Novel Mitigation Methods Against Reactive Jamming Attack

Permanent Link: http://ufdc.ufl.edu/UFE0041863/00001

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Title: Novel Mitigation Methods Against Reactive Jamming Attack Theoretical and Practical Solutions
Physical Description: 1 online resource (145 p.)
Language: english
Creator: Shin, Incheol
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010


Subjects / Keywords: reactive, security, wireless
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
Genre: Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Reactive jamming attacks have been considered as the most critical and fatally adversarial threats to subvert or disrupt the networks since they attack the broadcast nature of transmission mediums by injecting interfering signals. To overcome the problems for normal lower power sensors, we proposed an efficient centralized jamming-resistant routing approach and fully localized trigger node identification methods.
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.
Statement of Responsibility: by Incheol Shin.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Thai, My Tra.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041863:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041863/00001

Material Information

Title: Novel Mitigation Methods Against Reactive Jamming Attack Theoretical and Practical Solutions
Physical Description: 1 online resource (145 p.)
Language: english
Creator: Shin, Incheol
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010


Subjects / Keywords: reactive, security, wireless
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
Genre: Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Reactive jamming attacks have been considered as the most critical and fatally adversarial threats to subvert or disrupt the networks since they attack the broadcast nature of transmission mediums by injecting interfering signals. To overcome the problems for normal lower power sensors, we proposed an efficient centralized jamming-resistant routing approach and fully localized trigger node identification methods.
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.
Statement of Responsibility: by Incheol Shin.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Thai, My Tra.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041863:00001

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2010 Incheol Shin


Most of all, I would like to acknowledge my chair advisor Dr. My Tra Thai. From

the moment I started to work with her, she has encourage me, guided me through all

the researches, and gave me invaluable advices, suggestions and supports to pursue

this degree. I am heartily thankful to the members of my supervisory committee, Dr.

Randy Y. C. Chow, Dr. Tamer Kahveci, Dr. Prabhat Mishra and Dr. Panos M. Pardalos,

for their guidance and mentoring. Finally, I would like to show my gratitude to my family



ACKNOWLEDGMENTS ..................
LIST OF TABLES ......................
LIST OF FIGURES .....................
ABSTRACT .. .. .. .. .. .. .
1 INTRODUCTION ...................

Reactive Jamming Attacks in WSNs
Identification of Trigger Nodes ....
Construction of Routing Backbone .
Organization .............

2 JAMMING ATTACKS ...........
2.1 Effectiveness of Jammers .....
2.1.1 Packet Send Ratio (PSR)
2.1.2 Packet Delivery Ratio (PDR)
2.2 Jamming Attack Models ......
2.2.1 Constant Jammer ......
2.2.2 Random Jammer ......
2.2.3 Deceptive Jammer .....
2.2.4 Reactive Jammer ......
2.3 Existing Solutions .. .......
2.3.1 Physical Layer Approaches
2.3.2 Link Layer Approaches .
2.3.3 Network Layer Approaches
2.4 Conclusion .. ...........


3.1 Network Model and Problem Definition
3.2 Prelim inaries .. ............
3.2.1 Maximum Clique Problem .
3.2.2 Non-Adaptive Group Testing ..

3.3 Centralized Trigger Node Identification (CTNI) .......
3.3.1 Group Victim Nodes Based on Minimum Collection
Covers (GVN-MCDDC) Algorithm ..........
3.3.2 Detection of Trigger Nodes Based on Non-Adaptive
Group Testing (DTN-NCGT) Algorithm .......
3.4 Theoretical Analysis .. ..................

of Disjoint Disk


. 3



3.4.1 Estimation of Trigger Node Upper Bound D ... 45
3.4.2 Correctness .. ...... .. .. .......... ..47
3.4.3 Performance Analysis ......................... 48
3.4.4 Random Reactive Jamming Model ... 50
3.5 The TNLT-CDS Routing Algorithm ... 51
3.6 Performance Evaluation ................. ......... 52
3.6.1 Simulation Setup ................. ......... 52
3.6.2 Results and Analysis ..... .. ..... 55 Performance by the number of jammers J ... 55 Performance by the number of radios m ... 55 Performance by the number of nodes N ... 56 Performance by the density of the network ... 56 Performance by transmission range of the jammers .. 57
3.7 C conclusion . .. 57


4.1 Network Model and Problem Definition .... ....... 59
4.2 Overview and Fundamental Results ..... 60
4.2.1 Overview of Identification Procedure ... 61
4.2.2 Hexagon Tiling Coloring ..... ... 62
4.2.3 The k -Coloring Algorithm ....................... 63
4.3 Localized Trigger Node Identification (LTNI) ... 65
4.3.1 Partition of Nodes Based on Hexagon Tiling and Coloring 65
4.3.2 Trigger Nodes Detection Procedure ... 68 Sequential group testing based localized trigger node
identification (SGT-LTNI) algorithm ... 68 Identification of a single trigger node (ISTN) algorithm 69
4.4 Theoretical Analysis .. .. .. .. .. .. .. 70
4.4.1 Upperbound on Testing Rounds ..... 70
4.4.2 Message Complexity .......................... 72
4.4.3 Random Reactive Jamming Model ... 73
4.5 The TNLT-CDS Routing Algorithm ... 74
4.6 Performance Evaluation ................. ......... 74
4.6.1 Testing Rounds T ....... ........ .. ...... .. 76
4.6.2 Message complexity .......................... 78
4.6.3 Runtime ..... ..... 81
4.6.4 The number of nodes in quarantine areas ... 83
4.6.5 Random reactive jammers ... 83
4.7 C conclusion . .. 84


5.1 Overview of Dominating Tree ......................... 86
5.2 Hardness and Approximation ..... ........ 87
5.2.1 Inapproximability ................. ......... 87

5.2.2 Approximating Dominating Tree .. .. 89
5.3 Heuristic Algorithm and Analysis ..... .... 91
5.3.1 Algorithm Description ......................... 92
5.3.2 Runtime Com plexity .......................... 94
5.4 Performance Evaluation ............................ 95
5.5 C conclusion . .. 99


6.1 Overview of Virtual Backbone ..... .. ... ... 100
6.2 Related W ork ..... . 102
6.2.1 General G raph . 102
6.2.2 Unit Disk G raph . 103
6.2.3 Disk Graphs with Bidirectional Links . 104
6.2.4 Other Results in CDS ......................... 104
6.3 Wireless Communication Model and Preliminaries .... 105
6.3.1 N stations . . 105
6.3.2 Term inologies . 105
6.3.3 Definitions ................... ............106
6.4 Multi-Factors Model and Solutions .. .. 106
6.5 A Better Algorithm for CDS on Diameter .... 109
6.6 Progressive Algorithm (PA) and Analysis . ... 113
6.7 Further Improvements for The Progressive Algorithm .... 119
6.7.1 Reducing Multiple Paths ............... ....... 120
6.7.2 Removing Redundant Terminals . ... 121
6.7.3 Locating Central Area ................ ........ 123
6.8 Performance Evaluation ........................... 125
6.8.1 Performance for CDS-BD-D, CDS-BD and PA .... 126
6.8.2 Performance for BDA and PA ..................... 128
6.8.3 Performance Based on Different ... 130
6.8.4 Performance for Improvement Techniques ... 131
6.8.5 Performance for Multi-Factors Model ... 132
6.9 Conclusions .. .. .. .. .. ....... ... 133

7 CO NC LUSIO N . . 135

R EFER ENC ES . . 137

BIOGRAPHICAL SKETCH ................................ 145

Table page

3-1 Notations ..................... ................. 38

6-1 R untim e(m s) . . 130

Figure page

2-1 Constant jam ming attack ................... ......... 19

2-2 Random jam ming attack ................... ............ 21

2-3 Deceptive jamming attack .......... ... ...... .......... 22

2-4 Reactive jamming attack .......... ... ..... ............. 23

3-1 Since item 6 (6th column) is a trigger node (positive item), only the 2nd and
6th groups (rows) return negative outcomes. On the contrary, all other four
groups produce positive outcomes. . 44

3-2 5 Possible jammers activated by a trigger node t ... 46

3-3 Experimental results by various size of jammers ... 52

3-4 Experimental results by various size of channels ... 53

3-5 Experimental results by various size of nodes. . 53

3-6 Experimental results by various network densities ... 54

3-7 Experimental results by various size of a .. 54

4-1 The minimum distance between two nodes with same color ... 64

4-2 The coloring pattern for k = 4 . 65

4-3 Trigger nodes in a hexagon ............................. 71

4-4 Rounds by various parameters ..... ....... 76

4-5 Messages by various parameters ..... .. ..... 77

4-6 Runtime by various parameters ..... .. ...... 78

4-7 Nodes in quarantine areas by various parameters ... 79

4-8 The number of rounds T in random reactive jamming model with different values
of jamming probability P. . 80

5-1 Reduction from WDS G to DT G' ... 89

5-2 An example of reduction from G to G' ...................... 90

5-3 The execution of HeurDT algorithm ..... .. .... 93

5-4 Simulation results for HeurDT, MST-L and optimal results ... 96

6-1 Given node r as the root, node a, b, f, g are terminals. r is the parent of c and
e. Node a, b are siblings, f, g are siblings. Node a, b, f, g are r's 2-hops away
neighbors . . 106

6-2 An example for second phase in algorithm 12. .. 112

6-3 All the nodes in the ring are a CDS with diameter of 8 ... 117

6-4 An example for reducing multiple path ... 121

6-5 An example for removing redundant terminals . ... 122

6-6 An example of leaf nodes located at central area. The black nodes consist of
the tree.................... .................. .. 124

6-7 An example of selecting the node with maximum degree as the root of CDS 125

6-8 Performance for CDS-BD, CDS-BD-D and PA . ... 127

6-9 Performance for BDA and PA ............................ 128

6-10 Performance based on different ......... ....... ..130

6-11 Performance for the first and second improvement techniques 131

6-12 Performance for the third improvement techniques ... 132

6-13 Performance for multi-factors model ..... .. .. .. 133

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


Incheol Shin

August 2010

Chair: My Tra Thai
Major: Computer Engineering

Wireless Sensor Networks (WSNs) consist of many spatially deployed sensor

devices to cooperatively monitor selected target locations and communicate with base

stations. WSNs have potential applications in various complex environments such as

military surveillance, health-care systems, disaster area monitoring and etc. Due to the

requirement of large-scale and real-time data processing in WSNs, security is critical in

many sensor network applications.

The wireless communication of sensor devices in resource-constrained WSNs leads

to many challenging and intriguing security-sensitive problems that cannot be handled

using conventional security solutions. Especially, since jammers attack the broadcast

nature of the transmission medium by injecting interference signals, they are considered

the most critical and fatally adversarial threats to subvert or disrupt the networks.

Jamming attacks do not have to modify communication packets or compromise any

sensors in order to launch, which makes them difficult to detect and defend against.

Existing countermeasures against such attacks either consider sensor nodes

equipped with sophisticated hardware, which is infeasible for low cost resource

constraint WSNs, or have high overhead in term of time and message complexity and

energy consumption. However, to overcome the problems in existing methods against

reactive jamming attack, this dissertation introduces a novel approach by identifying the

trigger nodes, whose transmissions activate any jammers and then constructing routing
path based on the identification of sensor nodes.
This dissertation includes two main parts, identification of trigger nodes and

construction of virtual backbone based on the detection. First of all, the identification
of trigger nodes can help us (i) to design a better routing protocol by switching these

nodes into only receivers to avoid activating jammers and (ii) to locate the jammers

based on the trigger nodes, thus providing an alternative mechanism against reactive
jamming attacks. Secondly, an effective construction of virtual backbone provides

not only the jamming avoidance protocol but also efficient broadcast routing. For the
adaptive building of virtual backbone, this dissertation investigates dominating tree and
multi-factor model studying a joint optimization problem on Connected Dominating Set

(CDS) in wireless ad-hoc networks.
Theoretical analysis and experimental results endorse the suitability of these

identification algorithms in terms of time and message complexity. This work is the first
one to design novel countermeasures against reactive jamming attack.


Wireless Sensor Networks (WSNs) have enormous mission critical applications in

such different realms as military surveillance, disaster area alarm system and critical

infrastructure protection monitoring. Hence, the quality of service and security are

critical issues in WSNs which need an elite attention. Nodes in WSNs deliver packets

by radio transmissions in a hop-by-hop manner, and due to this broadcast advantage, a

transmitter can communicate a message to all its receivers within it's transmission range

by a single radio transmission.

Broadcast nature, however, increases the vulnerability of WSNs to various security

challenges mostly from Denial of Service (DoS) attacks as explained by [8]. Jamming

attacks, one of the DoS attacks, especially are light weighted, but the most fatal threats

to WSNs, because they attack the core of wireless broadcast advantage even without

modifying communication packets and compromising wireless sensor devices. Due to

the excessive hardware requirement on existing methods, threats cannot be neutralized

and nullified with conventional security solutions.

1.1 Reactive Jamming Attacks in WSNs

There are several types of Denial of Service (DoS) attacks, such as selective

forwarding, sinkhole, Sybil attack, flooding and etc. However, jamming attacks are

known as the most significant threats because of their effectiveness and lethal damages

to WSNs. In jamming attacks, the malicious disseminates out adversarial signals into

busy channels which are filled with legitimate sensor transmissions without following

any legitimate protocols. This will result in the slump of the Signal to Noise Ratio (SNR)

and network throughput. Furthermore, reactive jamming attack adopts more advanced

and efficient jamming strategy than any other active jammers in which jammers quietly

scan all the available channels to sense activities and blatantly start injecting adversarial

signals on that channel to corrupt on-going packets. Since it maintains lower energy

consumption to launch but greater hardness to be detected, reactive jammers can cause

more severe damages to WSNs. That is, the reactive jamming attack especially is the

most intelligent and stealthy type of jamming attack.

As the reactive jamming attack does not need any special hardware or a complicated

mechanism to launch, it is simple to initiate and hard to be detected in WSNs.

Importantly, it cannot be dealt with using conventional security mechanisms, such

as cryptography, authentication and authorization, as it cannot prevent messages from

being received by a malicious node if it is in range of the transmitter and operating at

the same radio frequency. Consequently, this is particularly dangerous to WSNs since

its main targets are the kernel characteristics of the networks, distributed large-scale

networks and the broadcast nature of wireless communication.

Even though the existing literature has various solutions for different jamming

models, the majority of them are not suitable to resource constrained networks and

suffer from hardware requirements in wireless devices. In order to overcome the

shortcomings from classic approaches, this dissertation introduces novel methods

against the reactive jamming attack in WSNs by detecting the trigger nodes and then

building jamming avoidance routing path according to the identification of wireless

devices. Consequently, this dissertation consists of two parts, identification of trigger

nodes and construction of virtual backbone procedure.

1.2 Identification of Trigger Nodes

The identification of trigger nodes can have several benefits for mitigation of the

attacks. First of all, routing algorithm can be constructed in which the triggers are only

the receivers, thus avoiding activating the jammers and minimizing the adversarial

effect of jamming attacks. This can overcome the limitations of excessive hardware

requirement of the channel surfing and frequency hopping methods. In addition, the

identification of trigger nodes will not create an unnecessary large size of jammed

regions like in [78]. Secondly, in case trigger nodes needs to send messages, they

may still utilize channel surfing, but only a few nodes may require this operation, thus

greatly reducing the computational costs required by existing methods. That is, after the

efficient identification of trigger nodes, victim nodes would be also scheduled to transmit

messages in order to minimize the damage from the attackers by keeping silent during

the transmission of the trigger nodes, thus preventing jamming. Finally, the location

information of the trigger nodes to later locate the jammers within networks, which is the

first attempt to provide location information in order to pinpoint the location of jammers.

In addition, this study introduces not only centralized and localized mitigation

methods but also random reactive jamming model in order to validate the fault-tolerant

identification approaches. The reactive jammers randomly react to legitimate on-going

communication activities with probability p < 1, which makes identification approach

challenging. However, both centralized and localized approaches are still applicable

against this models as well, so that their suitability can be verified in practical network


Even though this trigger identification is a non-trivial localized approach to be

realized in practical network environments due to the unknown and dynamic locations

of jammers with various behaviors, this study designs efficient centralized and localized

mitigation schemes with low time and affordable message complexity.

