. 4. The first constant distributed approximation algorithm for all-to-all broadcast scheduling. 5. A localized in-network algorithm for detection and tracking of phenomena cloud. 6. An energy efficient localized algorithm for detection and tracking of phenomena cloud boundary. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2010.
Local:
Adviser: Thai, My Tra.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-08-31
Statement of Responsibility:
by Ravi Tiwari.

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UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
8/31/2011
Resource Identifier:
004979692 ( ALEPH )
705931170 ( OCLC )
Classification:
LD1780 2010 ( lcc )

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Figure 5-11. 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























Figure 2-5. 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 2-5 (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 2-5 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 co-color hexagon algorithm, illustrated in Algorithm 1. In
Lemma 2, we prove that for any arbitrary distance d R+, Algorithm 1 optimally

identifies co-color 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 co-color hexagon h(i' + i,j' j) of h(i',j') in the first quadrant















SMiddle Region

Figure 5-1. 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 5-1. 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









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

interference-aware 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









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 multi-hop 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

micro-electronics and wireless technologies, various types of cost effective sensor

nodes are modeled and realized for different applications such as environment and

habitat monitoring [2-8], health monitoring [9-11], 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 NP-hard [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









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 5-6,5-7,5-8 and 5-9, 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 5-10. 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.









6-14 Comparison based on messages exchanged. . . . . . . . . ... 137

6-15 Comparison based on number of update messages at different phenomena
expansion speed . . . . . . . .. . . . . . . . .. 138

6-16 Comparison based on energy consumption at different phenomena expansion
spe ed . . . . . . . . . . . . . . . . . . . . 13 8

6-17 Comparison based on messages exchanged at different phenomena expansion
spe ed . . . . . . . . . . . . . . . . . . . . 13 8

6-18 Snapshot of phenomena in WSN. . . . . . . . ... ........ 139

6-19 Estimated boundary with 0% message loss. . . . . . . . ..... 139

6-20 Estimated boundary with 15% message loss. . . . . . . . . ... 139

6-21 Estimated boundary with 30% message loss. . . . . . . . . ... 139

6-22 Estimated boundary with 45% message loss. . . . . . . . . ... 139










based on which region they fall in at a particular time and how they are utilized to

perform localized in-network 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 real-time tracking data

produced by the sensor network. Figure 5-3 pictorially depicts an example for detection

and tracking process of a single phenomenon cloud.




CI ore rei on
0


00 0 0 r I h-kig
0 o 0 o Candidate
Potential Candidate
0 Idle Sensors

Figure 5-2. Classification of the Participating Sensors


5.3.1 Classification of Sensors

Figure 6-2 shows the phenomenon cloud depicted in Figure 5-1 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:









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 5-14 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 5-15), 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









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 non-conflicting 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 interference-awareness described in Lemma 1. This helps in increasing the number

of simultaneous interference-aware 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









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 co-ordinates to its one hop
neighbors.
Step 3: Based on the color and hexagon information from one-hop 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 sub-graph generated by the bi-directional 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 co-ordinate

system, described in Section 2.3.









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









The ISA takes two consecutive layers Li and Lj as inputs and generates an

interference-aware transmission schedule from Li to Lj. In order to do this, ISA first

generates a maximal independent set MIS(Lj) of the sub-graph 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+,)
i-i-l
end while


2.5.2 O(1)-Approximation Ratio for Interference-Aware Broadcast Scheduling
Problem in 2-Dimension

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 interference-awareness described in Lemma 1, which results in

interference-aware transmission schedule. O









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 interference-awareness 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.









DislAIIToAll IVr'rim nial Ralio '
LnC..-l-ToA.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 4-4. Effect of on Average Experimental Approximation Ratio of All-to-All 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 4-4 shows the plots of localized all-to-all data broadcasting and distributed

all-to-all 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.









% .-
r' c %





S ,
'I I

~-I
d(,v % )>=rT^a+)


Figure 2-1. Sufficient conditions for interference-awareness 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 2-2. Sufficient conditions for interference-awareness 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 interference-aware and do not interfere each other.

Based on the above interference model, we describe sufficient conditions for

interference-aware transmissions in Lemma 1.

Lemma 1. For simultaneous transmissions Vtl + vr and vt2 vr, sufficient conditions

for ensuring interference-awareness 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.









[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 ad-hoc 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, "Energy-efficient tracking of continuous objects in wireless sensor networks,"
UIC '08, 2008.

[14] N. Kurata, B.F.Spencer, and M. Sandoval, "Efficient broadcasting in multi-radio
multi-channel, and multi-hop 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. 222-232.

[16] C. Ho, O. Katia, T. Gene, and V. Kumar, "Flooding for reliable multicast in multi-hop
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. 64-71, ACM.

[17] K. Obraczka, K. Viswanath, and G. Tsudik, "Flooding for reliable multicast in
multi-hop ad hoc networks," Wirel. Netw., vol. 7, no. 6, pp. 627-634, 2001.

[18] S.-Y Ni, Y-C. Tseng, Y-S. Chen, and J.-P. Sheu, "The broadcast storm problem in
wireless ad hoc network," in MobiCom '99, 1999, pp. 151-162.

[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 fault-tolerant 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 networks-problems analysis
and protocol design," IEEE Transactions on Communications, vol. 33, pp.
1240-1246, 1985.


146









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 [19-21], the authors proposed a distributed method to statistically estimate the

boundary of the phenomena, but they consider only static phenomena. In [69-71],

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 in-situ detection and tracking


123









5-11

5-12

5-13

5-14

5-15

5-16

5-17

5-18

5-19


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 . . . . . . .


5-20 Epoch-wise comparison based on number
and tracking process. ...........

5-21 Epoch-wise comparison based on number
Centralized Query Processor (CQP) . .


f active nodes involved in


f update messages send
. . . . . . . .


5-22 Epoch-wise comparison based on number of messages exchanged between
one-hop neighbors to implement the algorithms . . . . . . . . .

5-23 Epoch-wise comparison based on the Energy Consumption . . . . .

5-24 Comparison based on overall 50 Epochs . . . . . . . ... . . .

5-25 Comparison based on different grid size . . . . . . . . . .

5-26 Epoch-wise comparison based on number of active nodes involved in detection
and tracking process . . .. . .. . .. . .. . .. . .. . .. ..

5-27 Epoch-wise comparison based on number of update messages send to the
Centralized Query Processor (CQP) . . . . . . . . . . . .

5-28 Epoch-wise comparison based on number of messages exchanged between
one-hop neighbors to implement the algorithms . . . . . . . . .

5-29 Epoch-wise comparison based on the Energy Consumption . . . . .

5-30 Comparison based on overall 5 Epochs . . . . . . . . . . .

5-31 Snapshots of expanding phenomena cloud during Epochs t10, t15, t20. .....

5-32 Active Sensors during Epoch t10, for DistPDT. . . . . . . . . .

5-33 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









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 [41-43]. However, many real-life 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 non-deterministic, dynamic

temporal variations of cloud shape, size and direction of motion along multiple axes.

These events cannot be modeled in well-defined terms. Thus, it is difficult to apply

existing mechanisms in such situation due to the fact that current cloud-based tracking

techniques are oriented towards monitoring the motion of well-defined 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.









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 6-15 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 6-15 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 6-13 shows the Epoch-wise 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 6-16 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 6-14 and 6-17 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








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 interference-awareness 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 5R-1 is bounded by |SR 2 /3 1 During these Epochs all the sets S, 52,... 5R-1
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 5R-11 2/3 +1 Epochs, the set 5R-1 will be able to
completely forward all its remaining messages along with the messages it received
from SR. And by this time S1, 52,..., SR-2 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:
2|SR L3/2 + 12 2 ISR-1l I 3 +1 2
... 21S21 (+l)3 2
"'" v'-3-/ 2









[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 multi-hop radio networks,"
Journal of Algorithms, vol. 46, no. 1, pp. 1-20, 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. 702-712.

[28] D. R. Kowalski and A. Pelc, "Centralized deterministic broadcasting in undirected
multi-hop radio network," in APPROX-RANDOM '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. 426-433, 1991.

[30] M. Elkin and G. Kortsarz, "Logarithmic inapproximability of the radio broadcast
problem," Journal of Algorithms, vol. 52, pp. 8-25, 2004.

[31] M. Elkin and G. Kortsarz, "Polylogarithmic additive inapproximability of the radio
broadcast problem," In APPROX-RANDOM '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, "Minimum-latency broadcast
scheduling in wireless ad hoc networks," in INFOCOM '07, 2007, pp. 733-739.

[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. 129-137.

[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.
740-748.

[36] R. Mahjourian, F.Chen, R. Tiwari, M.T.Thai, H. Zhai, and Y. Fang, "An
approximation algorithm for conflict-aware broadcast scheduling in wireless ad
hoc networks," in MobiHoc'08, 2008, pp. 331-340.

[37] X. Chen, X. Hu, and J. Zhu, "Minimum data aggregation time problem in wireless
sensor networks," in In MSN 2005, 2005, pp. 133-142.

[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










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 5-3. 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








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 2-10. The Xt Yt Zt Co-ordinate System

The m2n-coloring Algorithm: We now present the m2n-coloring algorithm,
illustrated as Algorithm 2, for the Distance-d 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 2-11 shows the basic
coloring pattern generated by the m2n-coloring 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.









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 -- (5-1)
0 otherwise

1 if sensor / is a candidate
xf = (5-2)
0 otherwise

S= if sensor / is a tracking (5-3)
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)











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 4-1. Effect of No. of Nodes on Average Experimental Approximation Ratio of
All-to-All 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 4-1 shows the effect of number of sensor nodes in the WSN on all-to-all data

broadcasting. We observe that the performance of the localized all-to-all broadcast

algorithm is always better than the distributed one. The main reason for this is that in

case of distributed all-to-all 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.









=2(IS1 2+ + SRI) (a3l + 1i
=2 V-1 -+l/a 3 12 time slots.

Theorem 4.1. Distributed all-to-one data aggregation scheduling algorithm has an ap-
proximation guarantee of 2 L(3 + 1 2

Proof. The trivial theoretical lower bound for all-to-one 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 All-To-All Broadcast Scheduling Algorithm
The distributed protocol for all-to-all 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 all-to-one 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.










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 5-17. Effect of varying pT with n = 3 and m = 150


Figure 5-17 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 phenomena-defined 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 5-18 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









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 in-network 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









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 5-24, ODA

generates 86% and 39% lesser network traffic in terms of update messages comparing

to StreamPDT and DistPDT (FDA) respectively.

Figure 5-22 illustrates the epoch-wise comparison based on the number of protocol

messages collectively exchanged by all the active nodes with their one-hop neighbors.

StreamPDT is a straightforward algorithm in which all sensor nodes perform one-hop

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 5-24 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 epoch-wise comparison of the four algorithms based on the energy

consumption is shown in Figure 5-23. 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 5-24 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









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 sub-divided into multiple sub-epochs and each node

only broadcasts alerts during its assigned sub-epoch. 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 Phenomenon-Set and the candidate sensor transitions to a

tracking sensor node using rule R1 given in Section 5.3.3.









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.




























C d


Figure 2-8. 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 2-9. The tiling of space using truncated octahedrons


Zt axes are inclined as shown in Figure 2-10. The angle between Xt and Yt axes is

01 = cos-l( ), whereas, angles between Xt and Zt axes and Yt and Zt axes are equal

to 02 = cos-1( ). The angle between the Zt-axis and the Xt Yt plane is 03 = 450.

The side length of the truncated octahedron is -, the distance between its two parallel


















2.6693 2.2665 2.7656 3.5419 6.015(

217 187 227 291 50(


101 71 111 195 50(


Figure 5-30. Comparison based on overall 5

TTO




E 'u i: :
0 ;. : . .... . ..
"-, .


1,0 :.: .: :. : .: : : : *. ..

100 200 300 400 500
meters

Figure 5-31. 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 5-32. Active Sensors during
Epoch to1, for
DistPDT.


5-26-5-29 provide an epoch-wise comparison whereas Figure 5-30 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















a b



1 -
// 3 1 1,)
-- II
//T \ ,




c d
Figure 2-3. 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 2-3.
We observe that a regular hexagon of sides 1 has the maximum area. Consequently, we
select it as the unit partition shape. Figure 2-4 shows the regular hexagon tiling of 2D
plane.
We formally define the regular hexagon tiling and coloring of 2D plane as
Distance-d Hexagon coloring problem:
Distance-d 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.









subject to

xfP x- + xf < 1 Vi e V (5-4)

(xf + x,) (P, PT) > 0 Vi e V (5-5)

S(x +x) N-(i) (x+ x +x xf) < 0 Vi c V (5-6)
jCN(i)
S(xc x+) N(i)xf < n Vi E V (5-7)
jCN(i)
x, x, xix e {0,1} Vi E V (5-8)

The above IP identifies the potential candidate, candidate and tracking sensors in

the WSN based on the Probability and Phenomena conditions. Constraint 5-4 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 5-5, 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 5-6 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 5-7 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, = (5-9)
0 otherwise







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 m2n-coloring 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].








truncated octahedron tiling of the 3D-space, 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 ,,(3-3)



v = {(Yv Yb)- (Zv Zb) COs (01/2)/ tan 03}/rin (3-4)



xt = [(Xv Xb) {(Zv Zb) sin (01/2)/tan 03}-

5 /tan]rn (3-5)

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 interference-aware
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.









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 2-Disk 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, all-to-one 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









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









[52] R. Tiwari, T. Dinh, and M. T. Thai, "On approximation algorithms for
interference-aware 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 in-network 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, "Gps-less low cost outdoor location fer
very small devices," in IEEE Pers. Commun. (Special Issue on Smart Space and
Environments), 2000, vol. 7, pp. 28-34.

[61] A. Abbasi and M. Younis, "A survey on clustering algorithms for wireless sensor
networks," in Comput. Commun., Oct 2007, vol. 30, pp. 2826-2841.

[62] R. Bose, J. King, H. EI-Zabadani, S. Pickles, and A. Helal, "Building plug-and-play
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. EI-Zabadani, 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 service-oriented
sensor platform," in Proceeding of 1st IEEE International Workshop on Practical
Issues in Building Sensor Network Applications, 2006.


149









If we have d(vt1, vt2) > (a + 1)rTax as shown in Figure 2-1, 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 interference-aware.

If we have d(vr, vr) > (a 1)rmax as shown in Figure 2-2, 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 interference-aware.

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

Interference-Aware Broadcast Scheduling (IABS) problem: Given a multi-hop

WSN G = (V, E) and a sensor node vs V having a message m. The lABS problem

is to generate an interference-aware broadcast schedule for broadcasting the message

m from vs to all other sensor nodes. The interference-aware 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 interference-aware.

The number of time slots required by the interference-aware broadcast schedule to
complete the broadcast, known as the broadcast latency, should be minimized.

2.3 Tiling and Coloring of 2-Dimensional 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









With a new application and a broader concept of phenomena clouds, early

studies on boundary detection and tracking of well-defined shapes are no longer

sufficient [12, 13, 19, 44, 45]. Only one work recently studied on similar applications,

called Nile-PDT (a stream-based 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 in-network 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

in-network 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 energy-efficient and distributed algorithm, called Full Density

Algorithm (FDA) for real-time 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.









The plot for Localized Algorithm, in Figure 3-10, 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 3-11 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









detection and tracking process is executed in-network 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 co-operative 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 5-4, 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.









CHAPTER 4
ALL-TO-ALL DATA BROADCASTING AND ALL-TO-ONE DATA AGGREGATION

4.1 Introduction

In this chapter, we study all-to-all data broadcasting and all-to-one 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 all-to-one aggregation scheduling and 2) Minimum latency all-to-all broadcast

scheduling.

In minimum latency all-to-one 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 all-to-one aggregation

latency and it should be minimized.

In minimum latency all-to-all 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 all-to-all

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 interfere-aware.

The main contributions of this chapter are:

1. We present a localized algorithms for all-to-all broadcast scheduling in WSNs.









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









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 5-41. 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 5-41. In addition, Figures 5-42-5-47 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 5-41 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








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 3-3. An Example showing the functioning of a part of the broadcast structure.

Figure 3-3 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.









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 NP-hard [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.









We now introduce the second IP as follows:


min y-ITi xi

subject to

x,n + x- n > 0 Vi T (5-10)
jcN(i)
x,n- xj < 0 V/i T (5-11)
jcN(i)
x, {0,1} ViE T (5-12)

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 5-10 and 5-11 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













0 80

60
Z
<
40
E
=2
=20
4


S80-
.g,
2 60"

40

E 20
z


1 2 3 4 5
Epoch

Figure 5-26. Epoch-wise
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 5-28. Epoch-wise
comparison based on
number of messages
exchanged between
one-hop neighbors to
implement the
algorithms.


-A-ODA
-*-IPSol
-- FDA
-*-DistPDT
T-StreamPDT

F^


1 2 3 4 5
Epoch

Figure 5-27. Epoch-wise
comparison based on
number of update
messages send to the
Centralized Query
Processor (CQP)


I8 -ODA
0 1 -IPSol
+FDA
. 0.8 -A-DistPDT
-0.6 StreamPDT

8 4- r^ ^
0.!
0.
LJJ
0 2 3 4 5


Figure 5-29.


Epoch

Epoch-wise
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 5-26-5-30 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

NP-hard, 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
-v-StreamPDT









Algorithm 1 Co-color 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 co-color 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;


co-color 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 co-color hexagon centers forming a regular or irregular

triangular tiling of the area in which at least one triangle is non-equilateral. 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 non-equilateral triangle. Hence, the

number of non-overlapping 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 co-color hexagons, in comparison to Algorithm 1. Hence, a
contradiction. O









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 (5-13)
tan 600 2 13

y = (y yb) sin 600/ 3 (5-14)

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 (5-15)
tan 600 2 13

y = (y yb) sin 600/ 3 (5-16)

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 1-hop as the hexagon has the length (hexagon diameter) of

2 and the clustering partition can be done only one time during the deployment and

set-up 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 5-11, 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 on-line manner to schedule themselves into

active and sleep mode:








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 Interference-aware
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 all-to-all data broadcasting and all-to-one
data aggregation and propose:
1. A O(1)-distributed approximation algorithm for all-to-one data aggregation.
2. A O(1)-distributed approximation algorithm for all-to-all data broadcast.
3. A Localized algorithm for all-to-all data broadcast.
All-to-one 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 all-to-one data aggregation is the first in literature and has
a constant approximation guarantee of 2 2()3 + 1i Our distributed algorithm for
all-to-all data broadcasting is also the first in literature and has a constant approximation
guarantee of 4 2( ) +1 2.









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 5-4 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 in-network 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.









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 interference-aware 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 interference-aware

schedule for transmissions between two consecutive layers. The ISA is illustrated in

Algorithm 4.









[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, "Energy-effcient 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. 4918-4923.

[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









6. Validating our approaches using both real-world applications and simulations to

analyze its performance and resource requirements as well as comparing it with that of

stream-based 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.









6.2 System Model


Network Model: A set of in-situ 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 detect-positive if it detects the phenomenon

is existing, whereas if it detects the phenomena is not existing it is referred as

detect-negative.

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 6-1 & 6-2.

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 6-5 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 6-3 shows various types of messages that sensor nodes

may generate and exchange to implement the detection and tracking protocol. Figure 6-4

shows the set of transition rules governing the transition of a sensor node from one state


128









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 interference-awareness 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









[39] X. Xu, S. Wang, X. Mao, S. Tang, and X. Li, "An improved approximation algorithm
for data aggregation in multi-hop 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 mulyi-hop wireless sensor networks," in In ACM Mo-
bihoc 2009, 2009.

[41] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. Peh, and D. Rubenstein,
"Energy-efficient computing for wildlife tracking: design tradeoffs and early
experiences with zebranet," SIGARCH Comput. Archit. News, vol. 30, no. 5,
pp. 96-107, 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 uav-delivered 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, "Energy-efficient 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 sensor-network databases," in SSDBM'2005: Proceedings of the
17th international conference on Scientific and statistical database management,
Berkeley, CA, US, 2005, pp. 163-172, Lawrence Berkeley Laboratory.

[47] R. Kremens, J. Faulring, A. Gallagher, A. Seema, and A. Vodacek, "Autonomous
field-deployable wild land fire sensors," in International Journal of Wild land Fire,
2003, vol. 12, pp. 237-244.

[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- TR-2005-603, 2005.

[49] J. Cassels, "An introduction to the geometry of numbers," in Berlin: Springer-
Verlag, 1971.

[50] W. MathWorld, "Space-filling polyhedron," http://mathworld. wolfram. corn/
Space-FillingPolyhedron.html.

[51] S.-H. Huang, H. Du, and E. K. Park, "Minimum latency gossiping in multi-hop
wireless network," in In Proceedings of Mobihoc 2008, 2008, pp. 733-739.


148
































To my parents, Mrs Shashi Tiwari and Mr Vasudev Tiwari









Effect of / on Average Latency ..................

Effect of a on Average Latency ..................

Comparison of various heuristics algorithms . . . . . .


4-1 Effect of No. of Nodes on Average E
data broadcasting Algorithms.....

4-2 Effect of No. of Nodes on Average E
data broadcasting Algorithms.....

4-3 Effect of No. of Nodes on Average E
data broadcasting Algorithms .....


experimental Approximation

experimental Approximation


experimental Approximation
experimental Approximation


3-10

3-11

3-12


4-4 Effect of / on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................

4-5 Effect of 3 on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................

4-6 Effect of 3 on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................

4-7 Effect of a on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................

4-8 Effect of a on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................

4-9 Effect of a on Average Experimental Approximation Ratio of
broadcasting Algorithms ..................


5-1

5-2

5-3

5-4

5-5

5-6

5-7

5-8

5-9

5-10


All-to-All data


All-to-One data


One-to-All data


All-to-All data


All-to-One data


One-to-All 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 All-to-All
. . . . . 75

Ratio of All-to-One
. . . . . 76

Ratio of One-to-All
. . . . 76


77


78


78


79


80


80

85

86

88

89

93

100

100

100

100

100











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 5-4. 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

peer-to-peer fashion, where a sensor transitioning from one category to another notifies

its neighbors via a 1-hop broadcast without involving the centralized query processor.

We used ZigBee communication protocol in our system, which natively supports 1-hop

broadcasting. The category of a sensor and its neighbors determines their mutual

responsibilities towards each other. For example, a candidate sensor node A has










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 5-25. Comparison based on different grid size.