1.3 Construction of Routing Backbone

A WSN consists of sensor nodes communicating with each other using radio

transmission. Nodes that are within their own transmission ranges can exchange

messages directly, but nodes which are out of transmission range communicate through

intermediate nodes to route their messages. Importantly, constructing virtual backbone

with only non-trigger nodes after identification of all trigger nodes will help to maintain

the throughput of networks against reactive jamming attack. Furthermore, due to the

energy consumption of each node for transmissions, minimizing the size of intermediate

nodes would help to reduce network energy consumption. In other words, since the

sensor nodes in a WSN have limited resources and small transmission ranges, how to

construct a set of intermediate nodes to relay messages determines the efficiency of

routing in networks.

Consequently, an efficient method of constructing a virtual backbone would be able

to efficiently reduce not only the routing overhead of networks to maximize the network

lifetime but also the size of jammed area to minimize damages from jamming attack.

1.4 Organization

The rest of the work is organized as follows. Chapter 2 describes the evolution

of jamming strategies to reactive jammers and existing countermeasure against the

attacks. For the identification phase, Chapter 3 provides the solution for centralized

identification of trigger nodes, meanwhile the localized algorithm for the detection of

trigger nodes is presented in Chapter 4. Our proposed new problem of dominating tree

studied in Chapter 5 followed by the multi-factor model in Chapter 6 so as to provide the

efficient construction of jamming resistant routing protocol. Chapter 7 concludes this



We new briefly introduce the jamming attacks and conventional security service

mechanisms against them.

Current jammers have been evolving and reacting against countermeasures using

several strategies, including energy efficiency and lower probability of detection with

higher stealth. Especially, some of them are equipped with protocol-aware jamming

attack models in order to achieve jamming effectiveness with lower energy consumption

and higher stealth. In this chapter, various types of jamming attacks and existing

solutions against them using detection mechanisms will be introduced in order to show

how powerful jammers are with their evolving strategies.

2.1 Effectiveness of Jammers

At present, there are two ways to measure the effectiveness of jamming attacks:

Packet Send Ratio (PSR) and Packet Delivery Ratio (PDR). These two types of

measurements are useful to quantify the efficiencies of jamming techniques. Research

[52, 55, 69, 84, 86] describing jamming attacks based on these measurements. In this

section, the importance of jamming attacks and how powerful they are will be introduced

as they apply to PSR and PDR.

2.1.1 Packet Send Ratio (PSR)

This is the ratio of the number of packets that are successfully transmitted as

legitimate traffic compared to the volume of packets that were intended to be sent out.

This is defined as:
In most MAC layers in WSNs, carrier sensing multiple access (CSMA) control has

to be performed before legitimate communications in sender nodes. That is, sender

devices are required to sense activity in the channel for a certain duration of time before

transmission in order to avoid messages colliding. Jammers can drop the PSR by

attacking the CSMA control protocol.

A jammer can decrease the number of messages sent by injecting continuous

interference signals into the idle channel. Since interference signals in the channel are

sensed as busy in nodes that use the CSMA control protocol, senders have to hold the

MAC layer message buffer without any message transmission until sensing the channel

is idle. During holding, the message buffer fills with messages, and even new messages

may keep arriving for the full buffer. A series of new messages could easily be dropped

because the buffer is full. The worst scenario for the buffer would be a case when the

existing messages keep aging during their waiting in a buffer of MAC layer, resulting in

timeout and discard without transmission. In addition, the back-off time in each node

would be drastically increased, and in CSMA protocol it takes considerable time to

recover from the unnecessarily longer backoff time.

The measurement of PSR can easily be implemented without any sophisticated

hardware in the sensor devices since they only need to keep track of the number of

messages from the upper layer and the size of the messages sent via legitimate traffic.

Jammers attacking the PSR can be detected relatively easily by exploiting the

Cyclic Redundancy Check (CRC) in the MAC layer. Each node would be monitoring

the activities on the channel during adversarial messages from jammers, and if the

adversarial messages cannot be validly checked through the CRC, then nodes would

become suspicious of the presence of jammers in networks.

Stealth is critical to attackers, and jammers may able to emit regular packets for

higher stealth, but, the jammers need to acquire a way to generate legitimate packets,

which depends on sophisticated hardware to analyze the protocol in order to disguise

their packets as legitimate packets.

2.1.2 Packet Delivery Ratio (PDR)

This is the ratio of the number of packets that are successfully validated through the

CRC check compared to the size of packets received. The PDR is defined as:


A Cyclic Redundancy Check (CRC) is a simple non-secure hash function for detection

of errors in communication messages. Usually the CRC computation would be done in

the link layer by a long division operation where quotients are discarded and remainders

from the operation becomes the results of the CRC, which are appended to the end of

link layer frames. Receivers would be able to decode and validate received packets with

ease by utilizing the CRC check. The PDR ratio drops if jammers inject interference

signals into communication messages.

A jammer would be able to decrease the number of packets that are successfully

delivered to destination nodes by corrupting ongoing communication packets. Due to

the broadcasting nature of wireless communications, collisions among packets are

considered a critical problem, and the jammers attack the PDR from the viewpoint of this

weakness by corrupting interference signals.

Attacking the PDR not only drops the PDR, but also wastes the energy of sensor

networks due to the fact that collided messages require retransmission. The sensor

networks are resource-limited networks, and energy consumption has been much

studied because it dominates the network lifetime. In other words, invalidation of

packets by CRC checking imply retransmissions in sender nodes after notifications from

receivers, which wastes significantly energy and results in a shorter network lifetime.

As a result, we can say that attacking the PDR from jammers causes more serious

problems than attacking the PSR.

In addition, in terms of stealth, it would be better for jammers to drop PDR. It would

not be necessary for jammers attacking PDR to expose themselves to legitimate nodes

when emitting their adversarial signal. That is, it is harder to defend the jamming attacks

dropping the overall PDR of networks.

2.2 Jamming Attack Models

There have been a wide range of jamming strategies to prevent legitimate users

from transmitting or receiving communication messages. The objectives of the attacks

are to effectively reduce PSR and PDR by emitting interference signals. The efficiency

of attacks associated with PSR requires some knowledge about WSN communication

protocols, while reducing PDR does not. We will discuss more about the various types of

jammers according to their intelligence.

2.2.1 Constant Jammer

Jammer Victim Node

O Constantly

interference si nal
S rangrange a
/\-n norr nodenode
JAMMING 1^ \ .o.'"\

Figure 2-1. Constant jamming attackonstantly
interference signal

range ofa
normal node

Figure 2-1. Constant jamming attack

According to the Fig. 2-1, the constant jammer, a trivial jammer, is the most intuitive

strategy to implement, but it has the least energy efficiency among all jammers since

it does not follow the protocols in WSNs, just emitting a series of noise signals into the

channel. It can be implemented using a waveform generator, so as to emit continuous

interference signals by disregarding the MAC-layer protocol. The jammers can also

be a normal wireless device used to transmit random bits without any consideration of


While it does not require complicated monitoring architectures to sneak into

communication protocols, doing so drastically hinders the performance of PSR since

the most number of wireless networks exploit Carrier Sense Multiple Access / Collision

Avoidance (CSMA/CA) to physically monitor the traffic at communication parties. That

is, legitimate senders would not be able to initialize transmission procedures to send

packets as long as there are signal detections including jamming signals and legitimate

communication signals. As a result, the senders have to stall for a considerable length of

time to avoid collisions, and PSR would drop drastically. This attack might work well in

networks with high traffic.

A constant jamming attack is ineffective in terms of energy consumption due to

the fact that the constant jammers emit interference signals whether or not there is

legitimate traffic. The jammers are also wireless devices that emit interference signals

with limited resources, usually portable energy supplies, and demand high energy

consumption to hold a communication channel in order to prevent nodes from sending


In addition, the stealth of adversaries cannot be effectively achieved due to the fact

that their behavior disobeys to the protocols in networks. To maximize the stealth of

jammers, they must be invisible to legitimate nodes under the communication protocols.

The legitimate nodes can identify the presence of jammers with ease by monitoring

signals from any nodes, including jammers, and wait until the jammers disappear. As a

result, the constant jammer is easy for adversaries to launch, but hard to avoid detection

from legitimate nodes.

Figure 2-2. Random jamming attack

2.2.2 Random Jammer

As depicted in Fig. 2-2, the random jammer has evolved from the constant jammer

to conserve energy. Like the constant jammer, it emits jamming signals for a certain

amount of the time, but sleeps after turning its radio off in order to conserve energy for a

longer lifetime of jamming.

While the switching mechanism between sleeping mode and jamming mode can

save a significant amount of energy, it would drop the efficiency of attack to PSR.

Because, during its jamming phase, normal senders would not be able to transmit

messages for channel activities under jamming signals and would have to wait until

its sleeping phase begins. They could send out the stalled messages during the

jamming phase, and most of the messages would be successfully delivered without

interference during the jammers' sleeping mode. This becomes a trade-off between

energy conservation, and accommodating an attack, which leads to another evolution of

jamming strategy.

2.2.3 Deceptive Jammer

Figure 2-3. Deceptive jamming attack

By monitoring the protocols in WSNs, this is the first type of jammer that takes the

stealth of jammers into consideration. The deceptive jammer in Fig. 2-3 does not send

out random bits or waveforms by a generator, but regular packets in order to capture

the channel of legitimate communicators. The deceptive jammers emitting regular

packets forces legitimate communicators into the receiving state and prevents them

from converting their state into send mode. This method was initially implemented by

continuously sending out preamble messages, so that it is hard to detect and is an

effective method to disable a CSMA.

The deceptive jammer not only would drop the PSR, but also increase the stealth

against the detection system by transmitting regular frames into a MAC-layer channel.

Legitimate sensor devices have no way to identify the packets from deceptive jammers

without an authentication scheme, but an authentication procedure in the WSNs is

expensive. In addition, normal nodes have no choice but wait until timeout from the

receive mode when receiving the fake preamble messages from the jammers since

the preamble messages indicate a constant stream of incoming packets. Continuously

sending out regular preamble packets from the jammer would hurt PSR by holding the

channel without any suspicion of the presence of jammers. As a result, the falling PSR

causes a lower throughput int the networks.

[2] also mentions a periodic jammer, another adaptation of deceptive jammer.

Instead of sending out continuous preamble messages, it generates a series of short

pulses in every DIFS interval (50 nanosec), so normal nodes find the network always

2.2.4 Reactive Jammer

STrigger Node Victim Node
Jammer V5rV5

f. ,_:f /i ,(w-:.'

Monitoring communication Reactely
V2 legitimate activities V gimerating

Figure 2-4. Reactive jamming attack

Reactive jamming attacks are considered one of the most intelligent jamming

strategies due to their reactive behavior. The reactive jamming attack in Fig. 2-4 is

one such DoS security threat, in which a malicious node jammerr) quietly scans all the

available channels in a wireless network to sense any activity and, if it detects some

signal from a legitimate node on any channel, it starts injecting Noise on that channel in

order to interfere with all the receivers in its range resulting in a drastic decrease in the

signal to noise ratio and communication throughput of the network.

This kind of attack is straightforward to initiate and very effective as it has no special

hardware requirements, so the jammer only needs to keep listening for a legitimate

signal on the available radio channels.

Reactive jamming attacks are able to effectively attack the PDR by using a reactive

strategy. While attacking the PSR using the jammers introduced above would only be

able to hold a channel away from normal nodes and waste the channel resource. Just

dropping the PDR by using a reactive jammer inflicts more damage to networks than just

dropping the PSR because of the retransmission scheme in legitimate senders.

An intelligent jammer [2] with knowledge of the protocols is one of the implementations

of a reactive jammer and it can have several different strategies to corrupt messages,

including control messages and data messages. Importantly, it would be able to

distinguish between control messages and data messages based on the length of

each communication message or the intervals between them in WSNs. According to

the jamming strategies, there could be four types of intelligent jamming attacks, such as

CTS corruption jamming, Acknowledge corruption jamming, data corruption jamming,

and DIFS wait jamming.

*A clear to send (CTS) corruption jammer would wait until sensing an arbitrary
request to send (RTS) frame from any normal nodes wishing to send data. The
jammer initializes a short jamming pulse right after every end of an RTS packet
during a period of SIFS since it knows that a CTS messages follows a RTS
message as a next control message. After a period of SIFS, it will inject that
short pulse into the shared medium in order to corrupt CTS messages with less
energy consumption. As a result, the legitimate sender needs to reissue the RTS
message to initialize communication since the CTS message did not get through.

* An acknowledge corruption jammer disrupts acknowledgments after data packets,
but this strategy requires message identification schemes to locate the ends of
data packets, which means longer activation of the jammers in order to analyze
packets. This is the least efficient jamming strategy among other intelligent

A data corruption jamming attack strategy is relatively easier to launch than other
strategies due to the fact that the data packet is longer than any other packets.
However, it would drive poor PDR of WSNs due to the retransmission of data
packets with additional communication procedures.

A DIFS waiting jamming attack corrupts RTS packets or CSMA/CA data packets by
monitoring the medium idle for DIFS time in networks with high traffic.

2.3 Existing Solutions

There are many studies against jamming attacks [7, 26, 31, 32, 35-37, 43, 47,

61, 70, 78, 83, 85, 87], but the high computational overhead of these methods badly

reduces the effect in resource-limited network environments, such as WSNs. For

example, in the channel surfing methods from [7, 35, 37, 47, 78, 83, 85, 87] and

frequency hopping methods from [26, 31, 32, 36, 43, 58, 61, 70], the transmission

frequency or channel is changed to a range where there is no interference from

the adversaries. These strategies are not quite suitable for WSNs, especially in

multi-channel WSNs, since the sensors have to scan all the channels to detect the

jamming attacks and hop to new frequencies all the time, even in the middle of a

communication. Due to the fact that most of the sensor nodes have a half-duplex

transceiver on them, scanning the channels during transmission causes communication

stalls to check the availability of the current channel. Frequent communication stalls

result in a longer transmission duration and more energy consumption. Consequently,

these methods cannot avoid high overhead and resource consumption.

2.3.1 Physical Layer Approaches

Even though the spread-spectrum communication was introduced by the military

for secure communications and resistance against natural interference, the use of

spread-spectrum communication in the physical layer is one of the best-known

schemes to evade jamming attacks. In the literature, there are two ways to build

a spread-spectrum communications against jamming attacks, frequency hopping

(FH) [26, 31, 32, 36, 43, 58, 61, 70] and code division multiple access (CDMA)
[14, 21, 30, 53, 76, 89], forms of direct sequence spread-spectrum communication.

Since most jamming attacks are categorized into physical layer attacks, the beginning of

the defense mechanisms start in the physical layer. This section will introduce existing

physical layer countermeasures against the jamming attacks.

The frequency hopping technique was designed as a kind of secure solution against

jamming, eavesdropping, tempering, etc, in wireless communication. Jamming attacks

are able to attack WSNs with partial-band noise at the beginning stage of jamming

attacks, and the frequency hopping solution is utilized to defend against the jammers

with partial-band noise at that time.

The initial outline of the conventional FH method is to use each frequency slot

to transmit packets through one of orthogonal signals during a certain period of time,

signaling interval. That is, the transmitter hops between safe frequencies based on a

predefined algorithms.

However, the most important issue to exploit frequency hopping technique is

how to secretly establish switching sequences between two communication parties in

order to foil a third party. That is, reducing the probability of inference is the key of this

technique against jamming attacks. A pre-shared secret code for FH is not feasible in

wireless communication networks due to the dynamic behavior of sensor nodes and the

scalability of the networks. Since the main issues of FH approach are how to assign the

hopping sequences for shifting frequencies and how to synchronize them among the

nodes, there has been much research regarding those critical issues in FH mechanisms.

To remove the burden of distributing sequences, [61] proposed the uncoordinated

frequency hopping (UFH) technique for an anti-jamming point-to-point scheme to

establish a secrete key between two communication parties. This paper introduced

a UFH-based message transfer protocol for key establishment with an encapsulation

technique for message fragments even in the presence of a jammer, and sensor

nodes after the key establishment would be able to communicate each other with the

coordinated frequency hopping method. The key establishment problem is inherent

to the frequency hopping technique, but this paper tries to break the dependency

between them. Importantly, the fragmentation procedure utilizes a collision-resistant

hash function as well.

Since this scheme is based on the uncoordinated hopping model, it suffers from

lower communication throughput. That is, numerous sending attempts to transmit each

fragment so that the performance of the scheme is greatly effected by the number of

attempts. In addition, it incurs higher storage and processing costs in sensor nodes as

well, which are too expensive for resource limited sensor networks.

Recently, the message-driven frequency hopping (MDFH) technique [42] has been

introduced to achieve a more spectral efficiency than any other existing FH designs. In

the traditional models, FH techniques require a much wider spread bandwidth than they

actually use to transfer messages, which means the spectral efficiency from the total

number of available carrier frequencies is too low in practical network environments.

[42] presented an innovative form of MDFH that exploited message streams as a
pseudo-random sequence for FH selection. The data stream is divided into multiple

blocks, and each block consists of additional carrier bit vectors to determine the hopping

frequencies and ordinary bit vectors that are actual data to transmit. A carrier bit vector

has Bc to specify a hopping frequency to transfer the data and Nh the number of hops

within a symbol period. The data blocks are fed into a serial-to-parallel (S/P) converter in

order to split two carrier bits and ordinary bits into two parallel data streams.

In addition, this paper presented enhanced MDFH to utilize multiple transmissions

at each hop by exploiting all the available carriers. This solution helps to increase the

resistance against jamming attacks using an unpredictable message-driven hopping

pattern, which also removes the burden of synchronization somewhat between

the communication parties. However, this frequency hopping technique also has a

fundamental limitation concerning a follower jammer, also called repeater jamming


Since the follower jammers with determinator circuits attempt to determine the hop

frequencies and generate jamming signals in a range of frequencies, importantly, the FH

technique has a critical limitation against follower jamming attacks. Initially, the simplest

solution for follower jammers was a technique using fast hopping in order to prevent the

follower jammers from having sufficient time to determine the current frequency and emit

interference signal on that. However, this approach was not feasible in resource-limited

network environments. Despite this, there have been several studies on the follower

jamming attacks [26, 31, 32, 36, 70], no complete solution to the problem of follower

jamming attacks has so far been reached.

The frequency hopped m-ary frequency shift keyed (FH/MFSK) was designed as

a countermeasure against a partial-band noise jammer [36]. The implementation of

FH/MFSK utilizes M non-overlapping frequency synthesizers in each transmitter and

receiver to hop each MFSK signal since the performance from conventional FH/MFSK

implementation is greatly effected by the deviation of a single carrier. However, this

approach requires complicated hardware to realize in a practical system, which is not

infeasible for resource-limited sensor networks.

[31, 32] introduced a different approach as a countermeasure evolved from

FH/MFSK against follower jammers. The multiple orthogonal signals during a certain

time period, signaling interval, would be emitted in each frequency slot that is divided

from total spread bandwidth.

Furthermore, there is conventional mode and unconventional mode in order to

synchronize communicators. In the case of conventional mode from pseudo-random

probability of pc in both senders and receivers, a receiver would determine the

transmitted data by the largest output via a dehopper. The unconventional mode

from the probability of 1 pc does not require sending any information, but a receiver

determines the data based on the presence of energy in the selected frequency slots.

This approach might relieved the burden of the hardware requirement a little, but it still

suffers from a synchronization problem between transmitters and receivers and lower

spectral efficiency of total bandwidth.

Direct Sequence Spread Spectrum (DSSS) is one implementation of spread-spectrum

communications against jamming attacks in the physical layer by using narrow band

jamming suppression capability. In this, data packets are modulated with a continuous

and pre-defined chipping sequence, and the modulated signal is spread in frequency

domain thus becoming resistant against the narrow band jamming signal. Initially, the

wavelet packet modulated direct sequence Spread Spectrum (WPM-DS-SS) system

[89] was designed to be immune to an interference signal, but this requires sophisticated

modulating hardware in the sensors.

The main issue of the DSSS technique is also secret key sharing due to the fact that

the performance of suppression capability is limited by the pseudo random generator

with the keys among communicators. The key establishment to drive identical spreading

codes among the communicators is a critical issue for the wireless ad-hoc networks in

terms of scalability.

The secrets for the DSSS communication between the sender and the receivers

have to be in agreement before the start of legitimate communications, but this

pre-shared secret key has been considered a difficult problem to solve due to the

dynamic behavior of sensors. [53] proposed a solution called Uncoordinated DSSS

(UDSSS) for authentic spread spectrum anti-jamming communication in order to solve

the key sharing problem. This approach enables the implementation of DSSS without

prior establishment of secret keys among the communicators, and receivers keep a

certificate of the sender's public key instead of sharing secret keys.

The transmitters do not use predefined spreading code, but randomly choose one

of the codes that are available in public in order to prevent any receivers from inferring

a choice of transmitter. The receivers using the UDSSS scheme despread received

messages by applying each sequence out of the set using a trial-and-error method.

The networks they assume are not time synchronized, so that transmitters have to send

out a message with repetition, and receivers synchronize with senders by applying a

sliding window approach. That is, the time to identify a correct spreading code and

synchronization procedure in receivers dominate the overall performance in the UDSSS

method, and it has less efficiency than the DSSS method.

With respect to the last approach CDMA among spread-spectrum communications,

one study [14] related to utilizing the direct sequence CDMA (DS-CDMA), resorts

to high-power dynamic tree-remerging schemes to maintain the small number of

orthogonal codes in use and to avoid re-calculation of the codes. Spread spectrum

communication has been studied to resist jamming attacks in unicast communication

because the number of codes greatly effects the performance of DSSS. [14] developed

a broadcasting technique with a DSSS scheme with fewer number of codes by using a

binary key tree.

Due to the variation in nodes in dynamic environments, this method suffers from

the additional maintenance overhead of join-in and leaving behaviors, especially,

so computation of orthogonal codes takes much time. In addition, because of the

probabilistic nature of packet reception, it also has a problem of false alarms, and as a

solution for false alarms, networks are periodically required to reset their code in each

sensor and build the code tree repeatedly. This series of reconstruction procedures

necessitates high message complexity and additional computation overhead on the

networks as well. In these respects, a scheme with cryptographic key management has

a scalability problem and a stability problem when applied to various dynamic networks.

As explained above, the existing FH methods have a fundamental problem with

follower jammers when a determinator circuit attempts to determine the hop frequency

and generate jamming signals in a range of the frequencies. DSSS has limitations

against attacks based on Radio Frequency Memory (RFM) [30] as well since the

repeater jammers try to acquire the code by monitoring the on-going traffic and garble

the communication messages based on the acquisition of the code. [76] have analyzed

DSSS techniques attacked by repeater jammers in detail, but so far there has been no

complete solution for repeater jamming attack.

Due to the nature of a jamming attack, most defense schemes start from the

physical layer, FH and DSSS. FH methods from [26, 31, 32, 36, 43, 58, 61, 70]

hop communication frequencies seeking a safe one in order to avoid the jammed

communications based on the switching sequences. How to distribute the hopping

sequence and synchronize communication partners with the new sequences are the

main issues to overcome low spectral efficiency.

Code Division Multiple Access (CDMA) scheme communication [14, 21, 30, 53, 76,

89], a form of direct sequence spread spectrum is also one of the most common way to

resist jamming attacks. However, the problem of how to manage secret keys for efficient

suppression capability has to be solved for better performance of immunity against

attack in resource-limited networks.

2.3.2 Link Layer Approaches

The existing solutions in link layer can be divided into two categories, channel

surfing and modification of MAC protocols for better network resilience against jamming

attacks. There have been several papers [7, 35, 37, 47, 78, 83, 85, 87] regarding the

investigation of jamming attack from the viewpoint of link layers. In this section, we

describe various types of evasion techniques in the link layer.

Even though the channel surfing method in the MAC layer was motivated by FH, it is

the most reactive approach because it switches channels on demand after verification of

jammed communications. Most channel switching schemes are reactive, which means

that the shifting takes place only after communication is jammed. The reactive scheme

is efficient, but channel monitoring hardware is needed. In the proactive schemes, most

solutions are in physical layer and do not require a monitoring system, but result in low

spectral efficiency in a resource-limited network, because the frequency periodically has

to hop into safe one. The critical issues for this solution are synchronization, latency, and

scalability from the coordinated channel switching procedures across whole networks

and the overhead from scanning all the channels.

[83] introduced the channel surfing strategy, such that when the nodes with

detection sensors are jammed, they switch their communication channel into another

orthogonal channel in order to reconnect to the rest of a network. The boundary nodes

that lose their neighbors from a jamming attack can discover lost neighbors in new

channels and try to rebuild the connectivity of the entire network. There are two reasons

nodes lose their neighbors, poor connectivity and jamming attacks, and they provide

simple protocol to identify the reason for the lost neighbors by analyzing the channel

being used for reconstruction by the lost neighbors. However, this protocol forces

networks into an unstable state during connectivity rebuilding due to frequent link quality

degradations or the dynamic behavior of networks. Two methods have been proposed in

order to restore network connectivity after attacks. The first is the coordinated channel

switching technique when an entire network switches its current channel to a new

channel so as to reconstruct network connectivity. This technique suffers from unreliable

links, so that some nodes might miss the notification to shift their channel to a new one.

The second approach is the spectral multiplexing technique where boundary nodes

act as bridges to connect the nodes of old channel to the nodes of new channel. This

approach enables the networks to maintain multiple channels, so that the entire network

does not need to notify all nodes, just some, to switch to a new channel. There are,

however, several challenging problems to realizing a practical system, synchronization

among the nodes with different channels, initiation of channel shifting from jamming

attacks, and slot duration in a synchronous spectral multiplexing algorithm.

[87] also described a spatial retrieval method, called a physical evasion method, by

physical repositioning of mobile nodes out of jammed regions, but the networks would

be unbalanced and even isolated by the attacks. Since they assume stationary jammers

with mobile nodes, the nodes within a jammed region would be able to escape from the

jammed region after the presence of jammers was detected. The challenging issues of

the physical evasion method are how to determine which directions nodes should retreat

and how far they should retreat from their current positions, because these decisions

may cause disruption of network connectivity. In addition, this paper mentioned jammed

nodes moving into radio range after relocations, but this would result in shorter network

life time as well.

As another type of evasion technique, [85] designed a timing channel to recover

reliable communication links after jamming. The timing channel is a low-rate layer over

physical/link-layers used to detect the timing of interfered packets in the receivers by

utilizing CRC check or monitoring signal strength. This approach is for point-to-point

communication links, not for broadcast communications. The critical dependencies

of the timing channel scheme are how to detect the exact timing of the failure packet

receptions and how to map the occurrence of failed packets to the information to be

delivered. [7] proposed a jamming-resistant MAC protocol that adjusts the probability

for successful transmission by monitoring channel activities, and each node would be

able to transmit messages based on probability. The protocol also divides the time into

smaller or bigger time intervals according to successful message transmissions in order

to adapt transmission time. The main idea behind this is that adversaries observe the

activity of the current channel and, if there is not enough activity, they would not heavily

jam the channel. However, this protocol should include a mechanism to determine

successful transmissions of messages in remote nodes, which means that other

neighbors should be able to identify the result of transmission but communicators, and

it is not only difficult, but is also burden to WSNs. In addition, if the sum of probability of

each node is too high, then the nodes have less chance to observe the idle channel or a

successful transmission of a message.

A modified MAC layer protocol for defeating stealthy jammers based on IEEE

802.15.4-based hardware was proposed by Wood [78] in order to reduce the damage

from jamming attacks on communication packets. They introduced several strategies

to defend the MAC layer according to the type of attack. For example, frame masking

against an interrupting jamming attack, channel hopping against an activity jamming

attack, packet fragments against a scan jamming attack, and a redundant encoding

method against a pulse jamming attack. Frame masking is a DSSS technique using

shared keys between wireless nodes. The packet fragmentation method would be

used to transmit a message in multiple fragments during a jammer's channel activity

scanning, and the redundant encoding method is useful for the receiver to recover

corrupted messages due to jamming attacks. They want to combine all these techniques

into a MAC layer protocol to defeat jamming attacks. The fundamental limitations on

each defense mechanism are remained. That is, frame masking has a problem of

key distribution, and channel surfing has serious synchronization problem in practical

system as describe before. Packet fragmentation method might divide a packet into too

small fragments with additional redundant encoding data for recovery, which makes the

approach unfeasible in real communication systems.

There have been two main approaches to jamming attacks in the link layer, channel

surfing and modification of the MAC protocol. Both belong to a category called evasion

methods, and utilize the jammers' scanning time to transmit legitimate messages.

Channel surfing schemes from [83, 85, 87] are reactive in terms of switching channels,

but synchronization is a critical issue to implement in a practical system. Modification

of MAC protocol schemes require additional communication overhead among the

nodes in the jammed area, which might be unfeasible under heavy jamming signal from

dense networks. Link layer approaches are useful methods to detect jamming since

the jamming attacks usually disobey the MAC layer protocol, but this requires additional


2.3.3 Network Layer Approaches

There have been a few approaches addressing jamming attacks in the network

layer, and those are related to scheduling of messages transmissions, jammed area

mapping, or the linear programming model. Most of the defenses are focused on the

physical and link layers, so network layer approaches are newly designed and still being


A mapping-based evasion protocol has been introduced by [77]. In this system,

the jammed nodes cooperatively map a jammed region. Jammed nodes that are within

a jammed area transmit multiple blind messages to announce their jammed status to

the mapping nodes that are not in the jammed area, but have jammed neighbors. The

mapping nodes communicate with other mapping nodes to isolate the jammed area

and to identify bridge nodes. The bridge nodes participate in relaying messages around

the jammed area. One deficiency to this approach would be the possibly unnecessarily

large jammed region built against the reactive jamming attack. As a result, parts of

the network might be isolated. This is because many nodes in the exaggeratedly

large jammed region may still be able to transmit without activating the jammers, yet

they are isolated and the message deliveries are interrupted. During the mapping

procedure among the mapping nodes, the protocol requires an excessive number

of communication messages to build a detour route around the jammed region. The

multiple traffic topologies from [62] could be used to evade the jammed nodes under

attack from mobile jammers. The mobile jammers in this paper would be able to identify

the critical broadcasting paths in order to prevent downlink nodes from receiving any

messages. The nodes cooperatively construct the multiple paths and select a path

based on the position of the jammers but, according to the paper, each sensor node

needs to carry some secret and overall routing information before deployment into

the network. This prior network information might not be feasible in dynamic networks

and, due to the locality of sensor nodes, routing information in each node might not

be consistent. In addition, the synchronization problem has to be considered in this

protocol to change the current network topology into a new one. [63] designed a linear

programming model for a specific type of the jamming attack, but it focuses mainly on a

flow-based attack without considering of a protocol-based attack model. Unfortunately,

this might not apply to general jamming attacks. [16] investigate an efficient scheduling

technique for broadcasting messages when under a jamming attack. This approach

shows good performance only when there are power limitation on jammers, which might

not be a practical assumption since usually the jammers are much stronger than the

normal nodes in WSNs.

2.4 Conclusion

Through this investigation of various types of jamming attacks and existing

solutions, we can conclude that, in reactive jamming attacks, the jammers stay idle

until being triggered by messages disseminated within their transmission ranges,

thereby further reducing the jammers' operation overhead and making it difficult to

detect, thus this intelligent attack can be utilized by malicious users in more real-world

scenarios. An efficient defense mechanism against a reactive jamming attack will be

presented through this dissertation.


This chapter will focus on the identification of trigger nodes in a centralized manner,

which can provide a general framework to build an efficient countermeasure for reactive

jamming attacks in multi-channels WSNs. By utilizing traditional group testing (GT)

theory [22, 23] coupling with minimum collection of disjoint disk cover based grouping,

this solution can identify all the trigger nodes with low overhead in terms of running time,

computation and message complexity. The theoretical analysis and experimental results

show that our solution performs well in terms of time and message complexities, which

provides a good approach to defend reactive jamming attacks.

3.1 Network Model and Problem Definition

The WSN in our problem consists of N sensor nodes, each having the same

transmission range r and one base station (BS) with the transmission range p = pr

where 3 > 1. Up to J < N static jammer nodes, whose transmission ranges are

uniformly R = ar where a > 1, are deployed within the network. However, their positions

cannot be known beforehand, except that all jammers are assumed to be sparsely

deployed so that they can jam as large area as possible. Each sensor node or jammer

node is equipped with k channels and m radios (m < k).

We model the considered network as a connected graph G(V, E) where V is a set

of N nodes and E = {(u, v)S6(u, v) < r, u, v e V} representing communication links

between nodes. Any sensor nodes whose broadcasting can trigger some jammers are

called trigger nodes, while any sensor nodes whose communications are interfered by

jammers are called victim nodes. Therefore, any node v is a victim node if 6(J, v) < R

for some jammer node J, whilst w is a trigger node if 6(J, w) < r. Note that trigger

nodes are also victim nodes as the noise range (transmission range of jammers) R is

larger than sensor transmission range.