In the second set of simulations, we varied the grid size as shown in Figure 5-25.

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









In [1], Scott et. al. proposed a 3k2-hexagon coloring scheme for Distance-d

hexagon coloring problem. Figure 2-7, 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 3-Dimensional 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 2-8. We observe that

the truncated octahedron of sides 1 has the maximum volume. Hence, we selected

truncated octahedron as the partition shape. Figure 2-9 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 Distance-d truncated octahedron coloring problem:

Distance-d 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 Distance-d truncated octahedron coloring problem, we

introduce a new Xt Yt Zt coordinate system in 3D space, in which, Xt, Yt, and









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 stream-based 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 real-world 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 5-16, 5-17

and 5-18. Figure 5-16 shows the effect of varying parameter n which determines


106









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 in-network, 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 5-4.
25

20

-0 15

46E 10




0 S00 1000 150 2000 2500 3000 3500
Phenomena Cloud Size

Figure 5-5. Ratio of Total Active Sensors to Cloud Size in a Rectangular Sensor Grid


The plot in Figure 5-5 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

in-network 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









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 4-2. Effect of No. of Nodes on Average Experimental Approximation Ratio of
All-to-One data broadcasting Algorithms.

140
120










# of 3er,nor Nc,.es In WSN

Figure 4-3. Effect of No. of Nodes on Average Experimental Approximation Ratio of
One-to-All 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 4-2 shows the effect of number of nodes for all-to-one data aggregation

algorithm. The plot is similar to that of all-to-all data broadcast and can be explained

in the same manner. The experimental approximation ratio becomes almost constant,

after certain number of nodes because of non-varying network diameter.

Figure 4-3 shows the effect of number of nodes for one-to-all data broadcasting. The

plot is similar to the all-to-all and all-to-one. This is because, apparently the latency of
40



50 100 150 200 250 300 350 400 450 500
#of Bersbr Naaes In WSN

Figure 4-3. Effect of No. of Nodes on Average Experimental Approximation Ratio of
One-to-All 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 4-2 shows the effect of number of nodes for all-to-one data aggregation

algorithm. The plot is similar to that of all-to-all data broadcast and can be explained

in the same manner. The experimental approximation ratio becomes almost constant,

after certain number of nodes because of non-varying network diameter.

Figure 4-3 shows the effect of number of nodes for one-to-all data broadcasting. The

plot is similar to the all-to-all and all-to-one. This is because, apparently the latency of









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 3-4. 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 3-4, 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









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 :ll-ltlU'l:ll )!: !!
*II l -n'llnj. l-lh'ioii bl l" ,il'

0 100 200 300 400 500 100 200 300 400 500
meters meters
Figure 5-39. Active Sensors Figure 5-40. 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

6-1 shows snapshots of the expanding phenomena cloud at epochs t1o, t15, and t20.

Figures 5-32, 5-33, and 5-34 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 5-35, 5-36, and 5-37 and that of epoch t20 is presented in Figures 5-38, 5-39,

and 5-40. As can be seen, when the phenomenon expands, the number of active nodes


119









Purdue University. Nile-PDT is designed for detecting and tracking phenomenon clouds

such as gas clouds, oil spills and chemical waste spillage. Nile-PDT uses two custom

database operators, namely, SN-Scan and SN-Join to perform phenomenon detection

and tracking. The SN-Scan operator scans all the sensors in the network and chooses

candidate sensors which have a high probability of detecting the phenomenon. The

SN-Join 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. Nile-PDT uses feedback control to continuously tune the SN-Scan and SN-Join

parameters to maximize efficiency of the detection process. The main drawback of the

Nile-PDT 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 SN-Scan

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 on-board non-volatile 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 ad-hoc routing mechanisms and is primarily designed for

detecting individual discrete objects with well-defined 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, 19-22, 68-71]. As these studies are not

in the scope of this paper (we detect and track the entire area), we only briefly mention


122










80 / r rT T r T -- T r


'A GHA
'- ApproxAlgo
S40 v LocalizedAlgo

20.
20 ____. _, .__ _ _ __


1 1.5 2 2.5
Alpha

Figure 3-11. 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 3-11 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 3-11 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 3-12 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









on the practical viability of the entire smart space. This raises a need for a distributed

in-network 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

in-network 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 energy-efficient, localized, in-network algorithm for real-time

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 real-world smart

space and utilizes the phenomena detection and tracking mechanism described in this

paper, to solve critical challenges faced during its deployment.









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 NP-hard. 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









a trade-off 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 5-42-5-47) 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 5-47.

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, 44-46, 67, 68].

The most closely related work is Nile-PDT [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









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 one-to-all 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 3-7 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









1. StreamPDT [46]: A centralized stream-based algorithm where phenomena

detection and tracking is performed by a Centralized Query Processor (CQP). We

simulated Nile-PDT [46], a well-known 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 5-19. 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













5' "C1^ A GHA
'- -* ApproxAlgo
S40 vT LocalizedAlgo

20


0 1.5 2 2.5 3
Beta

Figure 3-10. Effect of 3 on Average Latency


Figure 3-9 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 multi-message multi-source

broadcasting.

3.3.2 Effect of 3 on Broadcast Latency

Figure 3-10 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.








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 3-Dimension
The localized broadcast scheduling algorithm can be applied to 3D WSNs, if we
consider the 3D-space is partitioned into truncated octahedrons of sides r forming a
10i-









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 In-Network 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 2-Dimensional Plane Using Regular Hexagons . .
2.4 Tiling and Coloring of 3-Dimensional Space . . . . . . . . .
2.5 Broadcast Scheduling Algorithm (BSA) . . . . . . . . . .
2.5.1 Algorithm Description .. . .. . .. . .. . .. . .. .
2.5.2 0(1)-Approximation Ratio for Interference-Aware Broadcast Sched
Problem in 2-Dimension ........................
2.5.3 0(1)-Approximation Ratio for Interference-Aware Broadcast Sched
Problem in 3-Dimension ........................
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 3-Dimension ...
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


.









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.









1.2 Efficient In-Network 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 [41-43]. However, many real-life events such as oil spills,

gas clouds, or random walking motion of people, henceforth called Phenomena Clouds,

are characterized by non-deterministic, dynamic temporal variations of cloud shape,

size and direction of motion along multiple axes. These events cannot be modeled in

well-defined 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 well-defined shapes are no longer sufficient [12, 13,

19, 44, 45]. Only one work recently studied on similar applications, called Nile-PDT (a

stream-based 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









2. We present a distributed algorithms for all-to-one data aggregation scheduling
and all-to-all data broadcast scheduling. Our distributed algorithm for all-to-one 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 all-to-all 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 all-to-all data broadcast. Section 4.3 describes a distributed approximation
algorithm for all-to-one data aggregation along with the theoretical analysis. In Section
4.4, we describe a distributed approximation algorithm for all-to-all 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 All-To-All Data Broadcast Scheduling Algorithm

Similar to one-to-all 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








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 Interference-Aware Broadcast Scheduling
Problem in 3-Dimension
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 interference-awareness described in Lemma 1, which results in interference-aware
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.









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 3-7 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 3-8 shows the average

height of the BFS trees in our sample networks for any given number of nodes. It can be

observed in Figure 3-8, 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.




Full Text

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ONBROADCASTSCHEDULINGANDDYNAMICPHENOMENADETECTIONINWIRELESSSENSORNETWORKSByRAVITIWARIADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2010

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c2010RaviTiwari 2

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Tomyparents,MrsShashiTiwariandMrVasudevTiwari 3

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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

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 16 1.1EfcientDataBroadcastingandAggregation ................ 17 1.2EfcientIn-NetworkDetectionandTrackingofDynamicPhenomena ... 21 2CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCE-AWAREBROADCASTSCHEDULING ....................... 24 2.1Introduction ................................... 24 2.2NetworkModelandProblemDenition .................... 26 2.2.1NetworkModel ............................. 26 2.2.2ProblemDenition ........................... 28 2.3TilingandColoringof2-DimensionalPlaneUsingRegularHexagons ... 28 2.4TilingandColoringof3-DimensionalSpace ................. 36 2.5BroadcastSchedulingAlgorithm(BSA) ................... 40 2.5.1AlgorithmDescription ......................... 40 2.5.2O(1)-ApproximationRatioforInterference-AwareBroadcastSchedulingProblemin2-Dimension ........................ 41 2.5.3O(1)-ApproximationRatioforInterference-AwareBroadcastSchedulingProblemin3-Dimension ........................ 43 2.6CentralizedGreedyHeuristicforbroadcastscheduling ........... 45 2.7Conclusion ................................... 45 3LOCALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCE-AWAREBROADCASTSCHEDULING ....................... 47 3.1Introduction ................................... 47 3.2LocalizedAlgorithmforBroadcastScheduling ................ 48 3.2.1LocalizedGenerationofBroadcastingStructure ........... 48 3.2.2BroadcastSchedulingofBroadcastMessage ............ 52 3.2.3AnExampleScenario ......................... 54 3.2.4LocalizedBroadcastSchedulingAlgorithmin3-Dimension ..... 58 3.3ExperimentalEvaluation ............................ 60 3.3.1EffectofNumberofSensorNodesonBroadcastLatency ..... 60 3.3.2EffectofonBroadcastLatency ................... 63 3.3.3EffectofonBroadcastLatency ................... 64 3.4Conclusion ................................... 66 5

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4ALL-TO-ALLDATABROADCASTINGANDALL-TO-ONEDATAAGGREGATION 67 4.1Introduction ................................... 67 4.2LocalizedAll-To-AllDataBroadcastSchedulingAlgorithm ......... 68 4.3DistributedAll-To-OneDataAggregationSchedulingAlgorithm ...... 70 4.4DistributedAll-To-AllBroadcastSchedulingAlgorithm ........... 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 5.3.9Real-TimeMonitoringbyApplications ................ 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

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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

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LISTOFFIGURES Figure page 2-1Sufcientconditionsforinterference-awarenessbasedontransmitters. ..... 27 2-2Sufcientconditionsforinterference-awarenessbasedonreceivers. ...... 27 2-3Comparisonofdifferentplanetilingpolygon.Figuresa,b,canddrespectivelyshowasquare,arhombus,atriangleandahexagon,havingmaximumdistancewithinthemequalto1. ................................ 29 2-4ThenewXh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhcoordinatesystem ........................ 30 2-5Closestpointsp1andp2intwohexagons ..................... 31 2-6Co-ColorHexagonsofh(0,0)fori=2andj=3.Theindexofsub-latticeRhinHi.e.jdet(A,B)j=i2+j2+ij=19. ....................... 34 2-7ComparisonofnumberofcolorsusedtocolorthehexagontilingusingourschemeandScottet.al[ 1 ]. ............................. 35 2-8Comparisonofdifferentspacingllingpolyhedra.Figuresa,b,canddrespectivelyshowatruncatedoctahedron,arhombicdodecahedron,acubeandahexagonalprism,havingmaximumdistancewithinthemequalto1. ............. 37 2-9Thetilingofspaceusingtruncatedoctahedrons .................. 37 2-10TheXt)]TJ /F3 11.955 Tf 11.95 0 Td[(Yt)]TJ /F3 11.955 Tf 11.96 0 Td[(ZtCo-ordinateSystem ....................... 38 2-11Coloringpatternford=1,dme=3anddne=3,Colorsassignedtothetruncatedoctahedronsarerepresentedbynumbers. ............... 39 3-1ElementsoftheBroadcastingStructure. ...................... 49 3-2HexagoncoloringgeneratedbyAlgorithm 7 fork=4,colorsassignedtothehexagonsarerepresentedbynumbers. ...................... 50 3-3AnExampleshowingthefunctioningofapartofthebroadcaststructure. ... 51 3-4AnEpoch ....................................... 53 3-5Abroadcaststructure ................................ 55 3-6Databroadcastingontopofabroadcaststructure ................ 55 3-7EffectofnumberofnodesonAverageLatency .................. 61 3-8AverageBFSheight ................................. 61 3-9Averageoptimalityratio ............................... 61 8

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3-10EffectofonAverageLatency ........................... 63 3-11EffectofonAverageLatency ........................... 65 3-12Comparisonofvariousheuristicsalgorithms .................... 66 4-1EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. ............................ 75 4-2EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. ............................ 76 4-3EffectofNo.ofNodesonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. ............................ 76 4-4EffectofonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. .............................. 77 4-5EffectofonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. .............................. 78 4-6EffectofonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. .............................. 78 4-7EffectofonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. .............................. 79 4-8EffectofonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. .............................. 80 4-9EffectofonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. .............................. 80 5-1DissectionofthePhenomenaCloud ........................ 85 5-2ClassicationoftheParticipatingSensors ..................... 86 5-3DetectionandTrackingofaPhenomenaCloud .................. 88 5-4ActionTakenbyaSensorNodewithrespecttoitsNeighborswhicharenotidle 89 5-5RatioofTotalActiveSensorstoCloudSizeinaRectangularSensorGrid ... 93 5-6Partitionshapeassquare. .............................. 100 5-7Partitionshapeasrhombus. ............................. 100 5-8PartitionshapeasEquilateralTriangle. ....................... 100 5-9PartitionshapeasRegularHexagon. ........................ 100 5-10TheHexagonLattice ................................. 100 9

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5-11Clusteringonthebasisofhexagonlattice ..................... 102 5-12GatorTechSmartHouse .............................. 103 5-13SmartFloorTilewithforcesensorsandAtlasPlatformNode .......... 103 5-14RippleEffectofaFootStepontheSmartFloor .................. 104 5-15WalkingmotionasaPhenomena .......................... 104 5-16EffectofvaryingnwithpT=0.4andm=150 ................... 107 5-17EffectofvaryingpTwithn=3andm=150 .................... 108 5-18Effectofvaryingmwithn=3andPT=0.4 .................... 109 5-19PowerConsumptionSpecicationsforAtlas .................... 110 5-20Epoch-wisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. ................................ 112 5-21Epoch-wisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) ........................ 112 5-22Epoch-wisecomparisonbasedonnumberofmessagesexchangedbetweenone-hopneighborstoimplementthealgorithms. ................. 112 5-23Epoch-wisecomparisonbasedontheEnergyConsumption. .......... 112 5-24Comparisonbasedonoverall50Epochs ...................... 113 5-25Comparisonbasedondifferentgridsize. ...................... 115 5-26Epoch-wisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. ................................ 116 5-27Epoch-wisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) ........................ 116 5-28Epoch-wisecomparisonbasedonnumberofmessagesexchangedbetweenone-hopneighborstoimplementthealgorithms. ................. 116 5-29Epoch-wisecomparisonbasedontheEnergyConsumption. .......... 116 5-30Comparisonbasedonoverall5Epochs ...................... 117 5-31SnapshotsofexpandingphenomenacloudduringEpochst10,t15,t20. ..... 117 5-32ActiveSensorsduringEpocht10,forDistPDT. ................... 117 5-33ActiveSensorsduringEpocht10,forFDA. ..................... 118 10

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5-34ActiveSensorsduringEpocht10,forODA. ..................... 118 5-35ActiveSensorsduringEpocht15,forDistPDT. ................... 118 5-36ActiveSensorsduringEpocht15,forFDA. ..................... 118 5-37ActiveSensorsduringEpocht15,forODA. ..................... 118 5-38ActiveSensorsduringEpocht20,forDistPDT. ................... 118 5-39ActiveSensorsduringEpocht20,forFDA. .................... 119 5-40ActiveSensorsduringEpocht20,forODA. ..................... 119 5-41Percentageofholesgeneratedwrtpercentageofupdatemessageslost .... 120 5-42DetectionandTrackingwith5%updatemessagelostforFDA. ......... 125 5-43DetectionandTrackingwith5%updatemessagelostforODA. ......... 125 5-44DetectionandTrackingwith10%updatemessagelostforFDA. ......... 125 5-45DetectionandTrackingwith10%updatemessagelostforODA. ......... 125 5-46DetectionandTrackingwith15%updatemessagelostforFDA. ......... 125 5-47DetectionandTrackingwith15%updatemessagelostforODA. ......... 125 6-1ClassicationofSensorNodesintheWSN .................... 129 6-2TypesofNodesintheWSN ............................. 129 6-3TypesofmessagesintheWSN ........................... 130 6-4TheTransitionRules ................................. 130 6-5StateTransitionDiagramforaSensornode .................... 131 6-6Expansionofthephenomenacloud ........................ 131 6-7Shrinkingofthephenomenacloud ......................... 133 6-8Xh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhco-ordinateSystemforHexagontilingH ................. 134 6-9Dataaggregationbasedonclusteringgeneratedbythehexagonaltiling .... 136 6-10Powerconsumptionspecicationsforasensornode ............... 136 6-11Comparisonbasedonnumberofboundarynodes. ................ 137 6-12Comparisonbasedonnumberofupdatemessages. ............... 137 6-13Comparisonbasedonenergyconsumption. .................... 137 11

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6-14Comparisonbasedonmessagesexchanged. ................... 137 6-15Comparisonbasedonnumberofupdatemessagesatdifferentphenomenaexpansionspeed. ................................... 138 6-16Comparisonbasedonenergyconsumptionatdifferentphenomenaexpansionspeed. ......................................... 138 6-17Comparisonbasedonmessagesexchangedatdifferentphenomenaexpansionspeed. ......................................... 138 6-18SnapshotofphenomenainWSN. ......................... 139 6-19Estimatedboundarywith0%messageloss. .................... 139 6-20Estimatedboundarywith15%messageloss. ................... 139 6-21Estimatedboundarywith30%messageloss. ................... 139 6-22Estimatedboundarywith45%messageloss. ................... 139 12

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyONBROADCASTSCHEDULINGANDDYNAMICPHENOMENADETECTIONINWIRELESSSENSORNETWORKSByRaviTiwariAugust2010Chair:MyT.ThaiMajor:ComputerEngineering MajorityofnetworkapplicationsdesignedontopofWirelessSensorNetworks(WSNs)involvedetectionandtrackingofsomephysicalphenomena.Additionally,theyutilizesomeprimitiveservicessuchasbroadcastingandaggregationfordisseminatingandcollectinginformation. Broadcastingisanoperationtopromulgatesomeinformationfromasourcenodetoallothernodesinthenetwork.Incontrast,aggregationisanoperationtocollectthesensedinformationfromallnodesinthenetworkataspecicsinknode.SensornodesinWSNscommunicateviaradiotransmissions.DuetoWirelessBroadcastAdvantage(WBA)ofradiotransmissions,performingefcientdatabroadcastingordataaggregationwithminimumlatencyisnontrivialandprovedtobeNP-hard.Floodingisastraightforwardapproachwhichcanbeused.Unfortunately,itgeneratesredundanttransmissions,contentionsandcollisions,whichaggravatesthenetworkthroughputandresultsinabroadcaststorm.Broadcastschedulingandaggregationschedulingaremoreintelligentandeffectivemechanismstoperformefcientbroadcastingandaggregationrespectively.Thesearebasedonschedulingtheinterferingtransmissions,whichavoidsbroadcaststormandimprovesnetworkthroughput. Existingresearchesonbroadcastschedulingandaggregationschedulingprovidecentralizedsolutions,whichcannotbeimplementedlocally.Additionally,theyconsiderveryelementarynetworkandinterferencemodels,inwhich,eitherallsensornodeshave 13

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thesametransmissionrangeortheirtransmissionrangesareequaltotheirinterferenceranges.Theseassumptionsarenotpractical.Furthermore,theyentirelyignoretheexistenceofWSNsin3D. MostoftheexistingresearchonphenomenadetectionandtrackingusingWSNsassumethephenomenaareinvariantinshape,sizeandmotion.However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgases,whicharecharacterizedbynon-deterministicvariationsinshape,sizeanddirectionofmotion.Thesedynamicphenomenaaretermedasphenomenacloud.Duetotheabsenceofanywelldenedmodelforphenomenaclouds,theirdetectionandtrackingthroughWSNsisextremelychallenging.Sincesensornodeshavelimitedenergyandprocessingpower,theefcientdetectionandtrackingofphenomenacloudwithanobjectivetomaximizenetworklifetimeisachallengingoptimizationproblem. Thefocusofthisdissertationismainlyonfollowingtwoimperativeoptimizationproblems: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena. Themaincontributionsofthisdissertationare: 1.AconstantapproximationalgorithmforbroadcastschedulinginWSNs,whichhasthestateoftheartapproximationratio. 2.TherstconstantlocalizedapproximationalgorithmforbroadcastschedulinginWSNs. 3.Therstconstantdistributedapproximationalgorithmforall-to-onedataaggregation. 4.Therstconstantdistributedapproximationalgorithmforall-to-allbroadcastscheduling. 5.Alocalizedin-networkalgorithmfordetectionandtrackingofphenomenacloud. 14

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6.Anenergyefcientlocalizedalgorithmfordetectionandtrackingofphenomenacloudboundary. 15

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CHAPTER1INTRODUCTION AWirelessSensorNetwork(WSN)isacollectionofsensornodesdeployedtosensesomephenomena,collectinformationandsendittothebasestationforfurtherprocessingonmulti-hoppaths.WSNshavelotsofapplicationsinvariouseldswherecontinuousmonitoringisextremelycriticalandcannotbeperformedbyhumansduetoissueslikerisk,reachability,accuracyandcost.Duetorecentadvancementsinmicro-electronicsandwirelesstechnologies,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,performingefcientdatabroadcastingordataaggregationwithminimumlatencyisnontrivialinWSNsandprovedtobeNP-hard[ 15 ].However,onestraightforwardapproachtoperformdatabroadcastingoraggregationisooding[ 16 17 ].Unfortunately,itgeneratesredundanttransmissions,contentionsandcollisionsinthenetwork,whichaggravatesthenetworkthroughputandresultsin 16