More importantly, since reactive jammers would keep track of the frequency shifting

sequences or channel selecting mechanisms, excessive exposure of these methods

against reactive jammers might be vulnerable to achieve effective communication

performances among victim nodes.

Since each sensor node has the same transmission range r and only the neighbor

nodes within r can receive its message, the graph G(V, E) is a Unit Disk Graph (UDG).

The objective of the problem is to find out all the trigger nodes within minimum

time and message complexity. After the identification, a new routing path would be

constructed to avoid activating any reactive jammers.

Some notations used throughout this chapter are depicted in Table 3-1.

Table 3-1. Notations
Symbol Meaning
r The transmission range of each sensor
R The noise range of the jammers
p The transmission range of the base station
V The set of nodes in WSN
N The number of nodes in WSN
W The set of victim nodes in WSN
W, The set of left victim nodes in WSN after cover i
n The number of victim nodes in WSN
.N, The number of victim nodes covered in cover i
ni The number of victim nodes before cover i
nj The number of victim nodes in group in cover i
U The set of trigger nodes in WSN
d The number of trigger nodes
d, The number of trigger nodes in group in cover i
k The number of channels in WSN
m The number of radios in WSN
A(G) The maximum node degree of graph G
,(D) The number of nodes disk D covers
6(u, v) The distance between two nodes u and v
H(6) Unit Disk Graph H with disk radius 6
ti The total number of testing rounds in cover i
C The total number of testing covers
T The total testing round

3.2 Preliminaries

In this section, we introduce some preliminaries on MAXIMUM CLIQUE PROBLEM

and NON-ADAPTIVE GROUP TESTING, based on which we discuss how to apply them to

our problem.

3.2.1 Maximum Clique Problem

The Maximum Clique Problem is defined as follows. Given an arbitrary undirected

graph G(V, E), a subgraph G'(V', E') (V' e V) is a clique if all its vertices v' V' are

pairwise adjacent. The maximum clique is a clique with max I V'. The maximum clique

problem is also one of the first problems shown to be NP-complete [9].

So far, the best polynomial-time approximation algorithm for the maximum

clique problem was developed by Boppana and Halldorsson [9], and achieved an

approximation ratio of n('1-o()). In [9], Hastad shows that this is actually the best we can

achieve and it cannot be approximated within a factor that of n1-' for any C > 0. There

are some other results in the literature concerning the approximation of the maximum

clique problem on arbitrary or special graphs [9, 10, 29].

In this chapter, the maximum clique problem is applied to obtain the upper bound of

the number of trigger nodes based on the number of reactive jammers. Since a jammer

can only be activated by the nodes within a certain distance, we can construct a unit

disk graph of all nodes with the radius twice the distance to estimate the upper bound of

the number of trigger nodes.

3.2.2 Non-Adaptive Group Testing

Non-adaptive Group Testing (GT) [22, 23] methods are to minimize the testing

period by sophisticatedly grouping and testing the items in pools simultaneously,

instead of individually testing them. The way of grouping is based on a 0-1 matrix Mt,,

where the matrix rows represent the testing group and the each column refers an item.

M[i,j] = 1 implies that the jth item participates in the ith testing group, and the number
of testing is the number of rows. The result of each group is represented as an outcome

vector with size t where 0 is a negative testing result (no trigger in this testing group)

and 1 is a positive result (some triggers in this testing group). To achieve the minimum

testing length for non-adaptive GT, M is required to be d-disjunct [23], where the union

of any d columns does not contain any other column.

Based on the properties of d-disjunctness, the decoding algorithm to identify the

triggers based on the testing results becomes very simple. We just need to remove all

the items appeared in any negative pools and the remaining item are positive [23]. In

this way, only 0(1) testing rounds and O(tn) decoding time are needed.

To utilize GT for our trigger detection, we need to solve the two most challenging

problems: (1) How to group the nodes to avoid interference between the results

among groups so as to test these groups simultaneously. (Any two groups are called

interference free if any jammers triggered by either group cannot jam the other group).

(2) How to accurately estimate the value of d which is the upper bound of the number of

trigger nodes. Since d determines the number of tests, the tighter d is, the better time

and message complexities we can obtain.

3.3 Centralized Trigger Node Identification (CTNI)

In this section, we devise CTNI algorithm to identify all trigger nodes in WSNs

so that reactive jamming can be avoided when these trigger nodes do not transmit


The basic idea of CTNI is as follows: We first detect all victim nodes WSNs by

using any existing scheme such as existing alarm forwarding scheme [60]. Then we

test these victims to identify the trigger nodes by calling two sub-procedures: 1) We use

the GVN-MCDDC algorithm Group Victim Nodes Based on Minimum Collection

of Disjoint Disk Cover to group as many as victim nodes without interference with

each other in each cover. Each cover includes a set of disjoint disks where the center

of each disk will act as a test outcome collector. Each of the disjoint disks can be tested

simultaneously. 2) For a set of victims in each disjoint disk, we use the DTN-NCGT

algorithm Detection of Trigger Nodes based on Non-adaptive Combinatorial GT

to detect all trigger nodes within these victim nodes. During the group testing process,

the collectors will collect the test outcome and perform the decoding process. We

continue covering and testing victim nodes until all victim nodes are tested. The details

of two major algorithms are elaborated next.

3.3.1 Group Victim Nodes Based on Minimum Collection of Disjoint Disk Covers
(GVN-MCDDC) Algorithm
After identifying all victim nodes, the goal of GVN-MCDDC algorithm is to group

victim nodes so as to simultaneously test as many interference-free victim nodes as

possible. The basic idea of this algorithm is as follows. For each victim node v, construct

two disks Dv and D2 centered at v with radius (R r) and (3R r) respectively. The

objective is to obtain a minimum collection of disjoint disk covers, where each cover

is a set of disjoint disks such that victim nodes within each disjoint disk can be tested

simultaneously without mutual interference. (Any two groups are called interference free

nodes if any jammers triggered by either group cannot jam the other group.) We adopt

a greedy method for this by selecting a node v whose corresponding R r disk covers

the maximal number of victim nodes, and then select another node u similarly after

removing all the nodes within 3R r from v from the graph. Iterate this until no node left

in the graph.

3.3.2 Detection of Trigger Nodes Based on Non-Adaptive Combinatorial Group
Testing (DTN-NCGT) Algorithm

Now, after finding the collection of disjoint disk covers, we start conducting the

group testing for each cover. Notice that for each cover which consists of a set of disjoint

disks, we will conduct the test for each disk simultaneously. For each diskj, i.e., Dv,

in cover i, gather all the victims in this disk into a group Gy for testing based on the

non-adaptive group testing technique. In order to apply this technique, we need to

estimate an upper bound Dy of the number of trigger nodes in each disk as shown from

line 7 to 11 in Algorithm 2. Based on this obtained value Dy, DTN-NCGTconstructs

Algorithm 1 The GVN-MCDDC Algorithm
1: Input: All left victim nodes W,_I after cover / 1
2: Output: The collection of groups in all covers G,1 ..., G 1 < i < C, 1 3: 1
4: while I WI / 0 do
5: > Construct double disks for each victim node
6: for w e W,-_ do
7: Construct D' and D
8: end for
9: k 1
10: ,W <-- 0
11: while I W,-l 0 do
12: Choose w e W;_, to maximize K(Dl)
13: Gik D'
14: W,-_, W,-_ \ D2
15: 2
15: W, -- W, U { D2 \ D }
16: k k + 1
17: end while
18: W -- W
19: end while

a D,-disjunct matrix accordingly. From this matrix, m pools (rows) will be tested at the

same time. The nodes in different rows broadcast the test messages in an orthogonal

way (i.e. on different channels) so that the testing result will not interfere with each

other. Consider the nodes in one group broadcast on the same channel, the jammer

is supposed to be activated and broadcast noise on this channel if some nodes in this

group are trigger nodes. Then the collectors will collect all the testing results in this

disk and start the decoding procedure. Or else, they can transmit the results to base

stations and the decoding procedure will be performed at the base station. During

communication with the base station, the collectors are required to perform channel

surfing method for successful delivery of the outcomes. By decoding these results,

trigger nodes will be identified.

Finally, the complete CTNI algorithm is presented in Algorithm 3.

Consider Figure 3-1 as an example where we have two jammer nodes J1 and J2.

Nodes vl, v2,..., v9 and v15, v16,..., v25 are the victims, and m = 3. According to our

Algorithm 2 The DTN-NCGT Algorithm on Group j in cover /
1: Input: Victim nodes set W, in one group, R, r
2: Output: Number of trigger nodes Dy in this group
3: Construct Gy = (Wy, E-), where E = {(u, v)16(u, v) < 2r, u, v c WVy}
5: > Find the upper bound Dy
6: Dy -- 0
7: for k = 1 to |Jy| do
8: Find the MAXIMUM CLIQUE c(Gy) on graph Gy
9: Gy -- Go \ Uwc(G,) w
10: Dy Dy + Ic(Gy)|
11: end for
12: > Test by using NON-ADAPTIVE GT
13: Construct a Dy-DISJUNCT MATRIX M-
14: Group the column in each row with entity 1 into one group
15: Test these groups simultaneously
16: Decode the testing result to identify all trigger nodes

Algorithm 3 The CTNI Algorithm
1: Input: WSN G(V, E)
2: Output: TNLT Broadcast Tree T
3: W -- The set of victim nodes
4: W, -- The set of left victim nodes from cover / 1
5: Gy <- The group j in cover i
6: U -- The set of trigger nodes
7: U, -- The set of trigger detected in cover i
8: T -- The TNLT broadcast tree
9: W 0, U -- 0, W -- Victim nodes
10: W, -- W
11: = 1
12: while W,I > 0 do
13: Gy -- Groups based on the GVN-MCDDC algorithm in cover i
14: Ui j- trigger nodes based on the DTN-NCGT algorithm
15: U-UU U,
16: i -- i+
17: end while

Figure 3-1. Since item 6 (6th column) is a trigger node (positive item), only the 2nd and
6th groups (rows) return negative outcomes. On the contrary, all other four
groups produce positive outcomes.

algorithm, two disjoint disks will be found and two groups G1 {v1, v2,... v} and

G12 = {v15, v16 ..., v25} are constructed accordingly. Testing will be conducted on these

two groups simultaneously. For simplification, Figure 3-1 just shows the detail testing

of Gil. After the estimation of Dy = 1, our algorithm will construct a 1-disjunct matrix.

Based on this matrix, the first three rows will do a one-hop broadcast message to three


channels accordingly (since we have m = 3 in this example). More specifically, nodes

v1, v2, v3 send a test message on channel 1, nodes v4, v5, v6 send a test message on

channel 2, and v7, v8, v9 send a message on channel 3. v, is a center of this disk and

will act as a collector. As v6 is a trigger, then the test outcome on this row (second row)

is positive. Next, the last three rows will broadcast the test message. After finishing all

rows, v1 will have a outcome vector as shown in Figure 3-1 where the second and sixth

rows have a positive result. Based on a simple decoding method mentioned earlier, we

can easily detect v6 as a trigger node.

3.4 Theoretical Analysis

3.4.1 Estimation of Trigger Node Upper Bound Dy

In order to construct d-disjunct matrix for testing in testing group Gy, we need to

obtain an upper bound on trigger nodes.

We assume that the interference radius is larger than legitimate transmission

radius, R = ar where a > 1 since jammers have more capabilities than normal sensor

nodes. Let J be the set of jammers that trigger node t could activate. We note that

the distances from jammers in J to t are at most r while the distance between any two

jammers must be larger than R = ar. Otherwise jammers will invoke each other and run

out of energy. We have the following lemma:

Lemma 1. Let J be the set of jammers that the trigger t could activate, then |J1 <

Proof. Let 0 be the location of t. Assume that J contains jammers with locations

Ji, J2,..., Jm in clockwise order like in Fig. 3-2, where m = |J|. We have OJ,(=

6(0, Ji)) < r Vi = 1... m and JiJj > R = ar VI < i < j < m.
Since -JOJ,+i 2=7 where Jmr = J1, let J OJi = 3 be the smallest angle, we
have j < 2- and |J| < 2.

Use the cosine's law: R2 < JJ = OJf + OJ2 20JOJ+l cos/3

As jammers will not revoke each other, we have JJ,+l > R > r > max{OJ,, OJi,+}.

Hence, ZJOJ,+ will be the largest angle of the triangle JIOJ,+ We obtain 3 > 2 i.e.

m < 6.

From 3 > 2, OJ2 + Oj2+ 20JOJ,+; cosp obtain the maximum value at

OJ, = OJ,+ = r. Hence, a r2 < r2(2 2 cos ) or / > arccos(1 ) = 2arcsin(2).
Therefor, J = m < 2n(

Following the lemma, we have:

* IJ < 1 when a > 2.

* J < 2 when a > V3.

* J< 3 when a > V2.

* |J < 4 when a >

5 5/

* |J < 5 when a > 1.

*Trigger Node

Figure 3-2. 5 Possible jammers activated by a trigger node t

Theorem 3.1. The upper bound Dy of the number of trigger nodes in one group is

k= 1

where ck(G) is the kth maximum clique on graph G.

Proof. According to LEMMA 1, the nodes in group Gy can trigger at most |Ju| jammers.

Intuitively, we know that a set of trigger nodes to activate the same jammer have a

distance less than 2r. In algorithm 2, we construct a unit disk graph G, = (Wy, Ed) with

disk radius 2r so that the nodes which trigger the same jammer must form a clique in

graph Gy.
In each iteration, according to Algorithm 2, we choose the first jth maximum cliques

and union all these cliques. That is, uJ l ck(Gu) Thus the proof is complete.

3.4.2 Correctness

Lemma 2. Any two nodes with the distance larger than R + r are interference-free


Proof. Assume that any two nodes u and v with distance 6(u, v) > R + r are not

interference-free. Then there exists a jammer J such that J can interfere both u and v.

Without lost of generality, we can assume that node v activates J. Thus 6(v, J) < r.

Plus, 6(v, J) < R and 6(u, J) < R, then 6(u, v) < R r, which contradicts our

assumption. O

Lemma 3. For each set of victim nodes in disk Dv, the center node v can be used as

the collector. That is v can sense the noises from any jammers triggered by any nodes

within the distance R r from v.

Proof. The proof is straightforward. Assume that a center node v in disk Dv cannot

sense the noise from a jammer J, which is activated by a node u in the disk Dv. Then,

we have 6(u, J) < r and 6(v, J) > R. Therefore, 6(u, v) > R r, contradicting to the fact

that u is in D'. O

Theorem 3.2. The CTNI algorithm can correctly identity all trigger nodes.

Proof. Since the jammer noise range R is always larger than normal transmission range

r, the trigger nodes must be included in the victim nodes. Therefore, if we test all victim

nodes, we must be able to identify all trigger nodes. Note that from Lemma 2 and the

fact that each disk Dv has a radius (R r), all the victim nodes in any two different

disjoint disks are interference-free. Thus the testing result is correctly collected. D

3.4.3 Performance Analysis

Lemma 4. Given the UDG H with radius 3R r, denote the maximum node degree in

H as A(H), the total number of rounds (where in each round, we use several disjoint

disks D2, D2, .- centered at node u, v, .. to cover nodes, i.e., contain as many nodes

as possible in their corresponding concentric circles D,, D,, ) needed to cover all the

sensor nodes is at most A(H).

Proof. This is a loose upperbound and can be obtained by considering the disks in

the same round as an MIS (Maximal Independent Set). For the ith round, denote the

maximum node degree of the current graph H as A,, and the set of any center u of the

selected disks D,2 form an MIS of H, then the size of such an MIS is lower bounded by
W1, where I W,I refers to the number of uncovered nodes at the beginning of this round.

Henceforth, the number of nodes covered in the ith round at least equals to the size of

this MIS, i.e. Wl"
Ai 1"
Since the number of uncovered nodes is decreasing round by round, A, is

non-increasing for each round, so straightforwardly at most A(H) + 1 rounds where

A(H) = A1 = maxi A, are needed. O

Lemma 5. The number of testing covers to detect trigger nodes in each group of victim
nodes no is upper bounded by

D' log n0
[min {(2 + o(1)) Iog2 (0 o n,}/m
log (Dy log, ny)

where Do = U Ck 1C(G)

Proof. The best upper-bound of the number of rows for d-disjunct matrix is min{(2 +
o(1)) jo ) n}, using Du's construction [22, 23]. In WSNs, as we defined there
are m radios so that at most m groups can be tested at the same time. According to
THEOREM 3.1, do are bounded by Dy and n. is the number of victim nodes, we complete
the proof.

Corollary 1. The total number of testing rounds in cover C, is upper bounded by

D log n
max[min {(2 o(1)) D02 u nn,}/m]
j log2(DU logn2 )

Theorem 3.3. The total testing round T is upper bounded by
A(H)+1 02 no2
maxFmin {(2 o(l)) '2 n}/m]
SIog(D log12 no)'

where D = Uk Ck c(G)

Proof. According to LEMMA 5 and COROLLARY 1, the covers for all victim nodes are
A(H) + 1 and the testing time for each cover is the maximum testing time among all
groups, that is,
D log nd
maxFmin {(2 o(1)) DJ2 n' n,}/m]
j log2(DU logn2 )
where D. = UJ 1 ck(G) The proof is complete.

Theorem 3.4. The Message Complexity per node w is (2 + o(1)) 0DOnn) -

Proof. In D,-disjunct matrix, the number of messages each node needs to transmit is

the number of 1-entries in the corresponding column. As we mentioned above, Du's

construction method [22, 23] for d-disjunct matrix, has the lowest upper-bound for the

matrix size. It is trivial to find that, each column has exactly s 1-entries in the matrix

constructed in that way, where

(D,- log, n,
s = (2 + o(l)) D092n
log2(D, log2 n,)

hence the message complexity per node is the same. O

We do not consider the false negative from random delay on emitting adversarial

signal from jammers since according to the definition of reactive behavior, the jammers

would only emit interference signals during the legitimate activities on channels.

3.4.4 Random Reactive Jamming Model

Our proposed solutions and analysis are based on a simple reactive jamming

model, of which a jammer will start jamming right away whenever it senses some

transmission activities. However, jammers may adopt a more sophisticated model to

evade the detection by not responding to some messages. This makes identification

approach more challenging due to the inaccurate testing outcomes.

Fortunately, the identification concept proposed in this work is still applicable. Under

this attack scenario, instead of using d-disjunct matrix during the testing procedure, we

will adopt the (d, e)-disjunct matrix, which is a binary matrix so that for any column c,

there exist at least e + 1 rows where c has a 1-entry but none of other d columns has.

There are several studies and results on the construction of such a (d, e)-disjunct matrix

that we can apply [22, 23]. Using (d, e)-disjunct matrix helps to correct at most e errors

in the testing outcomes, thus we are still able to correctly identify all the triggers.

We would like to note that in order to use the mentioned (d, e)-disjunct matrix, we

need to estimate the upper bound of e. In practical network environments under random

reactive jamming attacks, we could estimate this bound by analyzing the Packet Delivery

Ratio (PDR). PDR is a ratio of the number of packets which are successfully validated

through the Cyclic Redundancy Check (CRC) procedure and defined as:


The reactive jammers would be able to drop PDR effectively by the reactive

strategy, however, we could use this ratio against them to bound the unreliable testing

outcomes in the case of random reactive jamming behaviors because Pr(1 PDR)

is the probability of emitting adversarial signal from jammers, and PDR is also one

of well-known probabilistic methods to determine the presence of jamming attacks

by a simple calculation. In order to achieve highly accurate PDR, Strasser et al. [60]

introduced a bit-error identification technique to differentiate jammed packets from errors

caused by weak signal (e.g., because of fast fading or shadowing). Consequently, the

upperbound of errors over tests could be derived from investigation of PDR and sent

from sensors to base station so as to construct error-tolerant disjunct matrix.

3.5 The TNLT-CDS Routing Algorithm

One of the benefits for identifying the trigger nodes is to help construct a routing

protocol which does not activate any reactive jammer. In this section, we discuss a

simple routing algorithm called Trigger Nodes Leaves Tree based on Connected

Dominating Set (TNLT-CDS) which uses trigger nodes as only end receivers. Together

with the CTNI algorithm, TNLT-CDS will complete an efficient countermeasure for

reactive jamming attacks.

We utilize the Connected Dominating Set (CDS) to construct our TNLT-CDS as

CDS has been shown as one of the most efficient methods for constructing a broadcast

protocol. Again, consider network G = (V, E) with U c V as a set of trigger nodes

identified by CTNI. We will construct a directed graph G' = (V, E') by changing all the

undirected edges (u, v) c E where u e V \ U and v c U to the directed edge (u, v).

We then deploy a CDS algorithm in directed graph [64] on G'. It is easy to see that the

obtained CDS S will not consist of any node in U. Finally, we construct a broadcast tree

T by connecting nodes in S to the rest using newly added directed edges.

This simple idea is to show that it is quite easy to implement a routing algorithm

where triggers are as only receivers. Thus, the approach of trigger identification is a very

useful concept in the defense of reactive jamming attacks.

3.6 Performance Evaluation

In this section, we evaluate the efficiency of our design through a series of

simulations in terms of time latency and message complexity for sensor networks

with different parameters. The results of these experiments show that the proposed

solution is timely efficient for identifying trigger nodes and defending reactive jamming


S 400


: : / 300


S \ 200
max node degree A 150
/ # of total rounds T
# of disk cover c
max # of testing rounds per disk t

1 2 3 4 5 6 7 8 9 10 11 0
#ofjammersJ 1 2 3 4 5 6

# of messages M
# of victim nodes d


8 9 10

Figure 3-3. Experimental results by various size of jammers

3.6.1 Simulation Setup

In order to simulate a general sensor network, we randomly distribute a total of N

sensor nodes with one base station and J jammers to a square network field with width

s. As has been mentioned above, the base station, sensor nodes and jammers have

respectively transmission range, p, r and R. In order not to exaggerate the power of the


200 300
160 1 / \ \ 250 ,

120 200
80 max node degree A 150
-6 # of total rounds T # of messages M
60 # of disk covers c
40 max # of testing rounds per disk t 1 # of victim nodes d

\ --------------- 100 --- ---------

0 1 2 3 4 5 6 7 8 9 10 11 50 2 3 4 5 6 7 8 9 10
# of channels m # of channels m

Figure 3-4. Experimental results by various size of channels

140 1/
/ 180
80 max node degree A # of messages M
60 # of total rounds T 12 # of victim nodes d
60 # of disk cover c 100
40 max # of testing rounds per disk t

500 550 600 650 700 750 800 850 900 950 1000 40'
500 600 700 800 900 1000
# of nodes N # of nodes N

Figure 3-5. Experimental results by various size of nodes

base station, we assume p = r in this simulation, while larger p would make this solution

more efficient.

We have in total six benchmarks in the simulations with different input parameter

teams. On one hand, we study the average number of disk covers c in the GVN-MCDDC

algorithm, and the maximum node degree A to validate the bound of c proved in LEMMA

5. On the other hand, we show the overall test length (number of rounds T) analyzed

in THEOREM 3. Moreover, we record the number of victim nodes n and the total volume

140 250,
130 max node degree A
120 # of total rounds T
110 # of disk cover c
100 max # of testing rounds per disk t 200
7 150
50 /
30 100
20 # of messages M
1 0 00 # of v victim nod es d
10 2
0 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 50
width of square network region s (*103) 1500 2000 2500
width of square network region s

Figure 3-6. Experimental results by various network densities

800 8 U

.700 / 00

600 600

500 500

400 400

300 max node degree A 300
# of total rounds T # of messages M
200 # of disk cover c 200 # of victim nodes d
max # of testing rounds per disk t

2 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 020 22 24 26 28
noise range ratio a noise range ratio c

Figure 3-7. Experimental results by various size of a

of communication messages M between the sensors and the base station, to indicate

the message complexity of this method. To investigate the effects of a series of network

parameters, over the efficiency of this solution, we vary the values for the number of

jammers J, number of radios m, number of sensor nodes N, width of the square net-

work region s as well as noise range ratio a, hence the following five paragraphs and

Figure 5.2.1, 3.6, 3.6, 3.6 and 3.6 are the corresponding results and analysis. Note that

for each parameter team, 100 network instances are investigated and the results are


3.6.2 Results and Analysis Performance by the number of jammers J

Figure 5.2.1 (a) and (b) explain our protocol performance based on the various

numbers of jammers J in the network. In this test, we have N = 1000 nodes with

m = 3 radios, on a 1500 x 1500 network field, where J e [1, 10] jammers are randomly

deployed. Our protocol employs a sophisticated technique to perform as many parallel

testing as possible as shown in Algorithm 3, therefore the number of testing rounds, T,

can be stable while the number of jammers J and victim nodes n increase. As shown

in Figure 5.2.1 (a) and (b), T increases a little while n can vary from 50 to 450 when J

increases from 1 to 10.

More specifically, the number of disk covers c and maximum number of testing

rounds per disk t are smaller than 10, where the latter is much smaller than maximum

node degree A. This contributes to dramatically small number of overall rounds T, which

is no larger than 30 and stable for increasing J.

Moreover, since each (R r)-disk in our tests needs only one sensor node to send

the result back to the base station, the message complexity M is also much smaller (less

than 100) than the number of victim nodes n. Note that in individual testing method, M

should be as high as 0(n).

Therefore, our solution can promptly defend a jamming attack with increasing

number of jammers, in terms of time complexity and message complexity. Performance by the number of radios m

During the series of tests within (R r)-disk, we accelerate the overall testing

latencies by employing the multiple radios m since with a given d-disjunct matrix, m

number of rows can be tested simultaneously. The parameters for this simulation are

randomly distributed N=1000 nodes and J=5 jammers in a 1500 x 1500 network area,

where m e [1, 10]. In other words, the number of tests within an (R r)-disk can be

reduced by the factor m, which also shortens the overall test length. As illustrated in

Figure 3.6 (a), the maximum testing rounds per disk decrease as the radio size increase,

which assists to drop the total rounds, T, drastically. Especially, when m=2 from m=1 in

the Figure 3.6 (a), the overall total rounds drop rapidly. In conclusion, we learn that the

radio size can highly benefit the overall test length of our protocol. Performance by the number of nodes N

The number of nodes in the network is one of the critical aspects to consider

a mobile network solution in terms of scalability. For instance, the countermeasure

using DS-CDMA technique suffers from the number of codes for encoding/decoding

messages in each node of the network, since the newly joined nodes trigger the creation

of additional codes for the victorious battle against jammers who try to corrupt the

messages by pilfering the codes. However, the fact that our solution is a disk-based

test approach by exploiting parallel testing relieves the scalability problem fairly, and

the performance shows somehow constant movement where N e [500, 1000] in Figure

3.6(a) and (b). As shown in Figure 3.6(a) and (b), the victim quantity increases obviously

as the number of nodes increases, but the number of messages is quite constant.

Moreover, the total testing rounds increase slowly. This figure shows how our system

efficiently operates when the number of nodes increases from N=500 to N=1000 with

m = 3 and J=5 jammers in a 1500 x 1500 network area. From this evaluation, we

can conclude that our model is also a very suitable security solution for the majority of

sensor networks in various areas. Performance by the density of the network

Now, we show how the protocol we proposed reacts in the various network densities

where the network field size broadens. With the given number of jammers and the

increase of the network field, it is clear that the number of victim nodes decreases

where the system tries to deploy the nodes in order to cover the network field as much

as possible. As we discussed before, due to the fact that our approach is disk-based

classification of the nodes, sparse network would mainly help to reduce the number of

victim nodes, especially A, and then reduce the overall testing rounds as well. Figure

3.6 (a) and (b) shows the various simulation results with the increasing network field size

from 1500 x 1500 to 2500 x 2500 where N=1000 with m = 3 and J=5 jammers. As the

network is sparse, the number of victim nodes decreases as A gets smaller in this figure

as we discussed. Performance by transmission range of the jammers

Now let us consider the interference range of the jammers. Since noise range is

relatively larger than transmission range of sensor nodes, more messages of the sensor

nodes will be jammed, thereby increasing the number of victims nodes. However, the

number of trigger nodes may be kept the same. It implies that JAM [77] locks down the

whole jammed region while our system minimizes the jammed region size by identifying

the smaller number of trigger nodes.

In Figure 3.6(a) and (b), as the a gets larger, the number of victim nodes increases

since a jammer can transmit farther and contaminates more nodes during the activation.

Moreover, more victim nodes requires more testing rounds to cull out the trigger nodes

among them. In our result, the number of rounds rises as a gets larger. However, the

number of rounds is changing very slowly.

3.7 Conclusion

To efficiently tackle reactive jamming attacks in multiple-radio WSNs, we devise a

new mitigation for identifying trigger nodes, whose broadcasting triggers the jammers,

and a routing protocol to switch trigger nodes to receivers so as to keep jammers

idle. By utilizing nonadaptive group testing scheme, disjoint disk cover method, and

clique-based clustering, this countermeasure achieves low overhead in terms of time

and message complexity, thus is practical for general WSNs. Besides the analytical

complexity analysis, we also conduct a series of simulations to investigate the scalability

and stability of this method to various WSNs.

Throughout this chapter, we assume no packet-loss during all the transmissions,

while in real WSNs this is inevitable. In the case that all the broadcasting messages

of one trigger node do not arrive to the jammers nearby, due to the packet-loss, the

test outcomes of the corresponding groups might have error and fail to identify all the

trigger nodes out. Even in this extreme case, our method can also be adapted using

error-tolerant GT techniques [22, 23] discussed in Section 3.4.4.


The centralized approach from previous chapter cannot avoid inevitable burden

of the excessive communication overhead to base station, which can not realize a

prompt recovery system under the severe jamming attack. To this end, this chapter

designs a localized trigger detection scheme which employs two techniques: a hexagon

tiling coloring scheme and a sequential group testing (GT), which efficiently identifies

all trigger nodes without requiring any extra hardware on sensors. Different from our

previous work, this method can be distributedly implemented with a low time and

message complexity. Furthermore, a more sophisticated behavior of reactive jammers

is also investigated where they do not start injecting noise as soon as they sense some

signals. Instead, jammers randomly start jamming with some probability p under this

new model.

4.1 Network Model and Problem Definition

We consider WSNs consisting of n sensors having a uniform transmission radius

r. Thus the WSN can be abstracted as a Unit Disk Graph (UDG) G = (V, E), where V

represents the set of n sensors, and E = {(u, v) d(u, v) < r, u, v e V} representing

communication links between nodes

Up to J < n static reactive jammers at unknown locations, whose transmission

ranges of interference signals are uniformly R = ar where a > 1, are deployed within

networks. Since the basic goal of reactive jamming is to disrupt legitimate packets

with minimum energy cost and maximum stealthy, the damages from the reactive

jammer are limited to specific sensors on specific transmission channels by short

adversarial signals. Due to the fact that most of wireless sensor devices terminate

transmissions as soon as detection of jamming signal through existing detection

methods, it is unnecessary for the reactive jammers to drag down its energy efficiency

by transmitting interference signals for a long time. Moreover, from the standpoint of the

jammer, d(ji,j2) > R should be satisfied for any two jammers ji and j2 J in order to

avoid mutual invocation to each others

Random Reactive Jamming Model: We relax the jamming model and consider

that after sensing some activities, a jammer randomly starts jamming with probability

Any sensor node u e V is said to be a trigger node if there is a jammerj e J, such

that d(u,j) < r. and a sensor node v is said to be a victim node, iff d(v,j) < R.

The objective of the problem is to find out all triggers within minimum time and

message complexity in order not to limit the actual jammed area by transmission range

of R but r.

4.2 Overview and Fundamental Results

In this section, we briefly present an overview of our localized solution along

with some fundamental results that will be used later. Our localized algorithm can be

implemented as a network maintenance service and can be periodically invoked to

identifying all the trigger nodes.

We will use testing to identify these trigger nodes by allowing them to send out

a test message and listen if their is any noise. Especially, [60] proposed a highly

accurate detection scheme of reactive jamming attack, and all interference signals can

be correctly identified as noise by sensors from other external interference even in

lower and unsteady RSS. However, individual testing is too time-consuming, thus we

often test a number of nodes, called group testing (GT). However, testing a group of

nodes simultaneously encounter several difficulties. For example, if some Noise sensed

after performing testing, we may not know which ones in the tested nodes triggered

the jammers. Moreover, scheduling nodes in a testing group to perform the testing

synchronously may result in a lot of communication overhead in the network if tested

nodes are far from each other. In addition, if two group of nodes are testing at the same

time and the jammer triggered by the first group can jam nodes in the second group, the

testing result may be inferred incorrectly. Hence, an efficient grouping and scheduling

mechanism is essential to reduce the overall latency.