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abroadcaststorm[ 18 ].Amoreintelligentapproachtoperformefcientdatabroadcastordataaggregationistoscheduletheinterferingtransmission.Thisavoidsbroadcaststormandconsiderablyimprovesnetworkthroughputandlatency.IntheexistingliteratureonWSNs,broadcastschedulingandaggregationschedulingareformulatedastwoimportantoptimizationproblemswithobjectivetominimizelatency. MostoftheexistingresearchonphenomenadetectionandtrackingusingWSNsassumethephenomenaisinvariantinshape,sizeandmotion[ 19 23 ].However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgasesthatarecharacterizedbynon-deterministicvariationsinshape,sizeanddirectionofmotion.Thesedynamicphenomenaaretermedasphenomenacloud.Duetotheabsenceofanywelldenedmodelforphenomenaclouds,theirdetectionandtrackingthroughWSNsisextremelychallenging.Sincesensornodeshavelimitedenergyandprocessingpower,theefcientdetectionandtrackingofphenomenacloudwithanobjectivetomaximizenetworklifetimeisachallengingoptimizationproblem. Theinherentlydistributednatureofsensornodesintroducesmanyintriguingandchallengingoptimizationproblemswhichhaveenormousresearchpotential.EfcientlysolvingtheseproblemsispivotalforresourcefullydesigningcriticalapplicationsforWSNs.ThefocusofthisdissertationismainlyonfollowingtwoimperativeoptimizationproblemsinWSNs: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena(phenomenacloud). Intherestofthischapter,weprovideadetailedintroductionandbackgroundforthesetwoproblems. 1.1EfcientDataBroadcastingandAggregation Databroadcastinganddataaggregationaretwomostprimitiveoperationsinmulti-hopWSNs.Thepurposeofdatabroadcastingistoconveyamessagefromasourcetoallothernodes.Itslatencydirectlygovernstheperformanceofvarious 17

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delayconstraintdistributedprotocolsinWSNssuchasroutediscovery,servicediscovery,broadcastingupdatesetc,whichrequiredatapromulgation.Incontrast,dataaggregationisperformedtoefcientlycollectthesensedinformationfromallsensornodesatasinknodeorabasestationforfurtherprocessingorforwarding. AWSNcanbecloselymodeledusingagraphG=(V,E),wheretheverticesinsetVrepresentnetworknodesandedgesinsetErepresentthecommunicationlinks.Thedatabroadcastinwirelessnetworkhasbeenstudiedusingdifferentkindsofgraphmodelswithanobjectivetominimizethebroadcastlatency.ThetheoreticallowerboundonminimumlatencyistheradiusRofthenetworkwithrespecttothesourcenodevs2V.In[ 24 ],Chlamtacet.al.provedthattheminimumlatencybroadcastscheduleproblemisNP-hardforgeneralgraphs.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)andprovedthattheminimumlatencybroadcastschedulingproblemisNP-hard.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

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forassigningrankstothenodesofBFStree.In[ 35 ],Chenet.alstudiedthisprobleminamorerealisticmodel,theyconsideredtransmissionrangeissmallerthaninterferencerange.TheyproposedanO(2)approximationratio,whereistheratioofinterferencerangeandtransmissionrange,with>1.In[ 36 ]Rezaet.alstudiedthisproblem,considering>1proposedanO(2)approximationwithabetteranalysis.Apartfromtheinterferenceandtransmissionrangetheyalsoconsideredthecarriersensingrange.Usinga2-Diskmodel,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,all-to-oneaggregationschedulingismostlystudiedinUDGwithinterferencerangeequaltothetransmissionrange.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

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interferencerangetothetransmissionrangeand(+1)]TJ /F4 11.955 Tf 12.33 0 Td[(1)isthemaximumdegreeoftheconictgraph. InChapter 2 ,weformulatedatabroadcastinginWSNsasInterference-awarebroadcastscheduling(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 ,westudytheall-to-alldatabroadcastingandall-to-onedataaggregationandpropose: 1.AO(1)-distributedapproximationalgorithmforall-to-onedataaggregation. 2.AO(1)-distributedapproximationalgorithmforall-to-alldatabroadcast. 3.ALocalizedalgorithmforall-to-alldatabroadcast. All-to-onedataaggregationisafundamentaloperationinWSNs,inwhichthedatafromallthenodesisaggregatedinasinknodeforfurtherprocessingandforwarding.Ourdistributedalgorithmforall-to-onedataaggregationistherstinliteratureandhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2.Ourdistributedalgorithmforall-to-alldatabroadcastingisalsotherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. 20

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1.2EfcientIn-NetworkDetectionandTrackingofDynamicPhenomena Contemporarywirelesssensornetwork(WSN)researchdoneintheareaofdetectionandtrackinghasprimarilyconcentratedonobservingmotionofobjectswhoseshapeandsizeareinvariant[ 41 43 ].However,manyreal-lifeeventssuchasoilspills,gasclouds,orrandomwalkingmotionofpeople,henceforthcalledPhenomenaClouds,arecharacterizedbynon-deterministic,dynamictemporalvariationsofcloudshape,sizeanddirectionofmotionalongmultipleaxes.Theseeventscannotbemodeledinwell-denedterms.Thus,itisdifculttoapplyexistingmechanismsinsuchsituations. Furthermore,theutilityofphenomenaclouddetectionandtrackingisnotrestrictedonlytoapplicationdomainsinvolvinggascloudsoroilspills.Infact,theycanalsobeutilizedinsituationswherethequalityofdataoriginatingfromindividualsensorscannotbetrustedinisolation.Insuchcases,therawsensordataoriginatingfromthesystemistypicallyextremelynoisywhichmakesitverydifculttodistinguishactualeventsfromrandomstimuli.Hence,aquorumofmultiplesensors,whicharelocatedincloseproximitytoeachother,isrequiredtoreducetheprobabilityoffalsepositives.ThroughourcollectiveresearchandsystemsexperienceovertheyearsinbuildingSmartSpacesatUniversityofFlorida'sMobileandPervasiveComputingLaboratory,wehavefoundasignicantutilityinapplyingthephenomenacloudconceptforefcientlyandaccuratelymonitoringvariouseventsinthespace,suchasdetectionofbarefootwalking,whichisacriticalapplicationfordiabetespatients. Withanewapplicationandbroaderconceptofphenomenaclouds,earlystudiesonboundarydetectionandtrackingofwell-denedshapesarenolongersufcient[ 12 13 19 44 45 ].Onlyoneworkrecentlystudiedonsimilarapplications,calledNile-PDT(astream-basedmechanism)maybeapplicable[ 46 ].However,thiscentralizedapproachdoesnottakeintoaccountthecostofacquiringandtransmittingsensorreadingsandtypicallyrequiresparticipationfromallsensorsinthenetwork.Unfortunately,sensorsamplingcostsandnetworkingandprocessingoverheadscanhaveacriticaleffect 21

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onthepracticalviabilityoftheentiresmartspace.Thisraisesaneedforadistributedin-networkdetectionmechanism,wherethedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofaphenomenonatanygiventimeanddoesnotrequireallthesensornodestoremainunnecessarilyactive. Alongthisdirection,inChapter 5 ,weintroduceamathematicalmodelandin-networkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergy-efcient,localized,in-networkalgorithmforreal-timedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizingtheenergyconsumptionofthephenomenacloudsdetectionandtracking.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 4.Providinganovellocalizedalgorithmwhichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinareal-worldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 22

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6.Validatingourapproachesusingbothreal-worldapplicationsandsimulationstoanalyzeitsperformanceandresourcerequirementsaswellascomparingitwiththatofstream-basedapproaches. Furthermore,inChapter 6 ,weprovideanenergyefcientlocalizedinnetworkdetectionandtrackingprotocolfortrackingtheboundaryofthephenomenacloud.Thisprotocolismorerelevantforscenariossuchasoilspills,gasleakage,etc,whereitismoresensibletodetectandtrackonlythephenomenaboundaryengulngtheaffectedareainsteadoftrackingtheentirephenomena.Simulationresultsareprovidedtoshowthattheproposedprotocolismoreefcientthantheexistingworks.Finally,inChapter 7 ,weprovideabriefsummaryofthisdissertationandconcludeit. 23

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CHAPTER2CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCE-AWAREBROADCASTSCHEDULING 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. SincebroadcastschedulingisNP-hard[ 15 ],weproposeO(1)-centralizedapproximationalgorithmsforWSNsin2Dand3Drespectively.Forthis,westudytwosubproblems:1)Tilingandcoloring2Dplaneusingregularhexagons,and2)Tilingandcoloring3Dspaceusingtruncatedoctahedrons.SolutionstothesetwoproblemsleadtoO(1)-approximationratiosin2Dand3Drespectively.OurO(1)-centralizedapproximationalgorithmistherstapproximationalgorithmfor3DWSNsandin2Douralgorithmhasthebestapproximationrationforthemodelweconsidered. 24

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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 ,wedescribethenetworkandtheinterferencemodelalongwiththeformaldenitionoftheinterference-awarebroadcastschedulingproblem.Weintroducethetilingandcoloringof2DplaneusingregularhexagonsinSection 2.3 .Section 2.4 describesthetilingandcoloringof3Dspaceusingidenticaltruncatedoctahedrons.TheO(1)-centralizedapproximationalgorithmsforbroadcastschedulingin2Dand3DWSNs,alongwiththeoreticalanalysisaredescribedinSection 2.5 .InSection 2.6 ,weintroducean 25

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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)2Eandthereexistsabi-directionallinkbetweenviandvj. The3DNetworkModel:Similarto2D,in3D,theWSNisrepresentedbyadirectedballgraphG=(V,E).AtransmissionballBTiandaninterferenceballBIiareassociatedwitheverysensornodevi2VcenteredatviwithradiusrTiandrIirespectively.IfanodevjislocatedwithinBTi,thereexistsadirectedlink(vi,vj)2E.Further,ifviisalsolocatedwithinBTjthen(vj,vi)2Eandthereexistsabi-directionallinkbetweenviandvj. Basedontheabovenetworkmodel,wedenetheinterferencemodelasfollows: 1.IftheEuclideandistancebetweenatransmittervt1andareceivervr1i.e.d(vt1,vr1)
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Figure2-1. Sufcientconditionsforinterference-awarenessbasedontransmitters. Figure2-2. Sufcientconditionsforinterference-awarenessbasedonreceivers. 3.Simultaneoustransmissionsvt1!vr1andvt2!vr2areinterfering,ifd(vt1,vr2)
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Ifwehaved(vt1,vt2)(+1)rTmaxasshowninFigure 2-1 ,accordingtotriangularinequalityd(vt1,vr2)rTmaxandd(vt2,vr1)rTmax.Thiswillensurethattransmissionsvt1!vr1andvt2!vr2willbeinterference-aware. Ifwehaved(vr1,vr2)(+1)rTmaxasshowninFigure 2-2 ,accordingtotriangularinequalityd(vt1,vr2)rTmaxandd(vt2,vr1)rTmax.Thiswillensurethattransmissionsvt1!vr1andvt2!vr2willbeinterference-aware. Hence,toensuresimultaneoustransmissionsvt1!vr1andvt2!vr2donotinterfereeachother,itissufcienttohaved(vt1,vt2)(+1)rTmaxord(vr1,vr2)(+1)rTmax. 2.2.2ProblemDenition Interference-AwareBroadcastScheduling(IABS)problem:Givenamulti-hopWSNG=(V,E)andasensornodevs2Vhavingamessagem.TheIABSproblemistogenerateaninterference-awarebroadcastscheduleforbroadcastingthemessagemfromvstoallothersensornodes.Theinterference-awarebroadcastschedulemustsatisfyfollowingconditions: Thesourcenodevsisscheduledtotransmitduringthersttimeslott1. Anodeu,ifscheduledtotransmitintimeslottj,musthavereceivedthemessageminsomeearliertimeslotti,wherei
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Figure2-3. Comparisonofdifferentplanetilingpolygon.Figuresa,b,canddrespectivelyshowasquare,arhombus,atriangleandahexagon,havingmaximumdistancewithinthemequalto1. tilingregularpolygons:1)Square,2)Rhombus,3)EquilateralTriangleand4)RegularHexagon,astheunitpartitionshapeandcomparetheirareas,asshowninFigure 2-3 .Weobservethataregularhexagonofsides1 2hasthemaximumarea.Consequently,weselectitastheunitpartitionshape.Figure 2-4 showstheregularhexagontilingof2Dplane. Weformallydenetheregularhexagontilingandcoloringof2DplaneasDistance-dHexagoncoloringproblem: Distance-dHexagonColoringproblem:GivenaregularhexagontilingHof2Dplaneandadistanced2R+,ndtheminimumnumberofcolorsneededtocolorH,suchthattwohexagonsh1,h22HhavingthesamecolormusthavetheEuclideandistancedistance(h1,h2)d.Thedistancedistance(h1,h2)ismeasuredbetweentwoclosestpointsp1andp2,where,p1lieswithinh1andp2lieswithinh2. 29

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Figure2-4. ThenewXh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhcoordinatesystem InordertostudytheDistance-dHexagonColoringproblem,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 2-4 .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. AstherststeptoprovidethesolutionforDistance-dHexagoncoloringproblem,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 2-5 : p1istheupperrightcornerofh(0,0)andp2isthelowerleftcornerofh(i,j),inFigure 2-5 (i=3,j=5). p1isthemidpointofupperrightsideofh(0,0)andp2isthemidpointoflowerleftsideofh(i,j),inFigure 2-5 (i=0,j=7). 30

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Figure2-5. Closestpointsp1andp2intwohexagons p1isthemidpointoftherightsideofh(0,0)andp2isthemidpointoftheleftsideof(i,j),inFigure 2-5 (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 2-5 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. Wenowintroducetheco-colorhexagonalgorithm,illustratedinAlgorithm 1 .InLemma 2 ,weprovethatforanyarbitrarydistanced2R+,Algorithm 1 optimallyidentiesco-colorhexagons(i.e.hexagonshavingthesamecolor)foranygivenhexagonh(i0,j0)inH. TheAlgorithm 1 ,forthegivend2R+,rstcomputes(i,j)usingtheabovemethodandidentiestheclosestco-colorhexagonh(i0+i,j0+j)ofh(i0,j0)intherstquadrant 31

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ofXh)]TJ /F3 11.955 Tf 12.35 0 Td[(YhplaneandaddsittosetSofco-colorhexagons.ItthensequentiallyrotatestheXh)]TJ /F3 11.955 Tf 12 0 Td[(Yhplaneby60oforvetimestondrestofclosestco-colorhexagonsofh(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)anditsclosestco-colorhexagonsremainthesame.AnyhexagonwhichisidentiedforthersttimeisaddedtothesetSandabovestepsarerecursivelyrepeatedonit. TheFigure 2-6 showsco-colorhexagonsofh(0,0)identiedbyAlgorithm 1 fordistanced=p 31 2,wherei=2,j=3.Sixclosestco-colorhexagonsofh(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)).Wecanseethatcentersofco-colorhexagonsofh(0,0)formatriangularsub-latticeSandarhombicsub-latticeRhofthelatticestructuregeneratedbycentersofhexagonsinH.Unitvectorsofsub-latticeRhareA=i^i+j^jandB=j^i)]TJ /F4 11.955 Tf 12.7 0 Td[((i+j)^j.Thenumberofpossibleclassesi.e.theindexofsub-latticeRhinH,whichisthenumberofdisjointsub-latticessimilartoRhinHisgivenasjdet(A,B)j=i2+j2+ij[ 49 ].Thus,therearefRh1,Rh2...Rh(i2+j2+ij)gdisjointsub-latticessimilartoRhinH,unionofwhichformH.Ifweassigneachofthemauniquecolor,allhexagonsinHwillbecoloredwithi2+j2+ijcolorsandtheclosestdistancebetweentwoco-colorhexagonswillbeatleastd2R+.InTheorem 2.1 ,weprovethatthehexagoncoloringgeneratedthiswayistheoptimalsolutionforDistance-dhexagoncoloringproblem. Lemma2. Algorithm 1 optimallyidentiesco-colorhexagonsforagivendistanced2R+. Proof. Letsconsiderthehexagontilingofanarea.Weneedtoidentifymaximumnumberofco-colorhexagonsonthisarea,suchthatanytwoco-colorhexagonareatleastatagivendistanced2R+.Forthis,Algorithm 1 ,computesapair(i,j)andproducesasetSofco-colorhexagons,whosecentersformanequilateraltriangularlatticeofsidelengthp 3 2p (i2+j2+ij),asshowninFigure 2-6 .Thenumberof 32

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Algorithm1Co-colorhexagonalgorithm(H,d,h(i0,j0),c) Input:ThehexagonallatticeH,distanced,hexagonh(i0,j0)andacolornumbercassignedtoh(i0,j0). Output:AsetSofco-colorhexagonsofh(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; co-colorhexagonsinSisproportionaltothenumberofequilateraltrianglesofsidesp 3 2p (i2+j2+ij)inthetriangularlattice. LetsconsideranothermethodwhichprovidesabettersolutionthanAlgorithm 1 .Thismethodidentiesasetofco-colorhexagoncentersformingaregularorirregulartriangulartilingoftheareainwhichatleastonetriangleisnon-equilateral.However,itissimpletoobservethatforthesamesmallestsidelength,theareaofanequilateraltriangleisalwayssmallerthantheareaofanynon-equilateraltriangle.Hence,thenumberofnon-overlappingtrianglesinthetilingstructuregeneratedwiththenewmethodwillbeboundedbythenumberofequilateraltriangleofsidesp 3 2p (i2+j2+ij)inthetriangularlatticegeneratedbyAlgorithm 1 .Thisresultsinthenewmethodidentifyinglessernumberofco-colorhexagons,incomparisontoAlgorithm 1 .Hence,acontradiction. 33

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Figure2-6. Co-ColorHexagonsofh(0,0)fori=2andj=3.Theindexofsub-latticeRhinHi.e.jdet(A,B)j=i2+j2+ij=19. Theorem2.1. ThecoloringgeneratedbytheabovemethodisanoptimalsolutiontotheDistance-dHexagonCenterColoringproblem. Proof. AccordingtoLemma 2 ,Algorithm 1 optimallyidentiesco-colorhexagonswhichformsarhombiclatticeRhwithunitvectorsA=i^i+j^jandB=j^i)]TJ /F4 11.955 Tf 12.81 0 Td[((i+j)^j.Thenumberofsub-latticessimilartoRhinHisgivenasjdet(A,B)j=i2+j2+ij[ 49 ].Therefore,theminimumnumberofcolorsneededtocolorHarei2+j2+ij.Ifweusei2+j2+ij)]TJ /F4 11.955 Tf 12.87 0 Td[(1colorsthenatleasttworhombicsub-latticeswillbeassignedsamecolor.Asthedistancebetweenthehexagonsindifferentrhombicsub-latticesisnotguaranteedtobeatleastd,itwillnotbethesolutionforDistance-dhexagoncoloringproblem.Therefore,theoptimalnumberofcolorsneededwillbei2+j2+ij,hence,theprovidedsolutionisoptimal. 34

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Theorem2.2. ThenumberofcolorsforDistance-dHexagoncoloringproblemforanarbitrarydisboundedby4 3d2+8 3d+4 3 Proof. Considerthehexagonh(0,0)andoneofitsclosestco-colorneighborsintherstquadrantofXh)]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+j2andtheguaranteedminimumdistancebetweenclosestpointsoftwoco-colorhexagonsisasfollows: 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. Figure2-7. ComparisonofnumberofcolorsusedtocolorthehexagontilingusingourschemeandScottet.al[ 1 ]. 35

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In[ 1 ],Scottet.al.proposeda3k2-hexagoncoloringschemeforDistance-dhexagoncoloringproblem.Figure 2-7 ,showsthecomparisonbetweentheirsolutionandtheoptimalsolutiongeneratedbyourproposedscheme.ItcanbeseenthatmostlyourcoloringschemeperformsfarbetterthanScottet.al.Onlywheni=j,thenumberofcolorsusedbyScottet.alisequaltothenumberofcolorsusedbyourscheme. 2.4TilingandColoringof3-DimensionalSpace Inthissection,westudythetilingandcoloringof3Dspaceusingtruncatedoctahedrons,whichformsthekernelpartofoursolutionforIABSproblemin3DWSNs. Aregulartilingofthe3Dspaceresultsinpartitioningof3Dspaceintoidenticalcells.Basedonourrequirements,thediameterofaunitcellshouldbe1anditsvolumeshouldbeaslargeaspossible.Therefore,toidentifytheshapeoftheunitpartitioncell,wecomparevolumesofthefourpossiblespacetilingprimarypolyhedra[ 50 ]:1)TruncatedOctahedron,2)RhombicDodecahedron,3)Cubeand4)HexagonalPrism,consideringtheirdiametersareequalto1asshowninFigure 2-8 .Weobservethatthetruncatedoctahedronofsides1 p 10hasthemaximumvolume.Hence,weselectedtruncatedoctahedronasthepartitionshape.Figure 2-9 showsthetilingof3Dspaceusingtruncatedoctahedrons. Similarto2D,weformallydenethetilingandcoloringof3DspaceusingtruncatedoctahedronsasDistance-dtruncatedoctahedroncoloringproblem: Distance-dtruncatedoctahedroncoloringproblem:GivenatilingTOCof3Dspaceusingtruncatedoctahedronsofsides1 p 10andadistanced2R+,ndtheminimumnumberofcolorsneededtocolorTOC,suchthattwotruncatedoctahedronsto1andto2havingthesamecolormusthavethedistancedistance(to1,to2)d.Thedistancedistance(to1,to2)istheEuclideandistancebetweentwoclosestpointsp1andp2in3Dspace,suchthatp1lieswithinto1andp2lieswithinto2. InordertostudytheDistance-dtruncatedoctahedroncoloringproblem,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

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Figure2-8. Comparisonofdifferentspacingllingpolyhedra.Figuresa,b,canddrespectivelyshowatruncatedoctahedron,arhombicdodecahedron,acubeandahexagonalprism,havingmaximumdistancewithinthemequalto1. Figure2-9. Thetilingofspaceusingtruncatedoctahedrons ZtaxesareinclinedasshowninFigure 2-10 .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).TheanglebetweentheZt-axisandtheXt)]TJ /F3 11.955 Tf 12.48 0 Td[(Ytplaneis3=45o.Thesidelengthofthetruncatedoctahedronis1 p 10,thedistancebetweenitstwoparallel 37

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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). Figure2-10. TheXt)]TJ /F3 11.955 Tf 11.96 0 Td[(Yt)]TJ /F3 11.955 Tf 11.95 0 Td[(ZtCo-ordinateSystem Them2n-coloringAlgorithm:Wenowpresentthem2n-coloringalgorithm,illustratedasAlgorithm 2 ,fortheDistance-dtruncatedoctahedroncoloringproblem.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 2-11 showsthebasiccoloringpatterngeneratedbythem2n-coloringalgorithmford=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