We utilize two principles to efficiently reduce the number of testing rounds i.e.

overall latency:

1. If two nodes u, v are at the distance at least R + r they cannot trigger a same
jammer. This enable us to test u, v in a same round without having the outcome of
testing u and that of v interfered each other. In general, we can perform testing in
parallel for two sets of nodes U and V that are R + r far away from each other.

2. If u, v, w are identified triggers, then all nodes inside the triangle whose vertices
are u, v, w are also triggers. Furthermore, if T = {t1 .... tk} is a set of triggers,
then all the nodes inside the convex hull of T are also triggers. This holds as long
as R > 2r.

4.2.1 Overview of Identification Procedure

The overview of trigger identification procedure is depicted as follows: The sets of

nodes are locally divided into hexagonal groups, and each hexagonal group is colored

into disjoint interference-free groups, where the transmission of nodes within a group will

not activate the same jammer whose adversarial signals will disrupt the communications

with other groups. The diameter of each hexagon is small enough so that all nodes in

a same hexagon can communicate with each other directly and hence the latency of

forwarding messages is avoided. These groups are called testing groups in remainder

of this chapter. The set of nodes within testing groups with the same color are then

scheduled to fulfill a sequential GT procedure simultaneously in order to identify all

trigger nodes over each testing group. Notice that all nodes in a network do not need to

exchange additional messages in order to partition themselves into disjoint groups (to be

explained in detail later) and run a sequential GT procedure since the basic premise of

our network systems are loosely synchronized in the order of seconds.

The trigger identification algorithm within each pool use Sequential Group Testing

(SGT) to identify only nodes that belong to the convex hull of the set of triggers that is

often much less than the number of triggers.

In principle, the flow of the identification procedure is: (1) Partition the set of nodes

into hexagonal testing groups; (2) Assign colors to hexagons in order to maximize the

number of disjoint interference-free testing groups and schedule them according to the

colors; (3) Perform sequential group testing within each hexagonal testing group during

the assigned time slot for the each group, in order to discover all trigger nodes.

How to divide the set of nodes into interference-free testing groups and how

to discover all trigger nodes within minimum latency play fatal role in our localized

approach against reactive jamming attack. These will be illustrated along with theoretical

analysis in the following sections.

4.2.2 Hexagon Tiling Coloring

In this section, we propose a hexagon tiling coloring, which is the fundamental part

that will be used later in section 4.3 to locally partition sensor nodes in a given WSN into

a set of testing groups. In order to study the hexagon tiling coloring, we consider the

following new problem:

Definition 1. Hexagon tiling coloring problem: Given a distance d e R+ and

a hexagon tiling H dividing the 2D plane into regular hexagons of sides '. Find the

minimum number of colors needed to color H, such that any two hexagons h, and h2 in

H with same color are at distance greater than d.

The distance between two hexagons hi and h2, denoted as d(hl, h2), is defined as

the Euclidean distance between any two closest points pi and P2, such that pi is located

in hi and P2 is located in h2. This makes the hexagon tiling coloring problem different

from the channel assignment problem [56] in cellular network, where the distance

between two hexagon cells is measured from their centers.

centers of all the hexagons are placed on a triangular lattice. Therefore, we

consider a new coordinate system in the 2D plane, with axes inclined at 600. This

new coordinates system has two units vectors 7 (-, 0) and j (v, 3) as shown in

Figure 4-1. The centers of each hexagon h coincide with the integral coordinates in this

coordinate system. Now, each hexagon h can be identified by the coordinates (i,j) of
its center as h(i,j). The Euclidean distance between two hexagon centers h(i1,jj) and

h(i2,j2) is given as dc(hl, h) = /(i i2)2 +(i 2)(ji J2) + i J2)2
4.2.3 The k2-Coloring Algorithm
We now present our k2-coloring algorithm for the hexagon tiling coloring problem.
For a given distance d c R+, the k2-coloring algorithm uses k2 colors, where k =

3 + 1 to color the entire hexagon tiling and guarantees that any two hexagons
hi, h2 c H with d(hi, h2) < d have different colors. Figure 4-2 shows the coloring pattern
generated by the k2-coloring algorithm for d = 3 and k = 4. The k2-coloring algorithm
is used by the sensor nodes in our proposed localized algorithm to locally identify the
group they belong to.

Algorithm 4 k2-coloring algorithm
Input: Given a hexagon tiling H and a distance d e R+
OutpuColored H
Compute k = + 1]
for all hexagon h(i,j) c H do
Colorh(i,) -- (j mod k)k + (i mod k) + 1
end for

Lemma 6. For a given d c R+, the k2 -coloring algorithm colors the hexagon tiling H,
such that two hexagons hl, h2 c H have different colors if d(hl, h2) < d.

Proof. The lemma can be proved by showing that in the color assignment generated
by the k2-coloring algorithm, for any two hexagons h((i,,jj), h2(i2,j2) e H, the distance
d(hi, h2) will be greater than (k 1) (where k = [2 1).
If h1(i, ji) and h2(i2, j2) are assigned the same color by the k2-coloring algorithm,
then1 (mod k) x k+ i (mod k) + 1 =J (mod k) x k+ i2 (mod k) + 1. This happens iff

i /2 (mod k)

ji j2 (mod k)

(x=-k, y=0) (\3/2) x (k-1) (- 3/2) x (k-1) (x=k, y=0)

(3/2) x (k-l) (,3/2) x (k-l)

(x=O, y=-k) (x=k, y=k)

Figure 4-1. The minimum distance between two nodes with same color

Let x = il /2 and y = j j2. It follows that x and y will be multiple of k. The distance

between the centers of hi(i,ji) and h2(i2,J2) is given by

dc(h, h2) = x2 + xy y2

Consider the following cases:

If |x| > 2k: The distance between the centers of hi and h2: dc(hi, h2) =
( + y)2 X2 > 6(2k)2 > (k 1) + 1. Note that for every hexagon
the distance from a point inside it to its center is at most 1. Hence, the distance
between two hexagons d(hl, h2) will be at least dc(h, h2) 2(1) > -(k 1).

If lyl > 2k: We also obtain the same result as in the case xl > 2k.

If |x| and |y| < 2k: If x = y = k, then the distance between two hexagons
d(hi, h2) will be at least dc(hl, h2)- 2(1) > -k2 1 > (k 1). Otherwise there
are only six left cases of x, y as shown in Figure 4-1. The distance between two
hexagons in all of these cases is exactly -(k 1).
Hence, the lemma is completely proved.

Figure 4-2. The coloring pattern for k = 4

4.3 Localized Trigger Node Identification (LTNI)

As stated above, partitioning all node into testing groups will be done by hexagonal

tiling and coloring scheme and each hexagonal testing groups conduct sequential GT in

order to identify all trigger nodes based on assigned colors. In this section, we will look

into those algorithms in detail.

4.3.1 Partition of Nodes Based on Hexagon Tiling and Coloring

In this section, we discuss the localized partitioning of the sensor nodes into

groups. We consider 2D plane on which the WSN is deployed is partitioned into regular

hexagons forming a hexagon tiling, all the nodes located in the same hexagon form a

testing group. Let Dh be the diameter of a hexagon as follows:

* If 1 < a < 2, then Dh = r

SIf 2 < a<3, then Dh= R 2r

* If a > 3, then Dh = r

In all the above cases, nodes located within the same hexagon will have distance

less than or equal to r. Hence, they can communicate with each other in one hop.

We now discuss a method which a sensor node can use to locally identify the
hexagon it belongs to, thus the group it belongs to. By using Algorithm 4, a node can
identify the color of its hexagon and also the time slot assigned to its group in the
schedule. We consider that a node v c V knows its neighbors N(v) and using some
ad hoc positioning method [48, 49], it can identify its location as (xv, yv) with respect to
some reference node. We consider the sink node s c V in the WSN as the reference
node such that (xs, ys) = (0, 0). Now, we show that if a node v knows its coordinates
(xv, yv) in the Cartesian system then without having the global view of the hexagon tiling,
it can locally compute its coordinates (xh, yh) in new coordinate system on the hexagon
tiling and further, it can identify the hexagon it belongs to. For instance a node v at
coordinates (xv, y,) in the Cartesian coordinates can compute its coordinates (xh, yh) in
the new coordinate system as:

Xh x 3Yv 3Dh (4-1)
tan 2

yh = y sin /- (4-2)
3 2

The coordinates of the hexagon h(i,j) in which node v is located is given as:

y, 3Dh 1
yv / 2 {x (4-3)
i Xv tan -- + 2

J= yvsin 3/ D 1+ (4-4)

Now, using the k2-coloring algorithm and considering d = R + r, k = [(R + r)/3r =

[2(a+1)] (if a < 2 or a > 3) or k = [(R+ r)/ (R-2r) 2(a) ] (if 2 < a < 3), node v
can compute the color of the hexagon it belongs to as:

ColorH(i,) -- (j mod k)k + (i mod k) + 1 (4-5)

In order to show the correctness of our method, we prove the following lemmas:

Lemma 7. When a > 2, all trigger nodes located in a hexagon h trigger a single
common jammer.

Proof. Assume that there exists a hexagon h which has two trigger nodes vtl and
Vt2 triggering two different jammers ji and j2, respectively. Now, when 2 < a < 3,
Dh = R 2r, then max{d(vtl, vt2)} = R 2r and max{d(vtl,J1)} = max{d(vt2,2)} = r,
hence, in this case max{d(ji,j2)} = R, which is a contradiction as d(jj2) > R. Similarly,
when a > 3, Dh = r, max{d(vtl, vt2)} = max{d(vtl,l)} = max{d(vt2,2)} = r, hence,
max{d(j1,j2)} = 3r which is again a contradiction. O

Lemma 8. A node v located in a hexagon hi cannot be affected by the Noise injected
by a jammerj invoked by a trigger nodes vt located in another hexagon h2, where
d(hi, h2) > R + r.

Proof. Assume that the Noise injected by the jammerj affects node v, then d(j, v) < R
and as max{d(v,j)} = r, so max{d(vt, v)} = R + r, but as d(hl, h2) > R +r, so
d(vt, v) > R + r, which is a contradiction. O

Lemma 9. Given d = (R + r), the number of colors c use by Algorithm 4 to color the
entire hexagon tiling is:

( +a 1) + 1), when Dh r.

1) 2, when Dh = R- 2r.
Proof. In general, if a hexagon tiling H has hexagons of diameter Dh, then considering
a distance d c R+ the k2-coloring algorithm needs 2d + l colors, hence, it is
straightforward to show that when :

* D = rand d = R+ r = (a + )r,
k2-coloring algorithm needs c = (a + 1) + 1 colors

Dh = R- 2r= (a- 2)rand d= R + r = (a + )r,
k2-coloring algorithm needs c = 2(_-2 + 1)1] colors
73= (a -12

4.3.2 Trigger Nodes Detection Procedure

This subsection illustrates how to resort to sequential GT and convexity of trigger

nodes so as to identify all trigger nodes with minimum testing latency in each hexagonal

testing group. For each node i of hexagonal testing group of colorj, we devised

the SGT-LTNI algorithm (Sequential Group Testing based Localized Trigger Node

Identification) to detect all trigger nodes while all testing groups in the same color can be

tested simultaneously.

It is reasonable to set each testing round with a predefined constant time slot since

each hexagonal testing groups with the same color conduct sequential GT procedure

at the same time, and no new testing round would start until activated jammers turn

themselves into listening mode. As mentioned, we consider that our network systems

are loosely synchronized in the order of seconds.

As stated in Lemma 7, based on the constraint on distance between any two

jammers ji and j2, d(ji,j2) > R in order to avoid mutual invocation between them, we

proved that only one jammer can be activated by nodes within a hexagon.

Reactive Jamming Model Sequential group testing based localized trigger node identification
(SGT-LTNI) algorithm

In SGT-LTNI algorithm, by using SGT, all trigger nodes can be identified in

O(| CTI log A) where CT is the convex hull of the set of trigger nodes within a hexagon
(see Figure 4-3) and A is the maximum degree of all nodes in the network, hence, there

are no more than A + 1 nodes within a hexagon.

We use a method named Quick Identification in order to reduce the number of

testing rounds. According to Lemma 7, all triggers within a hexagon activate a same

jammer. Thus, a node is a trigger iff it belongs to the intersection of the hexagon with

the disk of radius r whose center is the jammer. The convexity of the intersection area

guarantee that all nodes within a triangle constructed by three identified trigger nodes

are also trigger nodes. In general, all nodes inside the convex hull formed by identified

trigger nodes v1, ..., vk are trigger nodes as well without further testing.

The complete SGT-LTNI algorithm is introduced in Algorithm 5. In every step, T

denotes the set of identified triggers, U denotes the set of unidentified nodes. We use

ISTN algorithm (presented shortly after) to find among U a single trigger vt that has the

maximum distance to the temporary convex hull of T. We show later that vt must belong

to the the (final) convex hull CT of all triggers inside the hexagon.

We safely eliminate all nodes whose distances from the convex hull of T are larger

than that of vt. We also use Quick Identification to include all triggers inside the new

convex hull of T u {vt}. The algorithm terminates when all nodes within each hexagon

are classified into either triggers or non-triggers. Identification of a single trigger node (ISTN) algorithm

The localized ISTN algorithm for identifying one trigger node with maximum 'index'

among an ordered set U is illustrated in Algorithm 6. The algorithm works in a same

manner with binary search algorithm as it sequentially divides the set into two halves.

However, it always tests for the presence of the triggers in the right half first so that if

there exist triggers among U, the one with the maximum index (the rightmost trigger) will

be returned. ISTN terminates as soon as one trigger node is identified.

Clearly, each identification of a trigger node among a set U of nodes by ISTN takes

at most log2,( U) rounds.

Random Reactive Jamming Model: In case of jammer randomly reacts with

probability p, we propose a simple and effective algorithm to identify triggers in

Algorithm 7. A set of nodes are identified as non-triggers only if after f testing rounds,

no Noise is sensed.

We first reveal if there are triggers within the hexagon as in lines 5 to 15. If it is the

case, further individual tests are performed to identify whether nodes are triggers.

Algorithm 5 SGT-LTNI Algorithm
1: INPUT: A set U of sensor nodes inside a hexagon
2: OUTPUT: Set of triggers T in U.
3: All nodes in a group Nh synchronously performs the following to identify all trigger
4: /* Check for the presence of triggers inside the hexagon */
5: All nodes in U transmit TEST1 packet in test time
6: if No Noise exists after test + then
7: Return T = 0 and exit
8: end if
9: T-0
10: /* Find the first trigger */
11: vo -- ISTN(ConvexHull(U))
12: U -U\ vo, T vo}
13: while U / 0 do
14: for vi U do
15: dT(vi) = Minimum distance from vi to the exterior of the ConvexHull(T)
16: end for
17: Sort U = {v ,..., vlu\} so that dT(vl) < ... < dT(VUI)
18: Find vt -- ISTN(U) or return T if no such trigger exists
19: U -- U \ {Vt,..., viul} /*Quick Elimination */
20: T TU {vt
21: T T U { nodes inside ConvexHull(T)} /* Quick Identification*/
22: U- U\ T
23: end while
24: return T

4.4 Theoretical Analysis

4.4.1 Upperbound on Testing Rounds

Lemma 10. Trigger identification ends as soon as all triggers in the convex hull CT are


Proof. All other triggers are also detected following Quick Identification. One more round

of group testing for all the remain nodes will show there are no more triggers among

them. D

Theorem 4.1. Algorithm 5 requires no more than O(| CTI log A) number of rounds where

I CTI is the number of vertices on the convex hull of the set of triggers.

Algorithm 6 Identification of A Single Trigger Node Algorithm ISTN based on Sequential
Group Testing
1: INPUT: U {v v, v2..., v}
2: OUTPUT: vk s.t k = max{i I vi is a trigger} or output no triggers.
3: low = 1, high = m
4: while low < hight do
5: mid= [-L(low+ high)]
6: T {Vmid, ... Vhigh}
7: All node in T transmit TESTi packet in test time.
8: if Noise exists after test + time then
9: if (low = high) then
10: Return vlow and exit;
11: else
12: low = mid
13: end if
14: else
15: high = mid 1
16: end if
17: end while
18: return No triggers

o Victim Node
Trigger Node

r ---* --- o

Figure 4-3. Trigger nodes in a hexagon

Proof. The key observation is that in every round of the while loop, the chosen vt by

ISTN will have the maximum distance to the temporary convex hull of the identified

triggers (since the nodes in U are sorted based on the distance to that convex hull).

That point must belong to the convex hull CT. Hence, the algorithm loops for at most

I CT times and requires at most O(| CTI log A) round. O

Algorithm 7 Fault-Tolerance SGT-LTNI Algorithm
1: INPUT: A set U of sensor nodes inside a hexagon, an integer f > 0
2: OUTPUT: Set of triggers T in U.
3: All nodes in a group Nh synchronously performs the following to identify all trigger
4: /* Check for the presence of triggers inside the hexagon */
5: for i = 1...f do
6: All nodes in U transmit TEST1 packet in test time
7: if No Noise exists after test + then
8: if (i k) then
9: Return T = 0 and exit
10: end if
11: else
12: Break
13: end if
14: end for
15: T-- 0
16: /* Individual testing */
17: for all x E U do
18: for i = l...k do
19: Let x transmit TESTi packet in test time and listen
20: if Noise exists no later than test + r then
21: T-- TU {x}
22: T T U { nodes inside ConvexHull(T)} /* Quick Identification*/
23: Break
24: end if
25: end for
26: end for
27: return T

Since, we can perform testing for all hexagons of same color at the same time, the

total number of rounds to identify all triggers in the network will be c x (max{ct} log A 1)

where c is the number of colors in Lemma 9 and max{ct} is the maximum size of

convex hull of a set of triggers within a hexagon. Although max{ct} may go up to A, the

algorithm's performance is often far better than its worst case.

4.4.2 Message Complexity

Theorem 4.2. The message complexity of algorithm 5 is O(TA) where T is the number

of testing round.

Proof. According to our assumption above, since jammers are activated upon receiving

a testing message from trigger nodes, the messages required for identification

procedure are closely related to testing rounds. Due to the fact that every node within

a hexagon does not required additional communication messages except testing

messages during running Algorithm 5 the number of testing messages within a

hexagonal testing group cannot be more than A in each testing round. The observation

underlies on the fact that the maximum diameter of a hexagon is at most r from the

Section 4.3. Considering the case that all trigger nodes consist of convex hull within a

hexagon, each iteration of testing round will identify at least a trigger node. Hence, the

message complexity of algorithm 5 is at most O(TA). D

4.4.3 Random Reactive Jamming Model

If triggers are only jammed with probability 1/2 < p < 1, then instead of stopping

checking for presence of jammers when no Noise sensed, nodes keep testing up to a

maximum number of f times.

Since we need at most f rounds to check if a hexagon contains any triggers and

at most f(A + 1) rounds for individual testing. The total number of rounds for finding

triggers in the network is at most cf(A + 2) where c is the number of colors and f is a

predefined parameter.

We calculate the expected number of identified triggers within a hexagon. Let d > 0

be the number of triggers within a hexagon (we ignore the hexagons without triggers

inside). The probability that some Noise sensed by f testing rounds in lines 5 to 14 in

Algorithm 7 is 1 (1 p)f. The probability that a trigger nodes is correctly identified is

also 1 (1 p)f (lines 17 to 25). Hence, the expected number of identified triggers will

be (1 (1 p)f)(l (1 p)f)d > (1 2(1 p)f)d.

To obtain an expected false-negative rate c i.e. the fraction of triggers that are

incorrectly classified as non-triggers, we need to set f = l[ogl_-p /2]. For example, if

p = 3/4 and the desired false-negative rate c = 0.01 i.e. 1%, we need f = 4. Note that

we only have false-negative but not false-positive (non-triggers that are classified as


Algorithm 7 also works for Reactive Jamming Model. Simply, setting p = 1, f = 1

we have an algorithm with the number of rounds is at most c(A + 2). Clearly, the number

of rounds does not depends on the size of network (the number of sensor nodes) but on

the ratio a = R/r and the maximum degree that is often decided by the density of the

network. Hence, the proposed algorithm is scalable for networks of arbitrary size.

4.5 The TNLT-CDS Routing Algorithm

One of the most important benefits from our decentralized identification procedure

is efficient minimization of the damage against reactive jammers by converting trigger

nodes into receivers only. By facilitating the shifting procedure, a routing protocol could

be constructed in order to avoid the activation of any reactive jammers. In this section,

we propose a simple routing algorithm called Trigger Nodes Leaves Tree based on

Connected Dominating Set (TNLT-CDS). TNLT-CDS will neutralize reactive jamming

attack as an effective countermeasure.

4.6 Performance Evaluation

In this section, an intensive series of simulations has been performed so as to

validate the theoretical results and to verify effectiveness of the Localized Trigger Node

Identification (LTNI) algorithm against a practical reactive jamming model in general

WSNs. In detail, LTNI solution is split into two types of approaches by Sequential

Group Testing based LTNI (SGT-LTNI) and Individual Testing based LTNI (IT-LTNI),

and comparison of both schemes will be illustrated to show effectiveness of GT in this

section. The performance of the LTNI algorithm against reactive jamming attack is

assessed and compared to the performance of JAM [77] approach in terms of latency,

message overhead and size of jammed regions (quarantine area) as well.

The purpose of these simulations is to validate our approach in various network

environments via different team of parameters in network density, quantity of jammers

and transmission ratio between jammers and sensors. In addition, the default set of

parameters is that n = 3000 nodes and J = 3 jammers are randomly planted using the

pseudo-uniform distribution in a square area of size 1000m x 1000m where transmission

range r = 20m and a = R = 3. To investigate the performance of our scheme, the
nodes are varied from n = 1000 to n = 5000 in order to be subjected density of network,

at most J = 10 jammers are placed for various size of jammers, and the transmission

range of a jammer is varied from a = R = 2.5 to a = = 8.
r r
Experimental implementation of these simulations do not consider packet losses,

link-congestion or MAC mis-behavior except jamming signals in order to evaluate the

identification performance only. Since we ran the simulations for each setup 100 times

and averaged the results, the results suffice to reflect the efficiency of LTNI algorithms.

We modeled the practical networks to validate our algorithm against reactive

jammers, one implementation of the reactive jammers, by utilizing ZigBee protocol.

A wide range of experiments was conducted based on simple ZigBee protocol using

Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) channel access

mechanism. Request To Send (RTS) of size 30 bytes and Clear To Send (CTS) of

size 30 bytes are implemented in these experiments. The processing time for any

type of messages is uniformly 10ms since sensors have limited resource to generate

communication messages, and the propagation speed is 3 x 108 m/s in both algorithms,

JAM and LTNI. To communicate with others, every node needs to send at least three

messages, a pair of RTS/CTS and a data message and wait the predefined intervals

between those messages, 20ms in these experiments in order to simulate practical

WSNs. We also assume that the size of a communication message is bigger than 2347

bytes, so that RTS/CTS should be sent before legitimate communications begin. By

implementing a real protocol ZigBee, we could report more reliable evaluation of our

algorithm based on that.

250 SGT-LTNI --
IT-LTNI ------
o 200



1000 1500 2000 2500 3000 3500 4000 4500 5000
# of nodes

IT-LTNI ------

1 2 3 4 5 6 7 8 9 10
# of jammers

IT-LTNI ----
.......... J A ..:::::::: :::..................................

3 4 5 6 7 8

Figure 4-4. Rounds by various parameters

4.6.1 Testing Rounds T

First of all, the number of testing rounds was measured for a variable size of nodes

where n c [1000, 5000] in Figure 4.6 (a), which directly reflects the latency of SGT-LTNI

algorithms due to the predefined length of a testing round. As shown in Figure 4.6

(a), the testing rounds required to complete the identification of all trigger nodes grow

steadily, compared to the incremental size of sensors in denser networks. During the

nodes in increments from 1000 until 5000, the testing rounds gradually ascend only

around 120 additional rounds in SGT-LTNI, but IT-LTNI tests at most 150 additional

rounds to detect all trigger nodes. That is, the design of SGT-LTNI algorithm with Quick

2 IT-LTNI ---- ...
JAM .......... .. ...
1.8 ... """"

1000 1500 2000 2500 3000 3500 4000 4500 5000
# of nodes

IT-LTNI I ----- -... .
JAM .... .-

1 2 3 4 5 6 7 8 9 10
# of jammers

3 4 5 6 7 8

Figure 4-5. Messages by various parameters

Identification and Quick Elimination in order to identify all trigger nodes only on convex

hull of each hexagon produces a great benefit over the time complexity.

Then, the impact to LTNI algorithms from different quantity of jammers are depicted

through Figure 4.6 (b) so as to show the effectiveness of our localized scheme in

massive jamming disruption. Since r = 20 and a = = 3 with J c [1, 10] are sufficient

conditions to investigate massive jamming attack over n = 3000 in WSNs, no additional

jammers beyond J = 10 is simulated. As jammers swell up to 10 times of initial size,

just 130 supplementary testing rounds take place in SGT-LTNI. Consequently, even with

massive impact scenario from large number of jammers against WSNs, the localized

identification algorithm produces great robustness and feasibility on practical systems.

IT-LTNI -----......
, ........ ..- **J A M '"""";""": ::" '

14000 SGT-LTNI 25000 SGT-LTNI-
IT-LTNI ------ IT-LTNI -
12000 JAM ............ 20000 JAM .......
S 8000 15000
6000 10000
4000 ..
20 5000 --- i:
0 0
1000 1500 2000 2500 3000 3500 4000 4500 5000 1 2 3 4 5 6 7 8 9 10
# of nodes # of jammers

25000 IT-LTNI ------
JAM ............
2 20000
5000... ...............
5000 .. .....

3 4 5 6 7 8

Figure 4-6. Runtime by various parameters

Finally, the testing rounds shows diversity due to the distance among interference-free

testing groups according to the size of a = R, while parameter a value bigger than 8

would be impractical scenarios. As indicated by Figure 4-1, disjoint interference-free

testing groups have to be far away at least R + r, therefore the distance between parallel

testing groups is tightly related to the number of colors. Due to the fact that bigger a

results in more colors with smaller number of interference-free testing groups, Figure 4.6

(c) discloses increasing trends of tests in both LTNI algorithms.

4.6.2 Message complexity

The volume of messages for total identification of trigger nodes is related to energy

consumption in resource limited sensor networks, which implies that less messages

180 1 1 1
160 SGT-LTNI --- .
160 JAM ... .. .........
100 1 2 2
80 .,.-."
60 ...... '
40 ..-""
1000 1500 2000 2500 3000 3500 4000 4500 5000
# of nodes

U) _________
CU JAM ............
S 400

U 300

0 200 .......


# 0

300 JAM ............

1 2 3 4 5 6 7 8 9 10
# of jammers

3 4 5 6 7 8

Figure 4-7. Nodes in quarantine areas by various parameters

result in longer network lifetime generally. The graphs in Figure 4.6 plot the numbers of

messages per node from three solutions, JAM, IT-LTNI and SGT-LTNI so as to report

comparative message complexity.

Figure 4.6 (a) provides the performance comparison of three approaches in

terms of messages per node when changing the network density. The messages

from JAM solution are higher than those from both LTNI schemes. In addition, Figure

4.6 (a) shows the superiority of message complexity in LTNI approaches over that in

JAM increases as more nodes are placed in networks. The graph explains that 40%

more messages are required to construct jammed areas in JAM where n = 1000,

however, around 47% less messages suffice to complete the classification of all trigger






100 3500
P = 0.6 '.a.................- P = 0.6 (Ind T) ................
10P = 0.7 -------- 3000 P = 0.7 (Ind T) -------
S 10 P = 0.8 ---- P = 0.8 (Ind T) ------
S. 0.9 2500 P = 0.9 (Ind T) .........
S 1 P = 1.0 (Ind T) ---
0.1 2 .. 000 --..
5 1500 .,-..-"."" ...... ..
0.01 .
L 0.001 500 .-
0.0001 0
1 2 3 4 5 6 1000 1500 2000 2500 3000 3500 4000 4500 5000
# of itertion # of nods

Figure 4-8. The number of rounds T in random reactive jamming model with different
values of jamming probability P.

nodes from SGT-LTNI in total where n = 5000. A part from the number of messages

between two approaches, JAM solution demands inevitably more energy than SGT-LTNI

does since JAM protocol has a couple of different types of communication messages

including BUILD and PROBE messages except blind message JAMMED in order to

quarantine jammed regions, but SGT-LTNI necessitates mainly small size of testing

messages to invoke jammers during identification of all trigger nodes.

In summary, our localized algorithm is promising approach to apply in practical

networks with affordable message complexity and energy consumption.

Simulations were also carried out to compare the performance of all three

approaches during increasing the number of attackers (jammers) as well as to see

how this affects their performances. As revealed in Figure 4.6 (b), both LTNI algorithms

significantly outperform JAM approach. Especially, the number of messages from LTNI

algorithms is 32 percent less than that of JAM where a single jammer J = 1, and LTNI

schemes require 45 percent less than JAM does where J = 10. In addition, When size

of jammers is greater than 7, the numbers of messages per nodes obtained from three

approaches keep constant trend, since the jammers covered most of nodes in networks.

However, when jammers are less than 7, JAM algorithm shows more rapid increasing

trend of curve than LTNI algorithms.

According to various size of a, comparison of messages per node obtained from

IT-LTNI and SGT-LTNI explain clear improvement over JAM solution. Due to the fact

that the message complexity of JAM is considerably dominated by the size of nodes

in jammed areas and neighbors of them which need to communicate with others to

set up perimeters around the jammed areas, increasing messages from bigger size of

adversarial transmission range, larger a, are straight forward. However, importantly,

the size of areas with only trigger nodes has nothing to do with a in our approaches,

which helps to maintain constant volume of messages. Figure 4.6 (c) shows the

messages per node required to complete three algorithms and not only more messages

in JAM than in LTNI algorithms but also growing size of messages per nodes in JAM

approach. Consequently, even in severe widespread reactive jamming against WSNs,

our identification approach validates great robustness and practicality.

4.6.3 Runtime

The evaluation of runtime indicates the feasibility of our localized mechanism

in various network environments. This observation underlies on the fact that in the

research of network security, the prompt recovery is one of key issues to study since

it could help to reduce the damage from attacks, so as to maintain stable throughput

of networks. In addition, immediate recovery help to keep longer network life time in

inherently resource-constraint and battery-limited WSNs as well.

Due to the concept of GT, the runtimes of both LTNI schemes are closely dependent

on the number of rounds and the size of nodes within hexagons containing trigger nodes

since all the hexagons with trigger nodes require further testing until completion of the

identification. However, since a hexagon tiling coloring scheme enables to perform

as many parallel testing as possible by utilizing the color assignment generated by

k2-coloring algorithm in section 4.2.2, the overall runtime for complete identification of all

trigger nodes does not drastically grow with the size of jammers or nodes.

In Figure 4.6 (a), during the increments of nodes from n = 1000 to n = 5000,

our approach delayed only 2 seconds to achieve the total identification of trigger

nodes, whereas, JAM takes 7 times as long time as LTNI algorithms do. That is, our

identification schemes introduce outperformance on scalability over the JAM. As

expected, the runtimes obtained from both LTNI algorithms shows similar increasing

trend of curves.

Figure 4.6 (b) compares the runtime based on various size of jammers with fixed

number of nodes, and SGT-LTNI is the best. Particularly, the runtime of SGT-LTNI is

slightly better than IT-LTNI, and the gap between JAM and LTNI approaches get bigger

when jammers increase.

As described before, bigger a = with fixed number of jammers J = 3 results in
smaller number of interference-free testing groups, which implies less parallelism on

identification consequently. Figure 4.6 (c) plots the time of quarantine procedures, and

due to the bigger impact of jammers from bigger a, JAM algorithm requires considerably

longer time to quarantine jammed regions when increasing a. In particular, SGT-LTNI

and IT-LTNI shows increasing trend of curves as a growing. Considering the runtime of

JAM approach this verification time of identification trigger nodes in LTNI algorithms

is quite reasonable. For example, JAM demands 30 seconds to block jammed regions,

but SGT-LTNI completes the identification of trigger nodes within only 15 seconds where

a = 8. In addition, IT-LTNI also shows good performance, but higher than SGT-LTNI


Consequently, overall length of runtime depends on the size of nodes in jammed

regions, however, hexagon tiling coloring scheme helps to keep small increments of

runtime by maximizing parallel testing.

4.6.4 The number of nodes in quarantine areas

After constructing a jamming-resistant routing path by shifting all identified trigger

nodes into receivers, there might be unreachable trigger nodes which are placed too

deep to be reached by communication messages. The volume of unreachable trigger

nodes could be compared to the number of jammed nodes from JAM algorithm so as

to determine the actual size of quarantine areas. The meaning of unreachable trigger

nodes in SGT-LTNI solution is the same to the jammed nodes in JAM algorithm, since

the jammed nodes would not able to receive any messages according to [77], and

unreachable trigger nodes also cannot receive any message either.