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Figure2-11. Coloringpatternford=1,dme=3anddne=3,Colorsassignedtothetruncatedoctahedronsarerepresentedbynumbers. Algorithm2m2n-coloringAlgorithm(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

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2.5BroadcastSchedulingAlgorithm(BSA) WenowpresentourcentralizedBroadcastSchedulingAlgorithm(BSA)forIABSproblem.BSAisapplicableto2Daswellas3DWSNs.Inthissection,werstdescribeBSAfollowedbyitstheoreticalanalysisforO(1)-approximationratiosin2Dand3DWSNsrespectively. 2.5.1AlgorithmDescription BSAtakesthegraphG=(V,E),representingtheWSNandthesourcenodevs2Vasinputs.Itgeneratesasoutput,theinterference-awarebroadcastscheduleforbroadcastingthemessagemfromvstoalltheothernodes. BSA,incaseof2DWSNs,considersatilingof2DplanewithregularhexagonofsidesrTmin 2andcolorsitusingthemethoddescribedinSection 2.3 ,assumingd=(+1)rTmax.Incaseof3DWSNs,itconsidersatilingof3DspacewithtruncatedoctahedronsofsidesrTmin p 10.Further,assumingd=(+1)rTmax,itcolorsthetilingusingm2n-coloringalgorithmdescribedinSection 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,ISAgeneratesaninterference-awareschedulefortransmissionsbetweentwoconsecutivelayers.TheISAisillustratedinAlgorithm 4 40

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TheISAtakestwoconsecutivelayersLiandLjasinputsandgeneratesaninterference-awaretransmissionschedulefromLitoLj.Inordertodothis,ISArstgeneratesamaximalindependentsetMIS(Lj)ofthesub-graphG[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)-ApproximationRatioforInterference-AwareBroadcastSchedulingProblemin2-Dimension Lemma3. ThetransmissionscheduleproducedbyISAfor2DWSNsisinterference-aware. Proof. WhenISAisappliedtoa2DWSN,eachhexagoncanhaveonlyoneMIS(Lj)nodeandhexagonshavingthesamecolorareatleastatadistanced=(+1)rTmax.AsMIS(Lj)nodesofthesamecolorstransmitsorreceivesimultaneously,theysatisfysufcientconditionsforinterference-awarenessdescribedinLemma 1 ,whichresultsininterference-awaretransmissionschedule. 41

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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.Basedonsufcientconditionsforinterference-awarenessinLemma 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

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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)-ApproximationRatioforInterference-AwareBroadcastSchedulingProblemin3-Dimension Lemma5. ThetransmissionscheduleproducedbyISAin3DWSNsisinterference-aware. Proof. ThiscanbeprovedsimilartoLemma 3 .WhenISAisappliedina3DWSN,eachtruncatedoctahedroncanhaveonlyoneMIS(Lj)nodeandtruncatedoctahedronshavingthesamecolorareatleastatadistanced=(+1)rTmax.AsMIS(Lj)nodesofthesamecolor,transmitorreceivesimultaneously,theysatisfysufcientconditionsforinterference-awarenessdescribedinLemma 1 ,whichresultsininterference-awaretransmissionschedule. Lemma6. MIS(Lj)nodesinISAarecoloredusingatmostlq 3 5(+1)+1m2lq 4 5(+1)+1mcolorsin3DWSNs. 43

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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,them2n-coloringalgorithmusesdme2dnecolors. 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

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Corollary2. Ifratiosandarebounded,theapproximationratiooftheBSAalgorithmforIABSproblemin3DWSNsisO(1). 2.6CentralizedGreedyHeuristicforbroadcastscheduling Inthissection,weintroduceacentralizedGreedyHeuristicAlgorithm(GHA)forbroadcastschedulinginWSNs.GHAdoesnotfollowalayerbylayerapproachusedinAlgorithm 2.5 ,inwhichallnodesinaBFSlayermustbeinformedbeforethebroadcastproceedstosubsequentlayers.Instead,GHAconsidersthesetofallinformednodesatanypointintimeaspotentialtransmitters.consequently,GHAschedulessimultaneoustransmissionsinmultiplelayers.Thus,itavailstheadvantageofspatialdistributionoftransmittersbyschedulingmorenon-conictingtransmissionsineachtimeslot.Furthermore,GHAusesamanualinterferenceavoidancetechniquebasedoncheckingindividualtransmitterswhethertheyareviolatingsufcientconditionsforinterference-awarenessdescribedinLemma 1 .Thishelpsinincreasingthenumberofsimultaneousinterference-awaretransmissionsineachtimeslot. Inordertoselectoneoutofpossibleinterferingtransmissions,mostofexistingheuristicsandapproximationalgorithms[ 15 32 35 ]usevarietyofcriteriatogivehigherprioritytoparticulartransmissionsinasetofinterferingtransmissions.Usually,higherpriorityisgiventotransmitterswithmoreneighborsinthenetwork,ortransmitterswithmorechildrenintheBFStree.Ontheotherhand,sincetheultimategoalofthebroadcastschedulingistoinformallnodesinthenetwork,wetriedtofollowagreedyruleforlocallyoptimizingtheprogressrateofthebroadcastbyinformingasmanynodespossiblewitheachnewtransmission.Thisgreedyrulegivesprioritytotransmitterswhichhavethehighestnumberofuninformedneighborsatthatpointintime.ThepseudocodeforGHA,whichemploysthisgreedyoptimization,isgiveninAlgorithm 5 2.7Conclusion Inthischapter,westudythebroadcastschedulingin2Dand3DWSNs.Weconsiderthatsensornodesmayhavedifferenttransmissionrangesandtheir 45

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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

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CHAPTER3CENTRALIZEDAPPROXIMATIONALGORITHMFORINTERFERENCE-AWAREBROADCASTSCHEDULING 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.Thisapproachisusedinouralgorithmstogenerateinterference-awaretransmissionschedulesfortransmitternodes.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

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3.2 andthecentralizedapproximationalgorithmandthegreedyheuristicdescribedinChapter 2 .Finally,Section 3.4 concludesthechapter. 3.2LocalizedAlgorithmforBroadcastScheduling Inthissection,weintroducealocalizedalgorithmforbroadcastschedulingin2DWSNsandprovideitsextensionfor3DWSNs.Thealgorithmrstgeneratesabroadcastingstructure,ontopofwhichmessagebroadcastingcanbeperformedwheneverneeded.Asthebroadcastingstructureisnotatreerootedatsomespecicsourcenode,itsupportsbroadcastinitiatedbyanynodeasthesourcenode.Werstdiscussthelocalizedconstructionofthebroadcastingstructurefollowedbydescriptionoftheprotocolforbroadcastingamessage. Algorithm6LocalizedAlgorithmforgeneratingaBroadcastingStructure Step1:Everynodevi2Vlocallyidentiesthehexagonhinwhichitislocatedalongwithitscolor. Step2:Nodevithenbroadcastsitsid,colorandhexagonco-ordinatestoitsonehopneighbors. Step3:Basedonthecolorandhexagoninformationfromone-hopneighbors,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 .Weassumethatthesub-graphgeneratedbythebi-directionallinksinG=(V,E)isconnected.Further,the2DplaneispartitionedintoregularhexagonsofsidesrTmin 2formingahexagontilingwhichcanberepresentedbytheXh)]TJ /F3 11.955 Tf 12.17 0 Td[(Yhco-ordinatesystem,describedinSection 2.3 48

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Thebroadcastingstructureisasub-graphGb=(Vb,Eb),whichspreadsoverallhexagonsinwhichWSNnodesarelocated.Ithastwokindsofnodes;SuppliernodesandProvidernodes,whichareconnectedthroughProvideredges(referFigure 3-1 ). Figure3-1. 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[(Yhco-ordinatesystem.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 3-2 showsanexampleofhexagoncoloringgeneratedbyAlgorithm 7 .Nodevbroadcastitsid,hexagoncoordinatesh(i,j)andcolortoitsone-hopneighborsandbasedonsimilarinformationitreceivesfromitsone-hopneighbors,itgenerates: 1.AsetHN(v)N(v),whichisasetofnodeslocatedinthesamehexagoninwhichvislocated. 49

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Figure3-2. 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

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WhenanodevisaSuppliernode,itbroadcastsaProviderRequestmessagetoallitsneighborsinPPv.Thenodesvj2PPvrespondwithaProviderResponsemessageandbecomeProvidernodesforvandedgesconnectingthemtovbecomeProvideredges.ThesetofSuppliernodes,ProvidernodesandProvideredgesformthebroadcaststructureGb=(Vb,Eb)fortheWSN. Figure3-3. AnExampleshowingthefunctioningofapartofthebroadcaststructure. Figure 3-3 showsaportionofthebroadcaststructurewithrespecttoasinglehexagonwhosecoloris11.BlacknodesdepictSuppliernodes,graynodesdepictProvidernodesandwhitenodesarerestofnodesinthehexagon.TheedgesshownareProvideredges.TheSuppliernodev1isberesponsibletoreceiveandforwardthebroadcastmessageinitshexagon,ifanyoneofitsProviderinneighboringhexagonswithcolorsf10,14,15,20,21,24gwhohasalreadyreceivedthebroadcastmessage. 51

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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

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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 Figure3-4. AnEpoch someEpochassignedtoitshexagon,thesourcenodevs2Vinitiatesthebroadcastbytransmittingthemessagemtoallnodesinitshexagon. AsshowninFigure 3-4 ,eachEpochisdividedintotwopartsEpochRandEpochT.EpochRisprimarilyusedbyaSuppliernodeinahexagonforreceivingthebroadcastmessagefromoneofitsProvidernodes.Further,itusesEpochTforbroadcastingthereceivedmessagetoallothernodesinitshexagon.EpochRisfurtherdividedintotwoparts;SelecttimeandReceivetime.SelecttimeforahexagonisdividedintosmallertimeslotscalledTrices,equaltothenumberofSuppliernodesinit.TheseTricesareallocatedtoSuppliernodesinincreasingorderoftheirids. DuringitscorrespondingTrice,aSuppliernodebroadcastsaRequestMessagetoallitsProvidersneighborsandifanyofthemhaveearlierreceivedthebroadcastmessagem,theyrespondwithResponseMessages.AsResponseMessagesare 53

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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 3-5 thehexagonsatadistancelessthandarehavingdifferentcolors. Figure 3-5 basicallyshowsanexamplewhereaWSNisdeployedonthe2Dplane,thenodesarerepresentedaspoints.ThemappingoftheWSNnodesonthehexagontilingalongwiththeformationofthebroadcaststructureshowninFigure 3-5 .Figure 3-6 showsthebroadcastschedulegeneratedwhenasourcenodesinthehexagonh(0,0)initiatethebroadcast.Followingistheepoch-wisedescriptionofthegeneratebroadcastschedule: Epoch1:Thesourcenodesinh(0,0)broadcaststhebroadcastmessagetoallthenodesinh(0,0). 54

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Figure3-5. Abroadcaststructure Figure3-6. Databroadcastingontopofabroadcaststructure 55

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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

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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,alltheSuppliernodesfollowthesufcientconditionsforinterference-awarenessintroducedinLemma 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

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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. 3.2.4LocalizedBroadcastSchedulingAlgorithmin3-Dimension Thelocalizedbroadcastschedulingalgorithmcanbeappliedto3DWSNs,ifweconsiderthe3D-spaceispartitionedintotruncatedoctahedronsofsidesrTmin p 10,forminga 58

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truncatedoctahedrontilingofthe3D-space,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,thelocalizedbroadcastschedulingalgorithmfor2DWSNscanbeusedforperforminginterference-awarebroadcastingin3DWSNs. Theorem3.2. TheapproximationratioforlocalizedbroadcastingalgorithmfortheIABSproblemin3DWSNis2lq 3 5(+1)+1m2lq 4 5(+1)+1m. 59

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Proof. Aslq 3 5(+1)+1m2lq 4 5(+1)+1mcolorsarerequiredbyAlgorithm 2 tocolorthetruncatedoctahedrontiling.Basedonthis,thetheoremcanbeprovedsimilartoTheorem 3.1 3.3ExperimentalEvaluation Inthissection,throughsimulations,wepresenttheexperimentalevaluationoflocalizeapproximationalgorithmforone-to-allbroadcastschedulingproposedinthischapterandcentralizedapproximationalgorithmandgreedyheuristicforbroadcastschedulingproposedinChapter 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 3-7 showsplotsofbroadcastlatenciesproducedbyApproxAlgo,LocalizedAlgoandGHAwithrespecttonumberofsensornodesinWSN.Thelatencyvalueforanynumberofnodesisaveragedafterrunningeachalgorithmonasetof100networkinstances.Asitwasexpectedthelatencyforthegreedyheuristicisthesmallest.Therearetwomainreasonsforthis:rstly,GHAdoesnotfollowthelayerbylayerbroadcastingapproach.Secondly,foranytimeslotGHAfollowsthemanualidentication,selectionandeliminationofsimultaneoustransmissionsamongdifferent 60

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Figure3-7. EffectofnumberofnodesonAverageLatency Figure3-8. AverageBFSheight Figure3-9. Averageoptimalityratio 61

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setsofinterferingtransmissions.Forthis,GHAconsidersexacttransmissionandinterferingrangesofinterferingsensornodes.IncaseofApproximationAlgorithmalayerbylayerapproachisusedbasedontheBFStreeofthenetwork.Andinatimeslottheidenticationandschedulingofinterferingtransmissionsisdonebasedoncoloringofthehexagontilingof2Dplane,whichconsidersthethetransmissionrangeandtheinterferencerangesasrTmaxandrTmaxrespectively.Thispossiblyresultsinconsideringextratransmissionsasinterferingtransmission,whichmightnotbeactuallyinterfering. Further,inFigure 3-7 weseethattheperformanceoftheLocalizedAlgorithmisnotgoodforsparsernetworks,butasthenetworkdensityincreasesthealgorithmstabilizedandafterthepointwhennumberofsensornodebecome80thealgorithmhaslatencycloseto80.ThoughtheLocalizedAlgorithmdoesnotusealayerbylayerapproachstillitslatencyisalittlehigher,thisisbecause,nodesneedtowaitforthetimeslotsassignedtotheirhexagonsinordertoreceiveortransmitthebroadcastmessage. Infact,weexpectedallthreealgorithmstorespectivelyconvergetoxedvaluesaftercertainnumberofnodes.Intuitively,theexpectedlatencyisdeterminedbytheheightoftheBFStree.Sincetheareaofournetworkisxed,afteracertainnumberofnodestheheightoftheBFStreecannotgrowanyfurtheronincreasingthenumberofnodes.Sinceasingletransmissionfromatransmittercaninformallnodesinitsneighborhood.Therefore,anincreaseinnumberofnodeswithoutincreasingtheBFSheightdoesnotaddmuchtothebroadcastlatency.Figure 3-8 showstheaverageheightoftheBFStreesinoursamplenetworksforanygivennumberofnodes.ItcanbeobservedinFigure 3-8 ,theBFSheightofthenetworkincreasestillthenumberofnodesreaches40,afterthatitstartstodecrease.Thisisbecauseofthelowerconnectivityinsparsernetworksresultsinsomelongerpaths,andwhenthenetworkbecomesdensertheconnectivityenhancesandthepathlengthsbecomesshorter.Afterthenumberofsensornodesarearound375theBFSheighttheremainscloseto5. 62

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Figure3-10. EffectofonAverageLatency Figure 3-9 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,initscurrentstateitcanalsohandlemulti-messagemulti-sourcebroadcasting. 3.3.2EffectofonBroadcastLatency Figure 3-10 showstheeffectofincreasingonlatenciesofallthreealgorithms.Wedeploy300sensornodesonasquareareaofside500m.Wevaryfrom1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreveryvalueof,wegenerate100networkinstancesandaveragedlatenciesproducedbyeachalgorithm. 63

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TheplotforLocalizedAlgorithm,inFigure 3-10 ,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 3-11 showstheeffectofvaryingonlatenciesofallthreealgorithms.Wedeploy300sensornodesonasquareareaofside500m.Theparametervariesfrom 64

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Figure3-11. EffectofonAverageLatency 1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreveryvalueofwegenerate100networkinstancesandaveragerespectivelatenciesproducedbyouralgorithms.Figure 3-11 showsthathasaneffectsimilartoonLocalizedAlgorithm.Thiscanbeexplainedasthenumberofcolorsneededtocolorthehexagontilingisdirectlyproportionalto,sohasadirectimpactonthelatencyofLocalizedAlgorithm. Further,inFigure 3-11 weseethattherearenotmuchvariationsinthelatencyofApproximationAlgorithmonchanging.ThisisbecausedoesnothaveanyeffectontheBFSheightofthenetwork,itonlyincreasestheinterferencerangeofanode.AsweknowthatincaseofApproximationAlgorithm,inagiventimeslotthetransmissionsareconsideredwithintwoconsecutiveBFSlayersbutnotintheentirenetwork,therefore,theeffectofonbroadcastlatencyisnotnoticeable.IncaseofGHA,weseeagradualincreaseinlatencywithrespectto.Thisisthedirecteffectofincreaseininterferingtransmissionswithincreasein. Figure 3-12 comparestheperformanceofvariousheuristicalgorithms,basedondifferentcriteriausedforschedulingvariousinterferingtransmissions.Foreachcriterion,theaverageoptimalityratiooverallthe11,000samplegraphsislisted.Itisinterestingtoseethatmanyofchosenoptimizationcriteriaactuallydegradetheperformanceofthealgorithm.Thisisbecausethecriteriawhicharebasedonthetopologyofthe 65

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Figure3-12. Comparisonofvariousheuristicsalgorithms network,arelikelytoprovidehigherprioritytophysicallyadjacentnodesinthenetworktotransmit.Thiscanaggravatethethespreadingofbroadcastmessageinthenetwork.Figure 3-12 showsthatitisbettertoprioritizenodeswhicharefartherfromthesourceratherthannodeswhichareclosertothesource.Thisisinlinewiththeobservationthatfarthernodesaremoreeffectiveinrapidlyspreadingthebroadcastmessageinthenetwork. 3.4Conclusion Inthischapter,westudiedlocalizedbroadcastschedulingintheinterferenceenvironmentmodeledbyprotocolinterferencemodel.Westudiedminimumlatencybroadcastschedulingandproposedtherstlocalizedapproximationalgorithms.Ourlocalizedalgorithmhasanapproximationguaranteeofl2(+1) p 3+1m2. 66

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CHAPTER4ALL-TO-ALLDATABROADCASTINGANDALL-TO-ONEDATAAGGREGATION 4.1Introduction Inthischapter,westudyall-to-alldatabroadcastingandall-to-onedataaggregationinWSNs.WeconsideraWSNmodeledasadiskgraphG=(V,E),whereeachsensornodevi2Vgeneratesamessagemi,westudyfollowingtwoproblems:1)Minimumlatencyall-to-oneaggregationschedulingand2)Minimumlatencyall-to-allbroadcastscheduling. Inminimumlatencyall-to-oneaggregationschedulingproblem,itisrequiredtoaggregateatnodevsallmessagesmigeneratedatnodevi2Vnvsrespectively.Theearliesttimeatwhichtheallmessagesreachesvsisknownasall-to-oneaggregationlatencyanditshouldbeminimized. Inminimumlatencyall-to-allbroadcastscheduling,itisrequiredtobroadcastallmessagesmigeneratedatnodesvi2Vrespectivelytoallthenodesinthenetwork.Theearliesttimeatwhichallmessagesreachallnodesinthenetwork,knownasall-to-allbroadcastlatency,shouldbeminimized. Theschedulesgeneratedforeachoftheaboveproblemsmustsatisfythefollowingconstraints: 1.Aschedulemustspecifyforeachnodev,whenitcantransmitorreceiveamessagem. 2.Anodevcanbescheduledtotransmitamessagemattimetjiffithadearliersuccessfullyreceivedthemessagemattimeti. 3.Twonodesuandvcanbescheduledtotransmitsimultaneouslyifftheirtransmissionsareinterfere-aware. Themaincontributionsofthischapterare: 1.Wepresentalocalizedalgorithmsforall-to-allbroadcastschedulinginWSNs. 67

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2.Wepresentadistributedalgorithmsforall-to-onedataaggregationschedulingandall-to-alldatabroadcastscheduling.Ourdistributedalgorithmforall-to-onedataaggregationschedulingistherstinliteratureandhasaconstantapproximationguaranteeof2l2(+1) p 3+1m2. 3.Wealsopresentadistributedalgorithmforall-to-allbroadcastscheduling,whichistherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. Therestofthechapterisorganizedasfollows:Insection 4.2 ,wedescribealocalizedalgorithmforall-to-alldatabroadcast.Section 4.3 describesadistributedapproximationalgorithmforall-to-onedataaggregationalongwiththetheoreticalanalysis.InSection 4.4 ,wedescribeadistributedapproximationalgorithmforall-to-alldatabroadcastingalongwiththetheoreticalanalysisofitsapproximationratio.WeprovidetheperformanceanalysisofthesealgorithmsinSection 4.5 .Finally,Section 4.6 concludesthechapter. 4.2LocalizedAll-To-AllDataBroadcastSchedulingAlgorithm Similartoone-to-allbroadcast,weassumethattimeisdividedintodiscreteEpochsandanyhexagonwithcolorciisassignedtheTthEpoch,suchthatCiTmodk2,wherek2isthenumberofcolorsusedtocolorthehexagontiling.EachEpochisdividedintotwopartsEpochRandEpochT.EpochRisprimarilyusedbyaSuppliernodetoreceiveamessagefromaProviderinitsneighborhood.EpochTisbasicallyusedfortwopurposes.Firstly,itisusedbynodesinahexagontobroadcasttheirownmessageswithintheirhexagon.Secondly,itcanbeusedbysomeSuppliernodetobroadcastinitshexagon,amessagewhichitreceivedfromoneofitsProvider.Thepreferencefortransmissionisgiventobroadcastmessagesgeneratedbythenodeswithinthehexagon.EachnodemaintainsaMessageList,whichisasetofbits,suchthatithasabitforeachnodeinthenetwork.Whenanodereceivesamessagegeneratedbysomenodewithidi,itsetsthebitattheithlocationinitsMessageList. WenowdiscusshowthetimedurationinanEpochisusedbythenodesinahexagon.EpochRisfurtherdividedintoSelecttimeandReceivetime.Selecttimeisdividedinto 68

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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. Asweassumethatthegraphgeneratedbythebi-directionallinksintheWSNisconnected,therefore,thereisatleastasinglepathbetweenanytwonodes.Let'sassumethatthemessagegeneratedbyanodeviisnotreceivedbynodevjatk-hopdistanceonpath(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

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path(vi,vi+1,...,vi+(k)]TJ /F7 7.97 Tf 6.59 0 Td[(1),vj)connectsvitovj,itiscertainthatvjwillreceivethemessagewithinnitenumberofEpochs,whichisacontradiction. 4.3DistributedAll-To-OneDataAggregationSchedulingAlgorithm All-to-onedataaggregationisanimportantoperationinWSN.Periodicallyitisrequiredthatthesensedinformationfromallthesensornodesbeaggregatedatthesinknodevsforfurtherprocessingandforwarding.Inthissection,weintroduceadistributedprotocoltogenerateaninterference-awareschedulefordataaggregationfromallthenodesv2(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

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somesetSiandreceivesmessagesfromsomeTransmitternodeinsetSi+1,or2)whenvactsaTransmitternodeandcollectsmessagesfromothernodesinitshexagon.TheForwardqueueshrinks:1)whenvforwardsmessagestoitsrespectiveTransmitternodeor2)whenvactsasaTransmitternodeandforwardsmessagetoitsCollector. DuringtheEpochRoftheallocatedEpochs,nodesinallhexagonsattempttotransferonemessagefromtheirForwardqueuetotheForwardqueueoftheirTransmitternodeusingRound-Robinschedulingbasedonincreasingorderoftheirids.TheTransmitternodethenduringtheEpochTforwardsamessagefromitsForwardqueuetoitsCollector,whichisonehopclosertovs.Inthismannerthedatamessagesareaggregatedfromallnodestothesinknodevsonmulti-hoppathswithoutinterference. 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.Asaresultofwhichtheysatisfythesufcientconditionsforinterference-awareness.Therefore,inter-hexagoninterferencecannotexist.Further,onlyasinglenodecantransmittoitsTransmitternodeduringtheEpochRoftheEpochallocatedtoitshexagon.Hence,therecannotbeintra-hexagoninterfere. Consequently,thereisnointerferencewhileaggregatingdatafromallthenodestothesinknodevs. Lemma12. Messagesfromallnodesareeventuallyaggregatedatthesinkvs. 71

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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+1satisfythesufcientconditionsforinterference-awarenessmentionedinLemma 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

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=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. Distributedall-to-onedataaggregationschedulingalgorithmhasanap-proximationguaranteeof2l(+1) p 3=2+1m2. Proof. Thetrivialtheoreticallowerboundforall-to-onedataaggregationisjV)]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. 4.4DistributedAll-To-AllBroadcastSchedulingAlgorithm Thedistributedprotocolforall-to-allbroadcastschedulingworksintwophases.Intherstphase,thedatemessagesfromallthenodesareaggregatedatthesinknodevs.Inthesecondphase,vsdistributesallthemessagesitreceivedintherstphasetoallthenodesinWSN.Fortherstphasethedistributedschedulingprotocolforall-to-onedataaggregationcanbeused.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

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Lemma14. Thedistributedall-to-allbroadcastisinterferencefree. 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 ,wehavethelatencyofall-to-allbroadcastschedulingis4jVjl(+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

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Figure4-1. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. algorithmsbasedonthreeimportantparameters:1)numberofsensornodesintheWSN,2)and3). 4.5.1ResultsforVaryingtheNumberofSensorNodes Inthissetofexperiments,weplacedthesensornodesinasquareareaofsides500m.Weconsidered=2,rTmin=100mandrTmax=200m(i.e.=2).WevariedthenumberofsensornodesjVjfrom10to500,withanincrementof10.ForeveryvalueofjVjweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 4-1 showstheeffectofnumberofsensornodesintheWSNonall-to-alldatabroadcasting.Weobservethattheperformanceofthelocalizedall-to-allbroadcastalgorithmisalwaysbetterthanthedistributedone.Themainreasonforthisisthatincaseofdistributedall-to-allbroadcastalgorithmallthemessagesarerstaggregatedatthesinknodevs.Andthenfromtheretheyarefurtherdisseminatedtoallothersensornodes.Thismayresultinbottlenecksonthepathsfromvarioussensornodestovs,causinghigherlatency.WeobservethatasthenumberofnodesinWSNincreases,thecurvesforboththealgorithmtendstobecomeconstant.Thiscanbeexplainedas,afterincreasingnumberofnodestoacertainextent,thediameteroftheWSNstartsdecreasingandbecomesalmostconstantaftercertainnumberofnodes.Thisresultsinalmostsamenumberofhopsamessageneedstotravelthedistancebetweenthemostdistantnode. 75

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Figure4-2. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. Figure4-3. EffectofNo.ofNodesonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. Thus,thelatencyincreasesonlybecauseoftheincreaseinnumberofnodesandnotbecauseofincreaseinthediameterofgraph.Therefore,theexperimentalapproximationratioismaintained. Figure 4-2 showstheeffectofnumberofnodesforall-to-onedataaggregationalgorithm.Theplotissimilartothatofall-to-alldatabroadcastandcanbeexplainedinthesamemanner.Theexperimentalapproximationratiobecomesalmostconstant,aftercertainnumberofnodesbecauseofnon-varyingnetworkdiameter. Figure 4-3 showstheeffectofnumberofnodesforone-to-alldatabroadcasting.Theplotissimilartotheall-to-allandall-to-one.Thisisbecause,apparentlythelatencyof 76

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Figure4-4. EffectofonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. thebroadcastisdrivenbytheradiusofthegraph.Whichtendstobecomeconstantaftercertainnumberofnodesinthenetwork. 4.5.2ResultsforVarying Inthissetofexperimentsweplaced300nodesinasquareareaofsides500m.Wexed=2andrTmin=100m.Wevariedfrom1.0to3.0withanincrementof0.1tocloselymonitoritseffect.Foreachvalueofweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 4-4 showstheplotsoflocalizedall-to-alldatabroadcastinganddistributedall-to-alldatabroadcastingonvarying.Weobservethereisalittleriseintheexperimentalapproximationratiosforboththeplotswhenchangesfrom1to1.2afterwhichtheexperimentalapproximationratiostendstobeconstant.Thiscanbeexplainedbythefactthatwhenincreases,thenumberofcolorsusedtocolortheWSNalsoincreases.Withthisthenumberoftimeslotsanodeneedtowaittotransmitthemessagealsoincreases.Thisdirectlyaffectsthelatency,resultinginincreaseintheexperimentalapproximationratio.But,whenisfurtherincreasedthesizeoftheneighborhoodofanodealsoincreasesanditstransmissioninformsmorenumberofnodes.Apartfromthisthediameterofthenetworkalsodecreaseswithincreasein.Hence,furtherincreasingdoesnoteffectstheexperimentalapproximationratio. 77

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Figure4-5. EffectofonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. Figure4-6. EffectofonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. InFigure 4-5 andFigure 4-6 ,theplotsfordistributedall-to-onedataaggregationandone-to-alldatabroadcastingonvaryingaregiven.Weobservethattheexperimentalapproximationrationinboththeplotsminutelyuctuatearoundacertainpointanddoesnotshowmuchincrease.Thiscanagainbeexplainedbythefactthatincreasingdecreasestheradiusofthegraph,asnodespossiblyhavelargerneighborhoodwhenislarge. atouralgorithmshowsamuchbetterperformance,incomparisontotheirproposedtheoreticalapproximationguarantees. 78

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Figure4-7. EffectofonAverageExperimentalApproximationRatioofAll-to-AlldatabroadcastingAlgorithms. 4.5.3ResultsforVarying Inthissetofexperiments,weplaced300nodesinasquareareaofsides500m.Weconsidered,rTmin=100,rTmax=200(i.e.=2)andvariedfrom1.0to3.0withincrementof0.1tocloselymonitoritseffect.Foreachvalueofweranallalgorithmson100randomlygeneratednetworktopologiesandaveragedtheirresults. Figure 4-7 showstheplotsoflocalizedall-to-alldatabroadcastanddistributedall-to-alldatabroadcast.Weobservethatboththeplotsdonotshowmuchvariationonincreasing.Thiscanbeexplainedbythefactthatincreasingdoesnotaffectsthediameterofthegraph,whichremainsconstantforsamenumberofnodes.Hence,theexperimentalapproximationratioremainsthesame.Figure 4-8 and 4-9 showstheplotsofall-to-onedataaggregationandone-to-alldatabroadcastingonvarying.Theplotsaresimilartotheplotsoflocalizedanddistributedall-to-allbroadcastandcanbeexplainedinthesimilarmanner. Inourexperimentalevaluation,weobservedthatthefactorssuchasnumberofnodesinthenetworkand,thatdirectlyaffectsthediameterofthenetwork,havereasonableimpactonthelatencyofdatabroadcastingandaggregationinWSNs.Further,weobservedthatouralgorithmshowsamuchbetterperformanceincomparisontotheirproposedtheoreticalbounds. 79

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Figure4-8. EffectofonAverageExperimentalApproximationRatioofAll-to-OnedatabroadcastingAlgorithms. Figure4-9. EffectofonAverageExperimentalApproximationRatioofOne-to-AlldatabroadcastingAlgorithms. 4.6Conclusion Inthischapter,westudiedlocalizedbroadcastschedulinginaninterferenceenvironmentmodeledbyprotocolinterferencemodel.Westudiedtwoproblems:1)Minimumlatencyall-to-oneaggregationschedulingand2)Minimumlatencyall-to-allbroadcastscheduling.Forminimumlatencyall-to-allbroadcastscheduling,weproposedtherstlocalizedalgorithmandtherstdistributedapproximationwithapproximationguaranteeof4l(2(+1) p 3+1m2.Further,forminimumlatencyall-to-oneaggregationschedulingweproposedtherstdistributedalgorithmwithanapproximationguaranteeofl2(+1) p 3+1m2. 80

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CHAPTER5DETECTIONANDTRACKINGOFPHENOMENACLOUD:NEWLOCALIZEDAPPROACHESANDAPPLICATIONS 5.1Introduction Contemporarywirelesssensornetworkresearchdoneintheareaofdetectionandtrackinghasprimarilyconcentratedonobservingmotionofobjectswhoseshapeandsizeareinvariant[ 41 43 ].However,manyreal-lifeeventssuchasoilspills,gasclouds,randomwalkingmotionofpeople,ormovementofagroupofpeople,henceforthcalledPhenomenaClouds,arecharacterizedbynon-deterministic,dynamictemporalvariationsofcloudshape,sizeanddirectionofmotionalongmultipleaxes.Theseeventscannotbemodeledinwell-denedterms.Thus,itisdifculttoapplyexistingmechanismsinsuchsituationduetothefactthatcurrentcloud-basedtrackingtechniquesareorientedtowardsmonitoringthemotionofwell-denedobjectsalongasingleaxisataparticulartime.Theyarenotequippedformonitoringtheshape,sizeandmotionofphenomenacloudswhosebehaviorcannotbereadilymodeledusingclassicaltheory. Moreover,theutilityofphenomenaclouddetectionandtrackingisnotrestrictedonlytoapplicationdomainsinvolvinggascloudsoroilspills.Infact,theycanalsobeutilizedinsituationswherethequalityofdataoriginatingfromindividualsensorscannotbetrustedinisolation.Insuchcases,therawsensordataoriginatingfromthesystemistypicallyextremelynoisywhichmakesitverydifculttodistinguishactualeventsfromrandomstimuli.Hence,aquorumofmultiplesensorswhicharelocatedincloseproximitytoeachotherisrequiredtoreducetheprobabilityoffalsepositives.Throughourcollectiveresearchandsystemsexperienceovertheyearsinacompletelydifferentdeploymentdomain(SmartSpaces,alsoknownasAmbientIntelligence),wehavediscoveredagreatutilityinapplyingthephenomenacloudconceptforefcientlyandaccuratelymonitoringvariouseventsinthespace,suchasdetectionofbarefootwalking,whichisanimportantapplicationfordiabetespatients. 81

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Withanewapplicationandabroaderconceptofphenomenaclouds,earlystudiesonboundarydetectionandtrackingofwell-denedshapesarenolongersufcient[ 12 13 19 44 45 ].Onlyoneworkrecentlystudiedonsimilarapplications,calledNile-PDT(astream-basedmechanism)maybeapplicable[ 46 ].However,thiscentralizedapproachdoesnottakeintoaccountthecostofacquiringandtransmittingsensorreadingsandtypicallyrequiresparticipationfromallsensorsinthenetwork.Unfortunately,sensorsamplingcostsandnetworkingandprocessingoverheadscanhaveacriticaleffectonthepracticalviabilityoftheentiresmartspace Thisraisesaneedforadistributedin-networkdetectionmechanism,wherethedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofaphenomenonatanygiventimeanddoesnotrequireallthesensornodestoremainunnecessarilyactive.Alongthisdirection,weintroduceamathematicalmodelandin-networkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergy-efcientanddistributedalgorithm,calledFullDensityAlgorithm(FDA)forreal-timedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained.Plus,theproposedalgorithmcanbeusedinanewapplicationdomain,i.e,detectionawalkingmotion. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizetheenergyconsumptionduringthephenomenaclouddetectionandtrackingprocess.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 82

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4.Providinganovellocalizedalgorithm,calledOptimizedDensityAlgorithm(ODA)whichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinareal-worldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 6.Validatingourapproachesusingbothreal-worldapplicationsandsimulationstoanalyzetheirperformancesascomparedtostream-basedapproaches[ 46 ]. Theremainderofthispaperisstructuredasfollows.Section 5.2 describesthephenomenaclouds,theircharacteristicsalongwiththecriticalchallengesandanalyzestheirstructuresusingthesetofproposedparameters.Ourrstin-networkdetectionandtrackingalgorithm,includingitsfaulttolerancemechanism,isproposedinSection 5.3 .InSection 5.4 ,weoptimizethepowerconsumptionandresourceutilization,onwhichweformulateanintegerprogramfordetectionandtrackingofaphenomenacloudandproposealocalizedprotocolbasedonthehexagontilingtechnique.Section 5.5 presentsaninterestingpracticalreal-worldapplicationofourphenomenadetectionandtrackingalgorithminthesmartspace.Section 5.6 providesevaluationandanalysisoftheperformanceofourapproachesthroughreal-lifeexperimentsandsimulations.Section 5.7 providestheoverviewoftheexistingliterature.Finally,Section??concludesthepaperwithsomefuturework. 5.2PhenomenaCloud:ChallengesandRepresentation Aphenomenoncloudcanbedenedasamanifestationofanumberofsimultaneouseventsreachingcriticalmassandspanningacontiguousspace.Assuchaphenomenonexpands,shrinks,ortranslatesrandomlyinanon-deterministicfashionoverthetime,itsshape,sizeanddirectionofmovementeithercannotbeanticipatedaccuratelyorhavemodelswhichareusuallytoocomplexforreal-timecomputing 83

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bysensornetworks,whichlargelyconsistoflow-endnodeswithlimitedprocessingcapabilities.Examplesofphenomenacloudsincludegasclouds,oods,oilspills,wildforestresorevenmovementoftouristsinamuseum. 5.2.1MajorChallenges Themajorchallengesthatarefacedduringdetectionandtrackingofphenomenacloudsareasfollows: 1.Initialdetectionofphenomenon.Initialoccurrencesofthephenomenonmightbescatteredthroughoutthespace.Detectionthereforemustbeattemptedatmultiplelocations. 2.Avoidingfalsepositives.Theprobabilityofasinglesensoroutputtingaccuratereadingsataspecicpointintimeisverylow.Itisquitepossibleforasensortotemporarilymalfunctionorbesubjecttoenvironmentalconditionswhichmightcauseittooutputvalueswhichincorrectlyindicatetheoccurrenceofaphenomenon.Thusdetectionmustrequireinputsfrommultiplesensorslocatedcloselytoeachother. 3.Trackingaphenomenoninreal-time.Aphenomenoncansuddenlygroworshrinkinsizeandalsomoveinmultipledirectionssimultaneously.Therefore,trackingitinreal-timecanbecomeamassivelycomplextask.Toenablecost-effectivereal-timetracking,therateofstatusupdatesfromthesensornetworktotheuserneedstobekeptataminimumtoreducenetworkcostandprocessingoverhead.4.Operatingunderharshconditionsresultingindisconnectedoperation:Hostilephenomenalikerescanleadtodisruptionofcommunicationsbetweenthesensornetworkandthebasestation.Therefore,thedetectionandtrackingprocessshouldbeabletooperateinanautonomousmannerwithoutrequiringremotesupervision. 5.2.2Representation Inthissection,weproposeasetofparameterstoformallydescribethestructureofphenomenaclouds.Werepresentaphenomenoncloudasa5-tuple,P=ha,b,pT,m,ni.Thelowerandupperboundsoftherangeofsensorvalueswhich 84

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Figure5-1. 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 5-1 .Theinnermostregion,calledtheCoreregionofthecloudiswherethephenomenonismoststronglyobserved.Clearly,thesensorslyinginthecoreregionsatisfythePhenomenonConditionandhence,aremembersofthePhenomenonSet.TheMiddleregionistheouterborderofthephenomenacloudwheretheProb-abilityConditionissatisedbutthePhenomenonConditionisnotyetsatised.TheOuterregiondenotesthefringeswhereuncertaintyregardingtheoccurrenceofthephenomenonishighest,hence,theouterfringeistheregionwherethephenomenaissparseandisnotdetected.Section 5.3.1 describestherolesassignedtothesensors 85

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basedonwhichregiontheyfallinataparticulartimeandhowtheyareutilizedtoperformlocalizedin-networkdetectionandtracking. 5.3ProposedSolutionforDetectionandTracking Inthissection,wepresentourproposedapproachforthephenomenonclouddetectionandtracking,calledFullDensityAlgorithm(FDA).Webeginwithclassifyingsensorsintodifferentcategoriesasdiscussedaboveaccordingtotheirrolesinthedetectionandtrackingprocess.Wethendescribevariousresponsibilitiesofanysensornodewithrespecttocategoriesofitsneighborsandlistasetofruleswhichgovernthetransitionofsensorsfromonecategorytoanotherwhichformthemainpartofourdetectionandtrackingstrategy.Therestofthissectioncoversthedifferentstagesofdetectionandtrackingprocessinchronologicalorder.Italsodescribesmechanismsforhandlingnodefailuresandhowapplicationscanutilizethereal-timetrackingdataproducedbythesensornetwork.Figure 5-3 pictoriallydepictsanexamplefordetectionandtrackingprocessofasinglephenomenoncloud. Figure5-2. ClassicationoftheParticipatingSensors 5.3.1ClassicationofSensors Figure 6-2 showsthephenomenonclouddepictedinFigure 5-1 superimposedoveragroupofsensors.Sensorsareclassiedaccordingtotheregionwheretheyarelocated,whichdeterminestheirroleindetectionandtrackingofphenomenacloud.Thedifferentcategoriesareasfollows: 86

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1.CandidateSensor:AsensorwhichsatisestheProbabilityConditioniscalledacandidatesensor.Ithastheresponsibilityofactivelysensingandnotifyingitsneighborsaboutitsstate.ItalsoreceivesnoticationsfromitsneighborsinordertoidentifywhetheritsatisesthePhenomenaConditiontobecomeapartofthePhenomenonSet.Asensorbecomesacandidatesensorwhenittransitionsfromthepotentialcandidatestageduringtheexpansionofthephenomena,orwhenittransitionsfromthetrackingstageduringtheshrinkingofthephenomena. 2.PotentialCandidateSensor:AsensorwhichisactivelysensingthephenomenonbutdoesnotsatisfytheProbabilityConditioniscalledapotentialcandidatesensor.Thesesensorskeepmonitoringtheirreadingtoenableaneighborcandidatesensorstocheckthevalidityoftheirobservations.Asensorbecomesapotentialcandidateifeither1)ithasbeenselectedbythecentralizedqueryprocessoraspartoftheinitialdetectionphase(describedinSection 5.3.4 ),or2)oneofitsneighborsbecomesacandidatesensorduringtheexpansionofthephenomena,or3)whenacandidatesensortransitionsfromcandidatestagetopotentialcandidatestageduringtheshrinkingofthephenomena.TheresponsibilityofthepotentialcandidateistonotifyitsneighboringcandidatesensorswheneveritsreadingsatisestheProbabil-ityCondition.Potentialcandidatesensorsformthefringesofdetectionandmakeuptheouterregionofthephenomenoncloud.Essentially,thesetofpotentialcandidatesensorsformsaphenomenonfrontwhichgrowsandshrinksdynamically. 3.TrackingSensor:Asensorwhichhasalreadydetectedaphenomenoneventandisnowactivelyengagedinthetrackingprocessiscalledatrackingsensor.AcandidatesensorbecomesatrackingsensorafteritsatisesthePhenomenonCondition(denedinSection 5.2.2 ).Trackingsensorscoversthecoreregionofthephenomenacloud.ThePhenomenonSetisthecollectionofalltrackingsensors,hence,eachcloudconsistsofsubsetsoftrackingsensorsfromthePhenomenonSet. 87

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4.IdleSensor:Allsensorswhichdonotbelongtoanyoftheabovethreecategoriesarecalledidlesensors.Thesesensorsarenotengagedinphenomenondetectionortrackinganddonotperformanymonitoringwhatsoever.Typically,mostsensorsinthespacewillfallinthiscategorysinceonlyselectedclustersofsensorswillbeactivelyengagedinthedetectionandtrackingofphenomenacloudsatanygiventime.Thisensuresthatthedetectionandtrackingprocessisexecutedinalocalizedmannerwithminimalexpenditureofenergy. Figure5-3. DetectionandTrackingofaPhenomenaCloud Remarks.Wehavemodiedthedenitionsofcandidateandpotentialcandidatesensorsascomparedtoourinitialdenitionsinthepreliminarywork[ 57 ].Morespecically,in[ 57 ],wedenedthatacandidatesensorisnotrequiredtosatisfytheProbabilityConditionandapotentialcandidatesensorcannothaveatrackingsensor,butonlycandidatesensorasitsneighbors.Consequently,evenifacandidatesensordoesnotsatisfytheProbabilityCondition,itunnecessarilyinvokesallitsidle 88

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Figure5-4. ActionTakenbyaSensorNodewithrespecttoitsNeighborswhicharenotidle neighborsaspotentialcandidates,therebycausingexcessiveresourceusage.Incontrast,inthispaper,acandidatesensormustsatisfytheProbabilityConditionandapotentialcandidatesensorcanhasatleasteitheronetrackingorcandidatesensorinitsneighborhood.Therefore,onlythoseidlesensorsareinvokedaspotentialcandidateswhichhavephenomenaoccurringintheirvicinity.Thisslightlymodicationhaveanimpactontheperformanceintermsofenergyandresourceconsumptionswhichweshowlaterinsection 6.5 5.3.2KeepingTabsontheNeighborhood Eachsensornodekeepstrackofthecategoryofitsneighbors.Thisisdoneinapeer-to-peerfashion,whereasensortransitioningfromonecategorytoanothernotiesitsneighborsviaa1-hopbroadcastwithoutinvolvingthecentralizedqueryprocessor.WeusedZigBeecommunicationprotocolinoursystem,whichnativelysupports1-hopbroadcasting.Thecategoryofasensoranditsneighborsdeterminestheirmutualresponsibilitiestowardseachother.Forexample,acandidatesensornodeAhas 89

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twoneighborsBandCwhereBisapotentialcandidateandCisatrackingsensor.Inthiscase,BwillalertAwheneveritsreadingssatisfytheProbabilityCondition.AndwheneverA'sreadingisnolongersatisedtheProbabilityCondition,AwillonlyalertCbutnotB.Therefore,asinglesensornodeplaysdifferentroleswithrespecttodifferentcategoriesofitsneighbors.Figure 5-4 liststheactionsasensornoderequiredtoperformwithrespecttothecategoriesofitsneighbors.ThecellsmarkedNotApplicableimplythatsuchcombinationsarenotpossibleaccordingtotransitionrulesgiveninnextsubsection. 5.3.3TransitionRules Wenowreadytopresentasetofrulesthatgovernthetransitionofasensorfromonecategorytoanother.Theserulesareexecutedin-networkandcontroltheentiredetectionandtrackingprocess. 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

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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.Anothercriterioncanbetheoff-lineuseofanavailablemathematicalmodelofthephenomenoncloudtodeterminelocationswheretheprobabilityofoccurrenceisthehighest.Incasesuchacriterionishardtoformulate,alternativelythesystemcanrandomlyselectsensorsasinitialpotentialcandidatessuchthattheyareuniformlydistributedoverthesensorspace.Thesesensorsandtheirrespectiveneighborhoodscanbeviewedasautonomousclustersofearlywarningsystemsfordetectingthesuddenmanifestationofpossiblymultiplephenomenaclouds.Sincesensordeploymentpatternstendtobehighlyapplicationandphenomenon-specic,wedonotgointodetailsoftheirdeployment.Forpurposesof 91

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discussionfortherestofthispaper,weassumethatsensornodesaredeployedinsuchamannerthateachsensorhasasufcientnumberofneighborstopotentiallyavoidfalsepositives. 5.3.5MonitoringforInitialOccurrences Thequeryprocessorpushesthephenomenoncloudparametersontoeachoftheselectedinitialpotentialcandidatesensornodesinthenetwork.Atthebeginningofeveryepoch,eachpotentialcandidatenodemonitorsitsreadingsandsendsa1-hopbroadcastmessageifitsatisestheProbabilityConditionandtransitionsintoacandidatesensornode.Inordertoenablesensornodestosendorreceivealertbroadcaststoandfrommultipleneighborssimultaneouslyduringthesameepoch,aslottedapproachisusedtoensurecollisionavoidancesimilartowhatisdescribedin[ 58 ].Eachepochissub-dividedintomultiplesub-epochsandeachnodeonlybroadcastsalertsduringitsassignedsub-epoch.ThecandidatesensornodeaggregatesalertsreceivedviabroadcastsfromitsneighborsanddeterminesifitsatisesthePhenomenonCondition.AcandidatesensorsatisesthePhenomenonConditionifitsreadingssatisfytheProbabilityConditionanditalsoreceivesbroadcastalertsfromatleastnneighborswhichalsosatisfytheProbabilityConditioninthesameepoch. 5.3.6NoticationofInitialOccurrence IfaninitialpotentialcandidatenodehassatisedtheProbabilityCondition,ittransitionstoacandidatesensornode.Furthermore,whenacandidatesensornodesatisesthePhenomenonCondition,itnotiesthequeryprocessorresidinginthebasestationthatithasdetectedpresenceofaphenomenoncloud.ThequeryprocessoraddsthecandidatenodetothePhenomenon-SetandthecandidatesensortransitionstoatrackingsensornodeusingruleR1giveninSection 5.3.3 92

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5.3.7GrowthofPhenomenonCloud WhenapotentialcandidatesensorsatisestheProbabilityCondition,itgetstransitionedintoacandidatesensorusingruleR2.Itnotiesallitsneighborsaboutthistransitionbybroadcastinganalertmessage.EachoftheneighborsensoronreceivingthealertmessagetransitionsintoapotentialcandidateiforiginallytheywereidlesensorsusingruleR3.Inthismanner,thedetectionmechanismgetsdistributedandpropagatedin-network,withoutinvolvementofthecentralizedqueryprocessor,asthephenomenoncloudgrowswithtime.Eachsensornodekeepstrackofitsneighborhoodviathebroadcastalertsthatitreceivesanddeterminestheactionstobeundertakenwithrespecttoaspecicneighborbasedonwhichcategoryeachneighborfallsin,asdescribedinFigure 5-4 Figure5-5. RatioofTotalActiveSensorstoCloudSizeinaRectangularSensorGrid TheplotinFigure 5-5 depictsanexampletoshowtheeffectagrowingphenomenoncloudhasonthenumberofactivesensors(tracking,candidatesandpotentialcandidatesensors)involvedinitsdetectionandtracking.Weobservethatinourdistributedin-networkapproach,thenumberofactivesensorsrequiredatanygiventimeisonlyslightlymorethanthenumberofsensorsactuallyneededtoparticipateindetectionandtrackingthephenomenoncloudandtheratioofactivesensorsversusphenomenacloudsizedecreaseswithincreaseincloudsize.Thisisduetothefactthatthe 93

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detectionandtrackingprocessisexecutedin-networkinalocalizedmannertoensuremaximumefciency.Onlythosesensornodeswhichareintheimmediatevicinityofaphenomenoncloudorarelyingwithinthecloudareactivelyinvolvedinthedetectionandtrackingprocess.Thepropagationofthisprocessinthenetworkisgovernedsolelybythebehaviorofthephenomenoncloudandhandledbythesensornodesinadistributedbutco-operativemannerusingtherulesspeciedinSection 5.3.3 ,withoutneedinganyassistancefromthecentralizedqueryprocessor. 5.3.8ShrinkingofPhenomenonCloud ThephenomenoncloudissaidtobeshrinkingwhenthesensorsfallinginthetrackingregionidentiesthattheynolongersatisfythePhenomenaCondition.AccordingtoFigure 5-4 ,afterasensortransitionsintotracking,itsneighborswillonlysendalertsiftheirreadingsfailtosatisfytheProbabilityCondition.AtrackingsensorisnolongerparticipatinginthetrackingofthephenomenoncloudifitdeterminesthatlessthannofitsneighborscurrentlysatisfytheProbabilityCondition.Insuchacase,thetrackingsensornodenotiesthequeryprocessorwhichremovesthetrackingsensorfromthePhenomenonSet,therebysignifyingthatthephenomenoncloudhasshrunk.ThetrackingsensornodethentransitionsintoacandidatesensorusingruleR4.WhenthephenomenacloudfurthershrinksandthecandidatesensordoesnotevensatisfytheProbabilityCondition,ittransformsintoapotentialcandidatesensorusingtransitionruleR5ifithasatleastonecandidateortrackingsensornodeinitsneighborhood.AndallofthepotentialcandidateneighborsofthissensornodetransitionsintoidlesensorsusingtransitionruleR6iftheydonothaveanyothercandidateortrackingnodeintheirneighborhood.WemakeanotethatifallthephenomenacloudsdisappearcompletelythenafterallthetransitionsareappliedasperrulesgiveninSection 5.3.3 ,thesensorspacewillrevertbacktothesetupdescribedinSection 5.3.4 ,whereonlytheinitialsetofpotentialcandidatesensorswillremainactive. 94

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5.3.9Real-TimeMonitoringbyApplications ThecentralizedqueryprocessorcontinuouslymaintainsthePhenomenonSetatanygiventime.Thequeryprocessorisabletotrackphenomenoncloudsinreal-time,withminimumprocessingandnetworkingoverheadofreceivingupdatesfromthesensornodes.ThePhenomenonSetisonlyupdatedwheneverasensortransitionstoorfromthetrackingcategory.Hence,thequeryprocessoronlyrequiresminimalupdatestocontinuouslytrackphenomenaclouds.WeevaluatethenetworkandprocessingcostsforthisupdateschemeinSection 5.6.2 Sincethelocationofeachsensornodeisknownbeforehand,anapplicationsuchasaGUI-basedphenomenoncloudvisualizationtoolcaneasilyreconstructaviewofthevariousphenomenoncloudsinreal-timeusinginformationfromthePhenomenonSetinconjunctionwithsensorlocationinformation.BylookingatwhichsensorsenterorleavethePhenomenonSet,themotionofmultiplephenomenoncloudscanalsobetrackedovertimeandmoresophisticatedanalysisandpredictionperformedatacentralizedlevel.Thisisextremelyusefulforapplicationssuchas[ 59 ]whichcandeterminesafepassagesforrescueworkersthroughmultipleoccurrencesofphenomenoncloudssuchasgasleaksandwildres. Inaddition,thecardinalityofthePhenomenonSettogetherwithsensorlocationcangiveapplicationssomeinformationaboutthesizeofvariousphenomenaclouds.Thesizeofaphenomenoncloudcanhavedifferentimpactsdependingontheapplicationcontext.Forexample,ifanapplicationisconcernedwithdetectionofphosphatedustclouds,aPhenomenonSetoflowcardinalitymaynothavemuchsignicance.However,ifanapplicationistaskedwiththedetectionofhydrogencyanide(HCN)leakage,thenthedetectionofevenasmallcloudindicatesseriousconsequences. 5.4OptimizingEnergyConsumptionandResourceUtilization Wenowturnourattentiontooptimizingtheenergyconsumptionandresourceutilizationofourproposedmechanism.Inordertominimizethenumberofactive 95

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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

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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<>:1ifi2Tisanactivenode0otherwise (5) 97

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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

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partitioningtheplaneintoregularidenticalpartitions,suchthatallnodeslocatedwithinthesamepartitionformsacluster.Thesizeofeachpartitionwillbedenedbythetransmissionrangerofasensornode,andweconsiderallthesensornodeshavethesametransmissionrange.Oncetheclusteringisperformed,thenodeswithinapartitionelectstheclusterheads.Atanypointintime,theclusterheadswillremainactiveandtherestofcoretrackingnodeswillsleepaslongaseachclusterheadhasatleastnactiveneighbors. Letusconsiderhowtoperformsuchpartitionbasedonthetilingtechnique.Whatistheoptimalshapeoftheregularunitpartitionsothatwecanpartitiontheplaneintotheminimumnumberofclusterssuchthatallnodesinadjacentclustersareneighborsofeachother?Suchapartitionwillminimizethetotalnumberofactivecoretrackingnodes. Therearefourpossibleplanetilingpolygons:1)square,2)rhombus,3)equilateraltriangle,and4)regularhexagon.Asweneedthenodesintwoadjacentpartitionsmustbeneighborsofeachother,consequently,themaximumdistancebetweentwopointslocatedintwoadjacentpartitionsmustber.Figure 5-6 5-7 5-8 and 5-9 ,showsthefourpossiblepartitioningusingdifferentplanetilingpolygons.Itiseasytoseethattilingaplaneusingtheregularhexagonscoversthemaximumarea,thuslessernumberofclustersforagivenarea.Therefore,weuseregularhexagonasapartitionshapeforourtilingtechniqueandnextpresenthowtolocallyperformthistiling. 5.4.2.1Clusteringmethod Wepartitionthe2DplanecoveredbytheWSNintoregularhexagonsofsidelengthr p 13toformahexagonaltilingasshowinFigure 5-10 .Allthesensorslocatedwithinthesamehexagonformacluster.Noticethattheirexistsacoordinatesysteminwhichtheaxisareinclinedat60o,suchthatallthehexagoncenterslieontheintegralcoordinatesofthisnewcoordinatesystem. 99

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Figure5-6. Partitionshapeassquare. Figure5-7. Partitionshapeasrhombus. Figure5-8. PartitionshapeasEquilateralTriangle. Figure5-9. PartitionshapeasRegularHexagon. WeassumethatallthesensorsareequippedwithalocationidenticationdevicesuchasaGPSorusedsomelocalizationmethods[ 54 55 60 ].Further,weassumethatallthesensorsareawareoftheEuclideanlocationofthebasestation.Thiscanbedonebyonebroadcastfromthebasestation.Wenowshowthatifanodevknowsitscoordinates(xv,yv)andthecoordinatesofthebasestation(xb,yb)intheCartesiansystem,thenwithouthavingtheglobalviewofthehexagontiling,itcanlocallycomputeitscoordinates(xhv,yhv)inthenewcoordinatesystem.Furthermore,nodevcanidentifytheintegralcoordinatesofthehexagoninwhichitislocated. Figure5-10. TheHexagonLattice 100

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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.Notethatthiscommunicationisonly1-hopasthehexagonhasthelength(hexagondiameter)of2r p 13andtheclusteringpartitioncanbedoneonlyonetimeduringthedeploymentandset-upofaWSN. 5.4.2.2Localizedprotocol WearenowreadytointroduceourlocalizedprotocolforoptimizingenergyconsumptionandresourceutilizationofthedetectionandtrackingprocessdescribedinSection 5.3 .Noticethatthepartitionallowsallnodesinonehexagonandthatofsixadjacenthexagonsbeneighborsofeachother.AsshowninFigure 5-11 ,nodesinclusterC1willhaveallnodesinclustersC2,C3,C4,C5,C6,C7intheirneighborhood. Nowasthephenomenacloudwillexpandandthecoretrackingregionwillenlarge,therewillbealargenumberofcoretrackingnodesinthenetwork.Thecoretrackingnodeswillrunthefollowingprotocolinon-linemannertoschedulethemselvesintoactiveandsleepmode: 101

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Figure5-11. 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

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Figure5-12. GatorTechSmartHouse Figure5-13. SmartFloorTilewithforcesensorsandAtlasPlatformNode 5.5APracticalApplicationofPhenomenaDetectionandTracking Wefeltthatitwouldbeinterestingtodescribeanewreal-worldapplicationofphenomenadetectionandtrackingwhichisradicallydifferentfromthegascloudandoilslicksimulationsthatareusuallypresented.TheapplicationthatwedescribeinvolvestheSmartFloor[ 62 ]intheGatorTechSmartHouse(Figure 5-12 )[ 63 ].Inaddition,weusethisapplicationtoevaluatetheperformanceofourapproachesasdescribedlaterinsection 6.5 TheSmartFloordeployedin2005,consistsofagridofpiezoelectricforcesensorsdeployedundertheraisedoortilesofthehouse.EachtilehasasinglesensorconnectedtoanAtlasPlatform[ 64 ]ZigBeenodeplacedbelowitscenter(Figure 5-13 ),whichallowsastepanywhereonthetiletobedetected.TheSmartFloorcovers 103

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theentireresidentialareaofthe2500sq.ft.houseandallowsittomonitoritsresidents'movementandlocationwithoutencumberingthemwithtagsorothertrackingdevices. WhiledesigningtheSmartFloorapplication,anaiveexpectationwasthatwhenapersonstepsonatile,onlythesensorunderneaththattileoutputsareadingofsignicantmagnitude.Unfortunately,basedonourexperienceovertheyears,wefoundthatthiswasclearlynotthecase.Duetovariousreasonsincludingseeminglyrandomvibrations,individualsensorssometimesoutputlargereadingsevenwhennobodyissteppingonthem.Thisresultsinaverynoisysensoryenvironmentwhereonecannotdistinguishbetweenagenuinestepandrandomspikesbyrelyingonindividualsensorsalone. Figure5-14. RippleEffectofaFootStepontheSmartFloor Figure5-15. WalkingmotionasaPhenomena 104

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Wealsoobservedthatwhenapersonstepsonatilenotonlydoesthisresultinthattile'ssensorregisteringastrongreadingbutsomeofitsneighboringtilesalsooutputsignicantlylargereadings.Hence,thesteppingactionofafootonaoortilecausesarippleeffectintheimmediateneighborhoodofthetile.Figure 5-14 showsanactualscreenshotofthisphenomenonoccurringintheSmartFloorwherereddotsindicatetilesregisteringreadingsofhighermagnitudeandgreenindicatestileswithloweryetsignicantmagnitude.Weusedthisobservationtodescribewalkingasaphenomenonbydeningastepintermsofaphenomenoncloud(asshowninFigure 5-15 ),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

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evaluatestheeffectivenessofourdetectionstrategyinarealworldsensordeploymentandanalyzestheeffectofvaryingphenomenaparametersdescribedinSection 5.2.2 .Thesecondsetofexperimentsusessimulationtoevaluatetheresourceusageandpowerconsumptionofourapproachescomparedwiththestream-basedmethod.Wereliedonsimulationinthiscasebecausewewantedtomeasureresourceusageandpowerconsumptioninlargesensornetworksofvaryingsizes.Anditwasnotpracticallyfeasibleforustophysicallydeploysensorsinsuchlargenumbersforthepurposeofexperimentation. 5.6.1EffectivenessofDetectionStrategy Inthisrstsetofexperiments,westudytheeffectivenessofourphenomenondetectionandtrackingmechanisminareal-worldsensordeploymentinsidetheGatorTechSmartHouse. 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 5-16 5-17 and 5-18 .Figure 5-16 showstheeffectofvaryingparameternwhichdetermines 106

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Figure5-16. 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

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besatisedinmostorallcases.WefoundthatfortheGatorTechSmartHouseSmartFloor,settingnequalto2or3ensuresareasonablygoodlevelofperformance,wherethenumberoffalsepositivesiscomparativelylowascomparedtothenumberofcorrectdetectionsandapproximately77%ofallfootstepsaresuccessfullydetected. Figure5-17. EffectofvaryingpTwithn=3andm=150 Figure 5-17 showstheeffectofvaryingthethresholdprobabilitypT.Weobservethatasthresholdprobabilityincreases,thenumberoffalsepositivesdecreasessinceitltersoutrandomspikes.Randomspikestypicallyresultinonlyafewreadingsofsignicantmagnitudewithinaxedsizeslidingwindow,hence,thereisasharpdropinthenumberoffalsepositivesevenwhenweonlyincreasepTfrom0.1to0.2.Howevermakingtheprobabilityrequirementmorestringentalsoresultsinanincreaseinthenumberoffalsenegatives/misses.Thisisduetothefactthatsinceweareusingaslidingwindowofxedsize,asthenumberofreadingsinthewindowthatarerequiredtoliewithinthephenomena-denedbounds[a,b]inordertosatisfytheProbabilityCondition(denedinSection 5.2 )increases,thechanceoftheProbabilityConditiongettingsatiseddecreases.FortheSmartFloorwefoundthatsettingpT=0.4resultsinareasonablygooddetectionratewithalownumberoffalsepositivesandmisses. Figure 5-18 showstheeffectofvaryingtheslidingwindowsizem.Weobservethatiftheslidingwindowsizeistoolow,thisresultsinalargenumberoffalsepositives 108

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Figure5-18. 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

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1.StreamPDT[ 46 ]:Acentralizedstream-basedalgorithmwherephenomenadetectionandtrackingisperformedbyaCentralizedQueryProcessor(CQP).WesimulatedNile-PDT[ 46 ],awell-knowndetectionsystemdevelopedatPurdueUniversity,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. Figure5-19. PowerConsumptionSpecicationsforAtlas 5.6.2.1Experimentalsetup Weperformedsimulationsinthefollowingfourdifferentsetups: 1.Intherstsetofsimulations,wesimulatedtherandommovementandexpansionofphenomenacloudfor50epochsonarectangularsensorgridofsize121121deployedoveranareaof1200m1200m. 110

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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)thenumberofnetworkmessagesexchangedbetweensensorsforthein-networkimplementationofproposedalgorithms,3)thenumberofupdatessenttotheCentralizedQueryProcessor(CQP),and4)energyconsumption.Wecalculatedtheenergyconsumptionofnodesasafunctionofprocessingcosts(includingsamplingsensors)andnetworkcosts(incurred 111

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Figure5-20. Epoch-wisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. Figure5-21. Epoch-wisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) Figure5-22. Epoch-wisecomparisonbasedonnumberofmessagesexchangedbetweenone-hopneighborstoimplementthealgorithms. Figure5-23. Epoch-wisecomparisonbasedontheEnergyConsumption. inreceivingandtransmittingdataovertheradio),whicharebasedontheAtlasZigBeenodehardwarespecicationslistedinFigure 6-10 5.6.2.2Resultsandanalysis SimulationresultsfortherstsetofexperimentsarepresentedinFigures 5-20 5-24 whichcompareperformancesofStreamPDT,DistPDT,FDAandODA.Ofwhich,Figures 5-20 5-21 5-22 ,and 5-23 provideepoch-wisecomparison,whereasFigure 5-24 providescomparisonbasedonanoverall50epochs. 112

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Figure5-24. Comparisonbasedonoverall50Epochs Figure 5-20 evaluatestheperformancesofthefouralgorithmsintermsofthenumberofactivenodesinvolvedinthedetectionandtrackingprocess.Ascanbeseen,ODAshowsthebestperformanceandStreamPDThastheworstperformance.PoorperformanceofStreamPDTisduetothefactthatitusescentralizedprocessing,inopposetothein-networkprocessingusedbyourproposedalgorithms.Consequently,StreamPDTrequiresallsensornodestoremainactiveatallthetime.Incontrast,DistPDTonlyneedsasetofpotentialcandidate,candidateandtrackingnodestoremainactive,whichresultsincomparativelyabetterperformance.FDAperformsslightlybetterthanDistPDTasitstringentlyactivatesthecandidatesandpotentialcandidates,resultinginmoreefcientresourceusage.ODAshowsthebestperformance,asitfurtheroptimizestheresourceusageofFDAbyreducingcoverageredundanciesinthecoretrackingregion.Morespecically,FDAneeds75%lessactivenodesincomparisontoStreamPDTand6%lessactivenodesincomparisontoDistPDTovertheperiodof50epochs,asshowninFigure 5-24 .Likewise,Figure 5-24 alsorevealsthatODAneeds84%lessactivenodesincomparisontoStreamPDTand40%lessactivenodesincomparisontoDistPDTovertheperiodof50epochs.ODAshowsaperformanceenhancementof36%overFDAduetotheoptimizationstep. Figure 5-21 showstheepoch-wisecomparisonofthefouralgorithmsbasedonthenumberofupdatemessagessendtotheCQP.Asthenumberofupdatemessages 113

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directlydependsuponthenumberofactivetrackingnodesinthecoreregion,thenumberofupdatemessagesisequalforbothDistPDTandFDA.Duetothelocalizedoptimizationprotocol,ODAgeneratestheminimumnumberofupdatemessageswithoutdegradingtheperformanceofdetectionandtracking.AsincaseofStreamPDT,allsensorsneedtoreporttotheCQPthroughupdatemessages;hence,itgeneratesthemaximumnumberofupdatemessages.Indetails,ascanbeseeninFigure 5-24 ,ODAgenerates86%and39%lessernetworktrafcintermsofupdatemessagescomparingtoStreamPDTandDistPDT(FDA)respectively. Figure 5-22 illustratestheepoch-wisecomparisonbasedonthenumberofprotocolmessagescollectivelyexchangedbyalltheactivenodeswiththeirone-hopneighbors.StreamPDTisastraightforwardalgorithminwhichallsensornodesperformone-hopbroadcastoftheirsensedinformation.Consequently,thenumberofprotocolmessagesexchangedinanepochisequaltothenumberofnodesinthenetwork.However,fortheotherthreealgorithms,onlyactivesensornodesbroadcasttheexchangedmessagebasedontheirrespectivecategories.ODAperformsthebestandgeneratesminimumnumberofexchangedmessages,whereasFDAcomparativelyperformsbetterthanDistPDT.Figure 5-24 showsthatFDAgenerates77%and6.41%lesserexchangedmessagesincomparisontoStreamPDTandDistPDTrepsectively.Furthermore,itshowsthatODAgenerates86%and42.5%lesserexchangedmessagesincomparisontoStreamPDTandDistPDTrespectively.ODAimprovesFDAbygenerating38.54%lessexchangedmessagesandithasahugesignicantimprovementoverStreamPDT. Theepoch-wisecomparisonofthefouralgorithmsbasedontheenergyconsumptionisshowninFigure 5-23 .Asexpected,StreamPDTrequiresallsensornodestoalwaysactivelysense,thusitconsumesenergythemost.ODAperformsthebest,whereasFDAisbetterthanDistPDT.Figure 5-24 showsthatFDAconsumes74.52%lesserenergyincomparisontoStreamPDTand5.86%incomparisontoDistPDT.Similarly,ODAconsumes83.15%lesserenergyincomparisontoStreamPDT 114

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and37.76%incomparisontoDistPDT.ODAimprovestheenergyconsumptionofFDAby34%,reectingthatapplyingtheoptimizationstepmakesasignicanthelp. Insummary,fortherstsetofexperiments,ODAperformsthebestandStreamPDTperformstheworstinallterms:thenumberofactivenodes,thenumberofexchangemessages,thenumberofupdatemessages,andenergyconsumption.AlsonoticethatthegraphforStreamPDTisaconstantlinewhenthephenomenacloudsareenlargingbecauseallsensornodesinthegridremainactiveatalltimeregardlessofthecloud'ssize.Fortheotherthreealgorithms,whenthephenomenaexpand,thegraphsareincreasing,butnotlinearly. Figure5-25. Comparisonbasedondifferentgridsize. Inthesecondsetofsimulations,wevariedthegridsizeasshowninFigure 5-25 .ItcanbeobservedthatDistPDT,FDA,andODAdonotshowmuchvariationinallfourcomparisonparameterswithrespecttoincreaseinthegridsize.Thisisderivedfromthefactthatforthesealgorithms,thedetectionandtrackingprocessislocalizedtotheimmediateneighborhoodofphenomenacloudatanygiventimeanddoesnotrequireallsensornodestoremainunnecessarilyactive.Incontrast,StreamPDTrequiresallnodesinthenetworktoremainactiveandsendupdatemessagesabouttheirdetectingstatustotheCQP.Therefore,asthegridsizeincreases,themoreactivenodesandthelargernetworktrafc.Consequently,theperformanceofStreamPDTdegrades.ThesimulationresultsshowthatDistPDT,FDA,andODAarescalabletothesizeofgrids 115

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Figure5-26. Epoch-wisecomparisonbasedonnumberofactivenodesinvolvedindetectionandtrackingprocess. Figure5-27. Epoch-wisecomparisonbasedonnumberofupdatemessagessendtotheCentralizedQueryProcessor(CQP) Figure5-28. Epoch-wisecomparisonbasedonnumberofmessagesexchangedbetweenone-hopneighborstoimplementthealgorithms. Figure5-29. Epoch-wisecomparisonbasedontheEnergyConsumption. andODAperformsthebestintermsofallthecomparisonparameters.TheperformanceofStreamPDTistheworstandnotscalable. Figures 5-26 5-30 presentsimulationresultsforthethirdsetofexperiments,ofwhichwecomparethesolutionsofthefouralgorithmswiththeoptimalsolutiongeneratedbytheIPdescribedinSection 5.4.1 .NotethatsincesolvingIPisactuallyNP-hard,weonlysimulatedthissetofexperimentsonthesmallsizegridof1010during5epochsofrandommovementandexpansionofphenomenaclouds.Figures 116

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Figure5-30. Comparisonbasedonoverall5Epochs Figure5-31. SnapshotsofexpandingphenomenacloudduringEpochst10,t15,t20. Figure5-32. ActiveSensorsduringEpocht10,forDistPDT. 5-26 5-29 provideanepoch-wisecomparisonwhereasFigure 5-30 summarizestheresultsoverallthe5epochs. Ascanbeseen,StreamPDTuses62.5%moreactivenodesincomparisontotheIPsolution.DistPDTimprovestheresultbyusing35.74%moreactivesensorscomparedtotheIPsolution.FDAfurtherimprovesthesolutionbyusingonly17.62%moreactivenodescomparedtotheIPsolution.Andasexpected,ODAshowsthebestperformanceandonlyuses13.82%moreactivenodesincomparisontotheoptimalsolution. IntermsofthenumberofupdatemessagessenttotheCQP,StreamPDTshowstheworstperformancebygenerating88.2%moreupdatemessagesthantheIPsolution.DistPDTshowsconsiderableimprovementbygenerating40%moreupdatemessages 117

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Figure5-33. ActiveSensorsduringEpocht10,forFDA. Figure5-34. ActiveSensorsduringEpocht10,forODA. Figure5-35. ActiveSensorsduringEpocht15,forDistPDT. Figure5-36. ActiveSensorsduringEpocht15,forFDA. Figure5-37. ActiveSensorsduringEpocht15,forODA. Figure5-38. ActiveSensorsduringEpocht20,forDistPDT. thantheIPsolution.AsthesetoftrackingnodesisthesameforDistPDTandFDA,thenumberofupdatemessagesthereforemustbethesame.ODAshowsaslightlyimprovementandgenerates33.33%moreupdatemessagesthantheIPsolution.Theprotocolmessagesexchangedbetweentheone-hopneighborsinStreamPDTis85.8% 118

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Figure5-39. ActiveSensorsduringEpocht20,forFDA. Figure5-40. 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 6-1 showssnapshotsoftheexpandingphenomenacloudatepochst10,t15,andt20.Figures 5-32 5-33 ,and 5-34 aretherespectivesnapshotsshowingtheactivenodesforDistPDT,FDA,andODAduringepocht10.Likewise,theresultofepocht15isshowninFigures 5-35 5-36 ,and 5-37 andthatofepocht20ispresentedinFigures 5-38 5-39 ,and 5-40 .Ascanbeseen,whenthephenomenonexpands,thenumberofactivenodes 119

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expandsmoothlyaswelltofullycoverandtrackthephenomenon'smovement.Also,attheborderofthephenomenon,theDistPDThasathickergreenlinethanthatofFDA,showingthatDistPDTrequiresmorecandidatenodesduetoourpreviousrelaxeddenition.Inaddition,attheinnerareaofthephenomenon,whilealltrackingnodesareactiveforDistPDTandFDA,ODAhassomeinactivetrackingnodes.Thisisduetotheoptimizationsteptocovertheentireareaandsatisfythequorumbutstillminimizetheenergyconsumption.Duringtheoverall20epochs,FDAinvolved10.84%lesseractivenodescomparedtoDistPDT.ODAfurtherimprovestheperformancebyusing36.54%lessactivenodescomparedtoDistPDT. Figure5-41. Percentageofholesgeneratedwrtpercentageofupdatemessageslost Toevaluatethedegreeoffaulttoleranceofourproposedalgorithms,wefurtherranthesimulationsallowingthelossofupdatemessageinthenetworkandsummarizetheresultsinFigure 5-41 .Inaddition,Figures 5-42 5-47 pictoriallyshowtheholesgeneratedforFDAandODAwhiledetectingphenomenacloud,whenpercentagesofupdatemessageslostare5%,10%and15%respectivelyduringtheepocht20.AholeisrepresentedasaredballandisgeneratedwhenthedetectionstatusofatrackingsensorcannotbedeterminedattheCQPbasedontheupdatemessagesreceived. Weobservedthatouralgorithmsshowedareasonableperformancewhenthenetworkisvulnerableofmessagelosses.Figure 5-41 showsthepercentageofholesgeneratedbyFDAandODAwithrespecttothepercentageofupdatemessageslost.Ascanbeseen,theholesgeneratesbyFDAisverynegligible,evenonly0.275%attherateof15%ofupdatemessagelost.Asexpected,ODAgeneratesmoreholes.Thisisclearly 120

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atrade-offbetweentheenergyconsumptionandfaulttolerance.Inordertoreducetheenergyconsumptionandmessagecomplexity,ODAleavesenoughactivecoretrackingsensorstosastiedtherequiredquorumwhereasalltrackingsensornodesinFDAareactive.WecanslighlymodifyODAtobemorefaulttolerancebyallowingmorecoretrackingsensorstobeactive.Morespecically,atstep(4)insection 5.4.2.2 ,insteadofrepeatinguntiltheminimumquorumnissatised,wecanrepeattheprocessuntilallactivenodesinaclustersatisfynquorumconditionwhere1.Thebiggeris,themoreactivenodesare,thelesserholesgenerated. Letusfurtherlookintothesnapshots(Figure 5-42 5-47 )toseethelocationoftheseholes.Theholesweremostlycreatedintheinnerpartofthecoretrackingregion.Thisispartiallybecauseweonlyallowsomecoretrackingnodes(whichlocateintheinnerregion)tobeinactive.Whenupdatemessagesofsomeactivecoretrackingnodesgetlost,itresultsinlackofinformationabouttheseactivecoretrackingnodesandthesleepingcoretrackingnodeswhichtheywerecovering.Asonlyafewholesaregeneratedattheboundaryofthecoretrackingregion,consequently,theregionwherethephenomenacloudiscurrentlylocatedcaneasilybeidentiedattheCQPevenif15%ofupdatemessagesarelost,asshowninFigure 5-47 5.7RelatedWork InanearlystageofthephenomenadetectionandtrackingusingWSNs,thephenomenonisstaticandconnedtoasetofpointsorwithinacertainarea,oftenknownasthecoverageproblem(see[ 23 66 ]andreferencestherein).Towardsnowadays,asthephenomenaaredynamic,haveirregularshapes,andinvariantmovements,therehasbeenrecentlyanongoingresearchondetectionandtrackingofphenomenacloud[ 12 13 19 42 44 46 67 68 ]. ThemostcloselyrelatedworkisNile-PDT[ 46 ],whichisaPhenomenaDetectionandTracking(PDT)frameworkrunningontopofcentralizedNiledatastreammanagementsystem,developedbyIndianaCenterforDatabaseSystems(ICDS)at 121

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PurdueUniversity.Nile-PDTisdesignedfordetectingandtrackingphenomenoncloudssuchasgasclouds,oilspillsandchemicalwastespillage.Nile-PDTusestwocustomdatabaseoperators,namely,SN-ScanandSN-Jointoperformphenomenondetectionandtracking.TheSN-Scanoperatorscansallthesensorsinthenetworkandchoosescandidatesensorswhichhaveahighprobabilityofdetectingthephenomenon.TheSN-Joinoperatorthenevaluateseachofthesecandidatesensorsandchecksiftheyjoinwithothercandidatesacertainnumberoftimesandhencedetectaphenomenonevent.Nile-PDTusesfeedbackcontroltocontinuouslytunetheSN-ScanandSN-Joinparameterstomaximizeefciencyofthedetectionprocess.ThemaindrawbackoftheNile-PDTapproachisthatittakesastreamingdatabaseviewoftheprocess.Itdoesnotconsideranymechanismsforcontrollingtheowofdataatthesourcesensorsthemselvesoraddresspowerconsumptionandnetworkbandwidthissuesinsidethesensornetwork.Furthermore,itrequiresallsensorstopumpreadingstotheSN-Scanoperatortoallowittochoosephenomenoncandidates,whichcanleadtopotentiallymassivescalabilityissues.Inthispaper,wehavecomparedouralgorithmstothiswork,referredatStreamPDT. Omotayoetal.[ 67 ]describeadataharvestingframeworkfortracingphenomena.Theyproposealgorithmsformaintainingadatafarmonthenodesbymaximizingtheutilizationoftheiron-boardnon-volatilestorage,forenablingbacktrackingtodeterminethecauseofaphenomenon.McErleanet.al.[ 42 ]proposeadistributedeventdetectionandtrackingalgorithmformovingobjectsusingWSNs.However,thissystemassumestheprioravailabilityofoptimalad-hocroutingmechanismsandisprimarilydesignedfordetectingindividualdiscreteobjectswithwell-denedshapeandsize,asopposedtophenomenoncloudswhoseshapeandsizetypicallycannotbedenedinexactterms. Therearealsosomeworkstudyingtheboundaryofthephenomenacloudsinsteadofdetectingandtrackingtheentirearea[ 12 19 22 68 71 ].Asthesestudiesarenotinthescopeofthispaper(wedetectandtracktheentirearea),weonlybrieymention 122

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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.Werstproposeadistributedalgorithmforin-situdetectionandtracking 123

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ofphenomenacloudsinthesensorspace.Wenextprovideamathematicalmodeltooptimizetheenergyconsumption,onwhichwefurtherproposealocalizedalgorithmtominimizetheresourceutilization.Ourproposedapproachesnotonlyensurelowprocessingandnetworkingoverheadatthecentralizedqueryprocessorbutalsominimizethenumberofsensorswhichareactivelyinvolvedinthedetectionandtrackingprocessesatanygiventime.Wevalidateourapproachusingbothreal-lifesmarthomeapplicationsaswellassimulationexperiments,whichanalyzetheeffectivenessandefciencyofourproposedalgorithms.Wealsoshowthatouralgorithmsresultinsignicantreductioninresourceusageandpowerconsumptionascomparedtothecontemporarystream-basedapproaches. Aspartofourfuturework,wearelookingforamodel-assisteddetectionandtracking,wheredistributionofdetectiontaskswillbestreamlinedbasedonpredictionsregardingthedirectionofmovementofthephenomenacloud.Wearealsosearchingforreal-lifedatasetsfromdifferentapplicationdomainsforfurthervalidatingandnetuningourapproaches. 124

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Figure5-42. DetectionandTrackingwith5%updatemessagelostforFDA. Figure5-43. DetectionandTrackingwith5%updatemessagelostforODA. Figure5-44. DetectionandTrackingwith10%updatemessagelostforFDA. Figure5-45. DetectionandTrackingwith10%updatemessagelostforODA. Figure5-46. DetectionandTrackingwith15%updatemessagelostforFDA. Figure5-47. DetectionandTrackingwith15%updatemessagelostforODA. 125

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CHAPTER6LOCALIZEDENERGYEFFICIENTDETECTIONANDTRACKINGOFDYNAMICPHENOMENABOUNDARY 6.1Introduction MostoftheexistingresearchinphenomenadetectionandtrackingusingWirelessSensorNetworks(WSNs)assumesthephenomenaisinvariantinshape,sizeandmotion[ 19 23 ].However,inreallifethereexistdynamicphenomenasuchasoilspills,mudow,diffusionorleakageofgasesthatarecharacterizedbynon-deterministicvariationsinshape,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

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somedrawbacksofTOCOB.Firstly,itneedsallthesensornodestoparticipateinthedetectionandtrackingprocess,whichisnotenergyefcient.Secondly,itprovidesverysparseboundaryinformationtotheCQP,whichlimitsthequalityofphenomenaboundaryestimation.Thirdly,themethodforidentifyingtheRNsisnotefcientandcouldsuppressalargeamountofboundaryinformationfromsendingtotheCQP,furtherdegradingthedetectionandtrackingofphenomenaboundary. Inthischapter,weproposeanenergyefcientlocalizedprotocolfordetectionandtrackingofdynamicphenomenaboundaryofanyirregularshape.Inourproposedprotocol,thedetectionandtrackingprocessislocalizedtothenodesintheimmediateneighborhoodofthephenomenaboundary.Thisresultsinonlynecessarynodesactivelyparticipatinginsensingthephenomenaboundary,whilerestofthenodesremaininactiveuntiltheyarerequired.Inordertoreducethetrafcgeneratedbyupdatemessages,weproposeanefcient,robustlocalizedclusteringalgorithmbasedonhexagontilingofthe2DplanecoveredbytheWSN.Theproposedclusteringalgorithmdoesnotrequirere-clusteringwhenthephenomenaboundarydynamicallyvaries. 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

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6.2SystemModel NetworkModel:Asetofin-situsensornodesVdeployedona2DplanealongwithasetofcommunicationlinksEformtheWSN.Eachsensornodev2Visequippedwitharadiotransceiverwithcommunicationranger.ThesetofnodeswithinthecommunicationrangeofvformsitsneighborhoodN(v).Furthermore,thereexistsaCentralizedQueryProcessor(CQP),wherethesensedinformationfromtheWSNiscollectedforfurtherprocessing. Asensornodeisactiveifitssensingfunctionalityison,otherwiseitisinactive. Anactivesensornodeisreferredasdetect-positiveifitdetectsthephenomenonisexisting,whereasifitdetectsthephenomenaisnotexistingitisreferredasdetect-negative. DynamicPhenomena:Adynamicphenomenarepresentstheoccurrenceofanyeventthatshowsdynamicvariationsinshape,sizeanddirectionofmotion.Themostsuitableexamplesofdynamicphenomenaareoilspills,mudow,diffusionorleakageofgases,etc. PhenomenaBoundary:Thephenomenaboundaryisdenedasacurvethatinscribestheareaaffectedbythephenomena.Itdelineatestheareaunderconsiderationintotheregionwherethephenomenaexistsandtheregionwherethephenomenahasnotyetreached.Basedonthephenomenaboundary,wepresenttheclassicationofthesensornodesdescribedinFigures 6-1 & 6-2 6.3DetectingandTrackingofDynamicPhenomenaBoundary Inthissection,wepresentourprotocolfordetectionandtrackingthedynamicphenomenaboundary.Figure 6-5 showsthestatetransitiondiagramforasensornode.Thestatesrepresentpossiblesensorclassesandtheedgesrepresentconditionsfortherespectivetransitions.Figure 6-3 showsvarioustypesofmessagesthatsensornodesmaygenerateandexchangetoimplementthedetectionandtrackingprotocol.Figure 6-4 showsthesetoftransitionrulesgoverningthetransitionofasensornodefromonestate 128

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Figure6-1. ClassicationofSensorNodesintheWSN Figure6-2. TypesofNodesintheWSN toanother.TheserulesareexecutedlocallytocontroltheentiredetectionandtrackingprocesswithouttheinterventionoftheCQP.Therestofthissectioncoversdifferentstagesofdetectionandtrackingprocessinchronologicalorder. A.Initialselectionofsensornodes:Themainpurposeofthisstageistodetecttheinitialoccurrenceofthephenomena.Thephenomenacanoccuratmultiplelocations, 129

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Figure6-3. TypesofmessagesintheWSN Figure6-4. TheTransitionRules hence,itisnotsufcienttomonitoronespeciclocation.However,monitoringtheentireareawithouttheoccurrenceofphenomenawouldbeextravagant.Therefore,wecanapplyatrade-offbetweenthetwoapproachesbyselectingthesensorsdeployedatvulnerablelocationsasOBnodesandkeepthemactive.Wecanselectthesevulnerablelocationsonthebasisofthetypeoflocationorthepasthistory.Forinstance,todetect 130

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Figure6-5. StateTransitionDiagramforaSensornode Figure6-6. Expansionofthephenomenacloud gasleakageinthepipeline,itmightbeusefultochoosethesensorslocatedatvalvesandjointsasOBnodesandkeepthemactive. B.Monitoringofinitialoccurrenceofphenomena:WeassumethattimeisdividedintodiscretetimeslotscalledEpochs.AtthebeginningofeveryEpoch,theinitiallyactiveOBnodeswillcollecttheirreadingstocheckiftheyaredetect-positive.Ifanyofthem 131

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aredetect-positive,theywillbroadcastanINVKmessagetotheirimmediateinactiveOneighborsandtransitionintoBnodes,basedonruleR2.AfterreceivingtheINVK,theinactiveOneighborswilltransitionintoOBnodesandbecomeactive,basedonruleR1.IfanactivenodeinanEpochisdetect-positive,itbroadcastsa+ivePHSTmessagetoitsneighbors,otherwise,itbroadcastsa-ivePHSTmessage. C.Growthofphenomena:WhenthephenomenagrowssomeoftheOBnodesbecomedetect-positive.TheseOBnodesbroadcastINVKmessagestotheirinactiveOneighborsandtransitionintoBnodes,basedonruleR1.TheinactiveOnodesonreceivingtheINVKmessages,transitionintoOBnodes,basedonruleR2.Further,duringthegrowthofphenomena,someBnodes,onreceiving+ivePHSTmessages,maynoticethatalltheirneighborsaredetect-positive.Additionally,iftheyhaveatleastoneBnodeintheirneighborhood,theytransitionintoIBnodes,basedonruleR3,elsetheytransitionintoInodes,basedonruleR4andbecomeinactive.Eventually,thephenomenaisalwayscoveredbythesetofcurrentlyactivenodesandtheinformationaboutthelocationofthephenomenaboundarycanbecollectedfromthesetofBnodes. D.Shrinkingofphenomena:Whenthephenomenashrinks,someofthecurrentBnodesbecomedetect-negative.IfanyoftheseBnodeshaveatleastonedetect-positiveBnodeintheirneighborhood,theytransitionintoOBnodes,basedonruleR7.Otherwise,theytransitionintoOnodesandbecomeinactive,basedonruleR8.Further,duringtheshrinkingphase,ifanIBnodeonreceivinga-ivePHSTnoticesthatithasanOBnodeinitsneighborhood,ittransitionsintoaBnode,basedonruleR6andbroadcastsanIVNKmessagetoinvokeitsinactiveIneighbors.TheseInodes,onreceivingtheINVKmessages,activateandtransitionintoIBnodes,basedonruleR5.ThiswaytheinformationaboutthelocationofthephenomenaboundaryisalwayscontainedinthecurrentsetofBnodes. E.AggregationandReportingUpdatemessagestoCQP:Whenthereisanyvariationinthephenomenaboundary,itshouldbereportedtotheCQPthrough 132

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Figure6-7. Shrinkingofthephenomenacloud updatemessages.InthefollowingsectionwedescribeanefcientclusteringanddataaggregationmechanismforeffectivelyreducingthetrafcgeneratedbytheupdatemessagesdestinedtoCQPwithoutcompromisingtheamountofinformationtobereported.SinceweassumetheCQPisawareofthelocationofeachsensornode,aGUI-basedphenomenaboundaryvisualizationapplicationcanbedeveloped.Thisapplicationwilltaketheon-lineinformationaboutthecurrentsetofboundarynodesandwillestimateanddisplaythemapoftheareaaffectedbythephenomena.Further,themapwilldynamicallyevolvebasedonthevariationsinthesetofboundarynodesB. F.Handlingfailures:ThefailureofsensornodesinWSNsisunavoidable.ThismayaffectthedetectionandtrackingprocessassomeOnodesmaynotactivateduetothefailureofsomeOBnodesduringthegrowthofthephenomena.Inaddition,itisalsopossiblethatduringtheshrinkingphasesomeIBnodesmayfailandwouldnotinvoketheInodestocovertheshrinkingofthephenomena.Insuchcases,ifinsomeEpoch,anOnodeoranInodedoesnotreceivea-ivePHSTor+ivePHSTfromtheirrespectiveOBorIBneighbors,thentheymustassumesomefailurehasoccurredandbecomeactivebytransitionintoOBandIBnodesrespectively.Thiswillascertainthatthefailuredoes 133

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notaffectthedetectionandtrackingprocessandphenomenaboundarywillalwaysbecoveredbythecurrentsetofactivenodes. Figure6-8. Xh)]TJ /F3 11.955 Tf 11.95 0 Td[(Yhco-ordinateSystemforHexagontilingH 6.4LocalizedClusteringandDataAggregation Inthissection,werstdescribealocalizedmethodforgeographicallyclusteringtheWSN.Wethendiscussadataaggregationmethodtoaggregatethephenomenaboundaryinformationattheclusterheadstoformupdatemessages. A.Localizednetworkclustering: WelocallygenerateageographicalclusteringoftheWSN.Thegeneratedclustersaredisjointandrespectivelylocatedwithinnon-overlappingregularhexagonsofsidesr 2formingahexagontilingoftheareacoveredbytheWSN,asshowninFigure 6-8 .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

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Xh)]TJ /F3 11.955 Tf 10.38 0 Td[(Yhco-ordinatesystemis(0,0).Basedonthis,anodev2Videntiesitscoordinates(xhv,yhv)andtheintegralcoordinatesh(i,j)ofitshexagoninXh)]TJ /F3 11.955 Tf 12.3 0 Td[(Yhco-ordinatesystemasfollows: 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.TheCQPformsahash-mapindexedonthebasisofhexagonco-ordinatesandstoresinitthesortedlistofnodesinthehexagon. B.DataAggregationandReporting:Theclusterheadgeneratesabit-arraycalledReportarray.TheReportarraycontainsabitforeachnodeinthehexagon,arrangedinsortedorderoftheirids.IfaclusterheadhasBnodesinitshexagon,asshowninFigure 6-9 ,itreceivesBINFOmessagesfromthemandgeneratestheReportarray,settingthebitscorrespondingtotheBnodesinthehexagon.ItthensendsthisRe-portarraytotheCQPalongwithitshexagoncoordinatesinaPINFOmessage.The 135

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CQPonreceivingthePINFOmessage,basedonthehexagoncoordinatesaccessesthehash-map.ItthenidentiestheboundarynodesinthehexagonusingtheReportarrayandstoresthisinformationinthehash-map.Theinformationabouttheboundarynodes,storedinthehash-mapcaneasilybeusedasaninputtotheGUI-basedphenomenaboundaryvisualizationapplicationtogenerateanddisplaythemapoftheareaaffectedbythephenomena. Figure6-9. Dataaggregationbasedonclusteringgeneratedbythehexagonaltiling Figure6-10. Powerconsumptionspecicationsforasensornode 6.5PerformanceEvaluation Inthissection,weevaluatetheeffectivenessandefciencyofourproposedprotocolintermsofresourceutilizationandenergyconsumptionthroughsimulations.WeconsideredaWSNhaving2000sensornodesdeployedonasquareareaofsides600m.Nodes 136

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Figure6-11. Comparisonbasedonnumberofboundarynodes. Figure6-12. Comparisonbasedonnumberofupdatemessages. Figure6-13. Comparisonbasedonenergyconsumption. Figure6-14. Comparisonbasedonmessagesexchanged. intheWSNcommunicatebasedonZigbeeprotocol(IEEE802.15.4).Eachnodehasasingleradiointerfacewithtransmissionrange10m.ThepowerconsumptionspecicationsforthesensornodesareprovidedinFigure 6-10 .WecomparedourproposedprotocolwiththeTOCOBprotocolproposedbyKimet.al[ 13 ].Thecomparisonwasbasedonthreeimportantfactors:1)BoundarynodesandupdatemessagessendtotheCQP,2)Energyconsumptionand3)Protocolmessagesexchangedbythenodestoimplementtheprotocol. Simulationswereperformedintwodifferentsetups.Intherstsetup,weperformanEpoch-wisecomparisonoftwoprotocols.Wesimulatedthedynamicphenomenabyspawningitsthreeoccurrencesatlocations(200,200),(400,200)and(400,300), 137

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Figure6-15. Comparisonbasedonnumberofupdatemessagesatdifferentphenomenaexpansionspeed. Figure6-16. Comparisonbasedonenergyconsumptionatdifferentphenomenaexpansionspeed. Figure6-17. Comparisonbasedonmessagesexchangedatdifferentphenomenaexpansionspeed. followedbytheirrandommotionandexpansionoverthesquarearea.Foreachfactor,weran100iterationsandaveragedtheresults.Eachiterationranfor60Epochs.Inthesecondsetup,weperformthecomparisonoftwoprotocolsbasedonexpansionspeedofthephenomena.Wesimulatedthephenomenabyspawningitsoccurrenceatlocation(300,300)followedbyitsexpansionatvariousspeeds.Foreachofthethreefactors,weran100iterationsandaveragedtheresults.Eachiterationranfor30Epochs. 138

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Figure6-18. SnapshotofphenomenainWSN. Figure6-19. Estimatedboundarywith0%messageloss. Figure6-20. Estimatedboundarywith15%messageloss. Figure6-21. Estimatedboundarywith30%messageloss. Figure6-22. Estimatedboundarywith45%messageloss. A.BoundaryNodesandupdatemessages:Figure 6-11 & 6-12 showthecomparisonoftwoprotocolsbasedonnumberofboundarynodesandupdatemessagesrespectively.ThetwogurestogetherreecttheefciencyofourproposedlocalizedclusteringanddataaggregationprotocolinreducingthenumberofupdatemessagesdestinedtoCQPwithoutleavingbehindtheinformationgeneratedbyanyboundarynode.Ourprotocolgenerates22%lesserboundarynodesand65%lesserupdatemessagesin 139

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comparisontoTOCOB,whichreectsbetterresourceusageandlessernetworktrafcdestinedtotheCQPcontainingtheinformationfromalltheboundarynodes. Figure 6-15 showstheeffectofphenomenaspeedontheupdatemessagesgeneratedforeachprotocol.Itcanbeobservedthatthenumberofupdatemessagesisproportionaltothephenomenaspeed.Thisisbecausewhenthephenomenonexpandswithhigherspeed,therearelargerchangesinthephenomenaboundary,whichresultsinlargerupdatemessages.ItcanbeseeninFigure 6-15 thatourprotocolhandlesthehigherphenomenaspeedmuchmoreefcientlyincomparisontoTOCOB. Furthermore,anupdatemessagegeneratedbyarepresentativenodeinTOCOBhasapayloadsizeof3bytesandcarriestheinformationofonlyasingleCVN,whereasinourcaseweobservethatanupdatemessage(PINFO)generatedbyaclusterheadhasapayloadsizeof3to4bytesandcontainsReportarraywhichcarriestheinformationofalltheboundarynodesinthecluster. B.EnergyConsumption:Figure 6-13 showstheEpoch-wiseenergyconsumptionofboththeprotocols.InTOCOB,asallthesensornodesactivateduringeachsamplingperiodtotakereadings,hence,itisnotveryenergyefcient.However,inourprotocolonlyIB,BandOBnodesactivatetocollectthereadingsduringeachsamplingperiod.Weobservethatourprotocolconsume90%lesserenergythanTOCOB. Figure 6-16 showsthatenergyconsumptionisproportionaltothespeedofthephenomena.OurprotocolshowsmuchbetterresultsincomparisontoTOCOBwhenthephenomenamovesathigherspeeds. C.Messagesexchangedforprotocolimplementation:Figure 6-14 and 6-17 showcomparisonofthenumberofmessagesneededtobeexchangedamongtheneighboringsensornodestoimplementthetwoprotocolinWSN.ItcanbeobservedthatTOCOBneedslesserprotocolmessagestocommunicate.Themainreasonforthisisthatourprotocolneedsthenodesclosetothephenomenaboundarytoremainactiveandthey 140

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needtocommunicatetheirstatustotheirneighbors,whichresultsinanincreaseintheexchangedmessageoverhead. D.EffectofmessagelossesonestimationofphenomenaboundaryatCQP:Ourprotocolworksfordetectingandtrackingphenomenaofanyirregularshape,butforeaseofimplementationweconsiderthephenomenashapetobeacirculardisk.Figure 6-18 showsasnapshotofadynamicallyspreadingphenomena.Figure 6-19 6-20 6-21 and 6-22 showtheestimatedphenomenaboundaryatCQPforthesnapshotinFigure 6-18 ,whenthemessagelossesintheWSNare0%,15%,30%and45%respectively.ItcanbeobservedthatourproposedprotocolisrobustagainstthenetworkmessagelossesandproduceareasonablygoodestimationofthephenomenaboundaryattheCQPevenif45%ofthenetworkmessagesarelost. 6.6Conclusion Inthispaper,weproposedanovelprotocolfordetectionandtrackingofdynamicphenomenaofanyirregularshapethroughWSN,withanobjectiveofminimizingtheresourceusageandenergyconsumption.Wealsoproposedarobustlocalizedclusteringanddataaggregationmethod,whichhelpsinreducingthenetworktrafcgeneratedbytheinformationpacketdestinedtotheCQP.Theexperimentalresultsshowsthatourproposedprotocolconsumed90%lesserenergyandgenerates65%lessernetworktrafcdestinedtotheCQP,incomparisontotheexistingwork.Furthermore,ourproposedprotocolisrobustagainstthenetworkmessagelossesandproducereasonablygoodboundaryestimationattheCQPevenif45%ofthenetworkmessagesarelost. 141

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CHAPTER7CONCLUSION ThisdissertationmainlyfocusesonfollowingtwoimperativeoptimizationproblemsinWSNs: 1.Efcientdatabroadcastingandaggregation. 2.Efcientdetectionandtrackingofdynamicphenomena(phenomenacloud). InChapter 2 ,weformulatedatabroadcastinginWSNsasInterference-awarebroadcastscheduling(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 ,westudytheall-to-alldatabroadcastingandall-to-onedataaggregationandpropose: 1.AO(1)-distributedapproximationalgorithmforall-to-onedataaggregation. 2.AO(1)-distributedapproximationalgorithmforall-to-alldatabroadcast. 3.ALocalizedalgorithmforall-to-alldatabroadcast. All-to-onedataaggregationisafundamentaloperationinWSNs,inwhichthedatafromallthenodesisaggregatedinasinknodeforfurtherprocessingandforwarding.Ourdistributedalgorithmforall-to-onedataaggregationistherstinliteratureandhas 142

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aconstantapproximationguaranteeof2l2(+1) p 3+1m2.Ourdistributedalgorithmforall-to-alldatabroadcastingisalsotherstinliteratureandhasaconstantapproximationguaranteeof4l(2(+1) p 3+1m2. InChapter 5 ,weintroduceamathematicalmodelandin-networkdistributedmechanismswiththefollowingspeciccontributions: 1.Analyzingthestructureofphenomenacloudsandproposingasetofparameterstocomprehensivelydescribethemwithoutrequiringcomplexmodels. 2.Presentinganenergy-efcient,localized,in-networkalgorithmforreal-timedetectionandtrackingofphenomenaclouds,whichdonotrequirecustomizationofthenetworkroutinglayers.Theproposedalgorithmworksinanautonomousmannerwithoutrequiringinterventionfromthecentralizedqueryprocessorresidinginthebasestationandhence,issuitablefordisconnectedmodeofoperation,whencontinuouscommunicationwiththebasestationcannotbemaintained. 3.IntroducingamathematicalmodelbasedonIntegerProgram(IP)tofurtheroptimizingtheenergyconsumptionofthephenomenacloudsdetectionandtracking.Thismodelprovidesanexcellentbenchmarkforevaluatingtheperformanceoftheproposedalgorithms. 4.Providinganovellocalizedalgorithmwhichcanfurtherenhancetheresourceutilizationbasedonanewtechnique,calledhexagontiling.Thisnewalgorithmlocallyallowssensornodestobeinactiveorsleepingmodeswithoutcompromisingonthequalityofdetectionandtracking. 5.Presentingapracticalapplicationwhichhasbeendeployedinareal-worldsmartspaceandutilizesthephenomenadetectionandtrackingmechanismdescribedinthispaper,tosolvecriticalchallengesfacedduringitsdeployment. 6.Validatingourapproachesusingbothreal-worldapplicationsandsimulationstoanalyzeitsperformanceandresourcerequirementsaswellascomparingitwiththatofstream-basedapproaches. 143

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Furthermore,inChapter 6 ,weprovideanenergyefcientlocalizedinnetworkdetectionandtrackingprotocolfortrackingtheboundaryofthephenomenacloud.Thisprotocolismorerelevantforscenariossuchasoilspills,gasleakage,etc,whereitismoresensibletodetectandtrackonlythephenomenaboundaryengulngtheaffectedareainsteadoftrackingtheentirephenomena.Simulationresultsareprovidedtoshowthattheproposedprotocolismoreefcientthantheexistingworks. 144

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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,inInPro-ceedingsofthesixthannualinternationalconferenceonMobilecomputingandnetworking.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.,Dynamicclusterstructureforobjectdetectionandtrackinginwirelessad-hocsensornetworks,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,Energy-efcienttrackingofcontinuousobjectsinwirelesssensornetworks,UIC'08,2008. [14] N.Kurata,B.F.Spencer,andM.Sandoval,Efcientbroadcastinginmulti-radiomulti-channel,andmulti-hopwirelessnetworkbasedonselfpruning,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,Floodingforreliablemulticastinmulti-hopadhocnetworks,inDIALM'99:Proceedingsofthe3rdinternationalworkshoponDiscretealgorithmsandmethodsformobilecomputingandcommunications,NewYork,NY,USA,1999,pp.64,ACM. [17] K.Obraczka,K.Viswanath,andG.Tsudik,Floodingforreliablemulticastinmulti-hopadhocnetworks,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,Secureandfault-toleranteventboundarydetectioninwirelesssensornetworks,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,Onbroadcastinginradionetworks-problemsanalysisandprotocoldesign,IEEETransactionsonCommunications,vol.33,pp.1240,1985. 146

PAGE 147

[25] M.ElkinandG.Kortsarz,Animprovedalgorithmforradionetworks,SymposiumOnDiscreteAlgorithms(SODA),2005. [26] I.GaberandY.Mansour,Centralizedbroadcastonmulti-hopradionetworks,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,Centralizeddeterministicbroadcastinginundirectedmulti-hopradionetwork,inAPPROX-RANDOM'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,InAPPROX-RANDOM'04:Proc.of7thInternationalworkshoponApproximationAlgorithmsforCombinatorialOptimizationProblems,2004. [32] S.-H.Huang,P.-J.Wan,X.Jia,H.Du,andW.Shang,Minimum-latencybroadcastschedulinginwirelessadhocnetworks,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,Aconstantapproximationalgorithmforinterference-awarebroadcastinwirelessnetworks,inINFOCOM'07,2007,pp.740. [36] R.Mahjourian,F.Chen,R.Tiwari,M.T.Thai,H.Zhai,andY.Fang,Anapproximationalgorithmforconict-awarebroadcastschedulinginwirelessadhocnetworks,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,Animprovedapproximationalgorithmfordataaggregationinmulti-hopwirelesssensornetworks,inInACMMobihoc2009,2009. [40] P.-J.Wan,S.-H.Huang,L.Wang,Z.Wan,andX.Jia,Minimumlatencyaggregationschedulinginmulyi-hopwirelesssensornetworks,inInACMMo-bihoc2009,2009. [41] P.Juang,H.Oki,Y.Wang,M.Martonosi,L.Peh,andD.Rubenstein,Energy-efcientcomputingforwildlifetracking:designtradeoffsandearlyexperienceswithzebranet,SIGARCHComput.Archit.News,vol.30,no.5,pp.96,2002. [42] D.McErleanandS.Narayanan,Distributeddetectionandtrackinginsensornetworks,inProc.36thAsilomarConferenceonSignals,SystemsandComputers,2002. [43] Palm,The29palmsexperiment:Trackingvehicleswithauav-deliveredsensornetwork:http://tinyos.millennium.berkeley.edu/29palms.htm.,2000. [44] S.Duttagupta,K.Ramamritham,andP.Kulkarni,Trackingdynamicboundaryfrontsusingrangesensors,inThefthEuropeanConferenceonWirelessSensorNetworks,January2008. [45] C.ZhongandM.Worboys,Energy-efcientcontinuousboundarymonitoringinsensornetworks,inTechnicalReport,http://www.spatial.maine.edu/czhong/boundary monitoring.pdf,2007. [46] M.Ali,M.Mokbel,W.Aref,andI.Kamel,Detectionandtrackingofdiscretephenomenainsensor-networkdatabases,inSSDBM'2005:Proceedingsofthe17thinternationalconferenceonScienticandstatisticaldatabasemanagement,Berkeley,CA,US,2005,pp.163,LawrenceBerkeleyLaboratory. [47] R.Kremens,J.Faulring,A.Gallagher,A.Seema,andA.Vodacek,Autonomouseld-deployablewildlandresensors,inInternationalJournalofWildlandFire,2003,vol.12,pp.237. [48] J.Heidemann,Y.Li,A.Syed,J.Wills,andW.Ye,Underwatersensornetworking:Researchchallengesandpotentialapplications,inUSC/ISITechnicalReportISI-TR-2005-603,2005. [49] J.Cassels,Anintroductiontothegeometryofnumbers,inBerlin:Springer-Verlag,1971. [50] W.MathWorld,Space-llingpolyhedron, http://mathworld.wolfram.com/Space-FillingPolyhedron.html [51] S.-H.Huang,H.Du,andE.K.Park,Minimumlatencygossipinginmulti-hopwirelessnetwork,inInProceedingsofMobihoc2008,2008,pp.733. 148

PAGE 149

[52] R.Tiwari,T.Dinh,andM.T.Thai,Onapproximationalgorithmsforinterference-awarebroadcastschedulingin2dand3dwirelesssensornetworks,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,Localizedin-networkdetectionandtrackingofphenomenacloudsusingwirelesssensornetworks,inProceedingsoftheInternationalConferenceonIntelligentEnvironments(IE),2009. [58] S.Madden,M.Franklin,J.Hellerstein,andW.Hong,Tag:atinyaggregationserviceforad-hocsensornetworks,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,Gps-lesslowcostoutdoorlocationferverysmalldevices,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.El-Zabadani,S.Pickles,andA.Helal,Buildingplug-and-playsmarthomesusingtheatlasplatform,inProceedingsofthe4thInternationalConferenceonSmartHomesandHealthTelematics,June2006. [63] A.Helal,W.Mann,H.El-Zabadani,J.King,Y.Kaddoura,andE.Jansen,Gatortechsmarthouse:Aprogrammablepervasivespace,inIEEEComputer,March2005. [64] J.King,R.Bose,S.Pickles,A.Helal,andH.Yang,Atlas-aservice-orientedsensorplatform,inProceedingof1stIEEEInternationalWorkshoponPracticalIssuesinBuildingSensorNetworkApplications,2006. 149

PAGE 150

[65] R.BoseandA.Helal,Observingwalkingbehaviorofhumansusingdistributedphenomenondetectionandtrackingmechanisms,inProceedingsof2ndInterna-tionalWorkshoponPracticalApplicationsofSensorNetworks,heldinconjunctionwiththeInternationalSymposiumonApplicationsandtheInternet(SAINT),Turku(Finland),2008. [66] M.Cardei,M.T.Thai,Y.Li,andW.Wu,Energy-effcienttargetcoverageinwirelesssensornetworks,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

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BIOGRAPHICALSKETCH RaviTiwariwasbornin1978,inthehistoriccitynamedAgra,locatedinnorthcentralIndia.HereceivedhisBachelorofEngineeringdegreeincomputerscienceandengineeringintheyear2001fromDr.BhimRaoAmbedkarUniversity(FormallyAgraUniversity),Agra,India.In2004,hereceivedhisMasterofEngineeringdegreewithspecializationincommunication,controlsandnetworkingfromRajeevGandhiTechnicalUniversity,Bhopal,India. 151