In Figure 4.6, the size of unreachable trigger nodes is always substantially less then

the size of jammed nodes from JAM algorithm. Especially, in Figure 4.6 (a) only less

than couple of nodes are unreachable trigger nodes and would not be able to receive

messages where n c [1000, 5000], but jammed nodes get significantly larger as higher

network density.

In Figure 4.6 (b), as predicted, the number of unreachable trigger nodes keep

small number, less than 10, even in 10 jammers, but jammed nodes sprout with higher

population from more jammers in WSNs.

With fixed number of jammers and sensor nodes, larger size of a results in bigger

impact against WSNs, which implies that more jammed nodes in JAM algorithm.

Yet, importantly, our identification approaches will not get affected from a in terms of

unreachable trigger nodes. That is, by utilizing the successful identification of all trigger

nodes, actual jammed areas in which no node would be able to send out any messages

to avoid reactive jamming signal would be very small, so that significantly more nodes

would be participated in secure communications than JAM algorithm does.

4.6.5 Random reactive jammers

Here the reactive jammers might adopt random responding strategy in order

to achieve high stealthy by not jamming some on-going legitimate communication

messages, which makes identification scheme more challenging due to the inaccurate

testing outcomes. For this possible attack scenario duplicated testing can be

performed to drop the error rate and our scheme still shows robustness against random

reactive jamming attack.

We shown in Figure 4.6 the false-negative rate of the Algorithm 7 in a log scale

(Recall that we do not have false-positive). The false-negative rate linearly decreases

in the log-scale i.e. exponentially decreases when the number of duplicated testing f

increases. Even with the p = 0.6, the false-negative rate quickly decreases to 1% with

f = 6. That is, we only need to repeat the test for 6 times.

When we fix the targeted false-negative rate to be 1%, the number of rounds

required is shown in Figure 4.6. The number of rounds increases slightly together with

the number of nodes in the network since putting more nodes in a same fixed area rise

the density i.e. degree of nodes. However, the rate of increase comes closer to zero

when n = 5000.

4.7 Conclusion

In this chapter, we devise a novel localized algorithm to efficiently tackle reactive

jamming attack problem in WSN by identifying trigger nodes. Our local identification

of all trigger nodes achieves high feasibility with low overhead in terms of time and

message complexity by leveraging sequential GT and hexagon tiling scheme. We

propose the hexagon tiling coloring to exploit the available spacial parallelism to test the

WSN for identifying trigger nodes. Based on the color assignment, all testing groups are

scheduled to conduct the localized trigger node detection algorithm using the sequential

GT Besides the analytical complexity analysis, an intensive series of experiments has

shown an outstanding performance of our solution on various WSN settings in terms of

scalability and stability. Furthermore, investigation on more stealthy and energy efficient

jamming model with simulations indicates robustness and potential of our scheme as


By embedding identifying the location of jammers based on identified trigger nodes,

improved countermeasure for more robust WSNs could be realized since elimination of

attackers is inevitably the best way to maintain the soundness of WSNs.


In this chapter, we study the following new problem, called Dominating Tree (DT),

defined as follows. Given an undirected weighted graph G = (V, E, w) representing

a wireless sensor network, where V is the set of the nodes in the network, E is the set

of all communication links in the network, and w is a non-negative weight assigned on

each edge e = (u, v). We wish to find a Dominating Tree T of G with the minimum

weight such that each node in V is either in T or has at least one neighbor in T. The

weight of T is defined as the sum of all edge weights in T.

5.1 Overview of Dominating Tree

The DT problem has several applications in network design and network routing.

For example, multicasting involves the distribution of same data from a central sever

to several nodes in the network. Under this setting, we can consider the edge weight

as the energy consumption to send a message along that edge. Thus the problem

becomes to choose a set of edges (or communication links) of minimum weight for the

sever to route the data, which is exactly the DT problem. Since all nodes are at most

one hop away from the tree, a message can be first forwarded to the closest node in

tree. Then the message can be routed within the DT until it reaches to its destination.

In addition, using DT as the routing backbone can help reduce the message overhead


However, no non-trivial approximation algorithm and its hardness were known for

the DT problem. From a practical view of energy in WSNs, since the sensor nodes

usually have no plug-in power, we have to conserve power so that each sensor node

can operate for a longer period of time. Many solutions for constructing a routing

backbone with minimum energy consumption have been proposed, including the

connected dominating set [66]. However, this problem only considers the size of the set

obtained, not the weight of edges. In other words, the weight is only associated with

each node in these approaches, not with edges where the energy consumption at each

link in the communication directly effects the energy consumption of routing.

In the theory community, there are some work [6, 72] studying the tree cover

problem which is defined as a connected edge dominating set with total minimum edge

weights. Arkin et al. first solved this problem in [6]. Later, in [71], this problem can be

approximated within a factor of 3 + c. In [72], the author presented a fast combinatorial

2-approximation algorithm for the tree cover problem. In contrast to the above work,

DT is defined as node dominating sets, not edge dominating sets. Usually, DT always

produces a smaller number of links and weight than tree cover, and it is more difficult

than tree cover problem.

5.2 Hardness and Approximation

In this section, we will show that DT is NP-complete and it is inapproximated within

(1 c) In I V1. Due to the reduction on the proof of NP-completeness preserving the

approximation gap, we only show the reduction in the proof of inapproximability. We then

present an approximation framework for the DT problem.

5.2.1 Inapproximability

Theorem 5.1. The DTproblem is inapproximable within (1 ) In IVI for any e > 0,

unless NP c DTIME(I Vlog log IV) in general graphs.

Proof. We will show an approximation ratio preserving reduction from weighted

dominating set (WDS) problem to DT WDS asks for the subset of vertices with the

minimum weight such that all nodes are dominated. In [25], WDS is shown to be

inapproximable within (1 c) In V for any e > 0, unless NP c DTIME(I V0lg log IV).

Given an instance of WDS, that is, a graph G = (V, E, w) and a weight function

w : V Z+, the problem is to find a minimum weight subset of nodes that dominates all

other nodes. We will construct a DT instance G' = (V',E',w') as follows. For each node

vi e V, we introduce two new nodes x, and y, shown as gray nodes and black nodes

in Figure 5-1B. Let X = {x,} and Y = {yi}. Let V' = V u X u Y. The set E' and w'

are constructed as follows. For all nodes in V, the edges are kept the same. For each
edge (vi, vj), let w'(v, vj) = M, where M is a very large number, for instance, we can

set M > I VI leE w(e). For all nodes in Y, we introduce a spanning tree on all nodes
in Y = {yi,..., yn} with the weight 0 of all spanning edges between yi. For each pair

(vi, yi), we create a new edge with weight w'(v,, yi) = w(vi). And finally, to connect the
layer V to X, for each node vi e V, we create a new edge (vi, xi) with weight M and
edges (vi, xj) with weight M if (vi, vj) e E.
Consider a minimum dominating set D e V on G with the minimum weight m,
we will show that G' has a dominating tree T with the minimum weight of m. Consider
the DT T = D u Dy u Ty, where Dy consists of the set of yi if v, e D, Ty e Y is the

nodes spanning all Dy. Since the set D dominates all nodes in X as well, the edges
between X and V will not be selected. Notice that M is much larger than w(vi) and 0,
the edges between vi e V will not be selected in the dominating tree. In addition, the

edges between yi e Y can be arbitrarily selected to form a spanning tree on Dy with no
increasing of the minimum weight. Notice that (vi, yi) has to be selected in T to induce

the tree, thus the weight of T is m.
On the other hand, given DT T of G' with the minimum weight m, we will show that
G has a minimum dominating set D of weight m as well. According to the construction, if
there exists a node x, e X is selected in T, in order to span this node into a tree, at least
one edge with weight M has to be selected. Since we know M is large enough, w.l.o.g,
we know M > Zy,1 w(i) will lead to be solution not optimal any more. By construction,

there exists an edge (vi, xj) if (vi, vj) c E such that the dominating set D c V can not
only dominate all nodes in V but also in X as well. However, in order to dominate the
nodes in Y, the edges between vi and yi have to be selected if vi e D. Thus, there is a
WDS D with weight m as well, which is optimal.
Therefore, DT problem is inapproximable within (1 c) In I VI for any e > 0 unless
NP c DTIME(I Vlo09 og0 V) for general graph. The proof is complete.

Y \ \ w2(1) ,
W3) (3)
W ( 4 ) W( 4

i0 0
W(5) W(5)
W(6) W (6)

Figure 5-1. Reduction from WDS G to DT G'

5.2.2 Approximating Dominating Tree

Before presenting our solution, we first give some basic definitions and lemmas

concerning the partial solutions for the DT problem. Then an approximation framework

is analyzed with the performance ratio of i(i 1)nll' in time O(n3') for any fixed i > 1,

where n is the number of nodes in a given graph.

Definition 1. Directed Steiner Tree (DST): In a directed graph G = (V, E) with weight

associated with each edge, given a root r e V and a set D c V, the Directed Steiner

tree asks us to construct a tree with the minimum weight rooted at r, ensuring that there

is at least a path from the root to each node in the set D.

We will show that the DT problem can be reduced to the DST problem in polynomial

time. And the algorithm for DST can be applied to the DT problem preserving the same

performance ratio. For the DT problem, in the graph G = (V, E, w), we introduce a

dummy vertex v* for each real vertex v e V, then we add the directional edges from all

the neighbors of v (including v itself) to dummy node v*, and we set the weight zero for

all these newly added edges. Also for the original edges, we make the edge bidirectional

and keep the weight the same as the edge in the original graph. In the new directed

graph G'=(V',E',w'), if we pick an arbitrary v e V as a root r, and let all dummy vertices

as terminals, we can obtain a DST rooted at r through existing DST algorithm [12] and

thus we can obtain an DT of G. It is clear that the reduction is completed in linear time.

This reduction is shown as an example in Figure 5-2.

A* B*



E D E* D*

Figure 5-2. An example of reduction from G to G'

Lemma 11. If r is in the optimal DT then the DT introduced by DST will get the same

optimal weight. Also, using the approximation algorithm for DST problem will get the

same approximation ratio for the DT problem.

Proof: Suppose there is an optimal dominating tree DT*, we can make all the

nodes in DT* appear in the DST. Since r is in DT*, for each node in DT, at least

one of its neighbors must be in DT, and for any terminal, we can add a directed edge

from that neighbor to it. And we know that these edges are zero weighted, so the

weight of that DST is w(DT*). Suppose there is an optimal DST ST*, then we have

w(DT*) > w(ST*). Also, for the optimal DST, we can eliminate all these zero weighted

edges. Since all the terminal nodes have a path from r to them, each node will have

at least one of its neighbor appearing in that tree, which means it is a DT So we have

w(ST*) > w(DT*). In conclusion, we have w(DT*) = w(ST*). This in turn implies that

we can get the same performance ratio for the DT problem as we have for the DST


In [12], the authors provided a polylogarithmic approximation for the DST problem in

quasi-polynomial time. Then we have an algorithm to obtain this ratio for the DT problem

as well:

Algorithm 8 Approximation Algorithm for DT
1: INPUT: An undirected weighted general graph G = (V, E, w)
2: OUTPUT: A DT of G
3: Initialize a list to save the DT and its weight
4: Find a vertex u in G with minimum degree
5: Transform G into G' = (V', E', w') by using the transformation technique
6: for each node v that (u, v) c E do
7: Run the DST algorithm [12] in G' and make v as the root r to get a DT
8: Save the DT and its weight in the list
9: end for
10: Return the DT with minimum weight in the list

Algorithm 8 is based on the idea of transforming the DT problem to the DST

problem, and then use the algorithm in [12] to solve DST problem, thus obtaining the

solution for DT Note that after the transformation, we need to find the right root for

applying that algorithm, since the ratio for DST is maintained if and only if r is in the

optimal DT. This can be done by enumerate the neighbors of the node with the minimum

degree, since at least one of the neighbors should be in optimal DT Therefore, from

Lemma 11, we can obtain the same approximation ratio for DT.

Finally, since the terminal nodes in G' are those dummy vertices which have

no outgoing edges, we can simply remove these dummy vertices and those edges

incident to them to obtain a DT By setting i = Ig n, the algorithm will obtain an O(lg2 n)

approximation in quasi-polynomial time which is nO(in)

5.3 Heuristic Algorithm and Analysis

In the previous section, we introduced the approximation framework. However, the

time complexity is quite high, due to that fact that constructing a DST usually results in a

long running time. From this point of view, a heuristic with low time complexity is highly


5.3.1 Algorithm Description

We begin this section by defining the terminologies used in our proposed solution

as follows.

* Leaf edge: An edge is called a leaf edge if it directly connects to a leaf node.

* Active edge: An active edge is a leaf edge which links a leaf node from a
single-node subtree to an internal node without considering its weight.

Inactive edge: This is an edge connecting two subtrees during the construction of
DT. In contrast with active edges, we do consider the weight for this inactive edge.
All inactive edges will be edges of the dominating tree.

The heuristic algorithm (HeurDT) is depicted in Algorithm 9. From the high level, the

algorithm consists of the following main steps:

1. Initialize a tree, where each vertex in a given graph is a separate subtree.

2. Create a sorted list of all edges in G by weights.

3. While all the subtrees are not merged into a tree DT

(a) Remove an edge with minimum weight from the sorted as an inactive edge.
(b) When the edge from the list connects two different subtrees without any

i. Merge them into a subtree by adding the inactive edge to DT.
ii. If new internal nodes converted from leaf nodes during merging subtrees
have some single-node subtree neighbors, then link these internal nodes
with them by active edges so as to maximize the size of leaf nodes in DT.
iii. If the new inactive edge connecting to a node which already has an active
edge incident to it, remove this active edge.

4. Prune all the leaf edges of the resultant DT.

The details of merging two subtrees are shown in Algorithm 10. The only purpose of

active edges is to maximize the number of leaf nodes without considering their weights

due to the fact that the total weight of DT does not include the weights from leaf edges.

Those edges are active since they might need to be removed when the leaf nodes in
active edges have been connected by other inactive edges while merging subtrees.
Note that since we do not consider the weights for these active edges, we only keep
these active edges as the leaf edges in order to prune them later. All other internal
edges must be inactive edges where we do consider the weight during the merging in
their increasing order, thus minimizing the weight of DT.
An example of removing an active edge during the merging is shown in Figure 5-3
which depicts the execution of heuristic algorithm. In the Figure 5-3 (b) and (c), since
leaf node g is a new internal node with single-node subtree i after merging, g links
i together by active edge. However, active edge (i, g) has to be removed when new
inactive connection (c, i) occurs connecting subtree c to i. Because all internal nodes
have to be connected by inactive edges, and if we do not remove active edge (i, g),i will
be internal node with an existing active edge (i, g) and thus increasing the weight of DT.
Inactive edge Active edge C Leaf node ( Internal node
b 8 7 94 8 7 uLinkb ingr e 4nod 7
/ 2 \ 9 \ /4 24 \1 \ internal / 2' \ \
/ 2 / 2 subtree ito new \
(d) 1 \ 14 (e) 211 4 14 (f) 11 A 4 14

7 6 l10 8 6 10 8 1 2 10
h I 2 h 1 2 hk&2_ \1 2
-8- 7-K b8-- c7--d b --8-- 17

SRemove active 2 \

(g) 1 4 14 (h 11 A 4 14 () 4 14

F 8 73 6 10 8 7 6 10 8 110
/\ 1 2\ 5 -3 /T 2 4 1ci 2o 9

Figure 5-3. The execution of HeurDT algorithm

Algorithm 9 Heuristic Algorithm for DT (HeurDT)
Input: Given an undirected weighted general graph G = (V, E, w)
OutputA DT of G
DT-- 0
for each vertex v in a given G do
Initialize a subtree Tsub(v) -- {v} /* Tsub(v) is the subtree which contains v */
end for
Sort all edges in G by weights
while the number of subtree Tsub > 1 do
e = (u, v) -- minimum weight edges from list of sorted edges
if u and v are connected by an active edge then
convert the active edge into inactive edge
else if Tsub(v) == Tsub(u) then
continue /* e creates a circle in DT */
Merge TwoSubtrees(e, DT)
end if
end while
Prune all the leaf edges in resultant DT
Return the DT

5.3.2 Runtime Complexity

Let n be the number of nodes, m be the number of edges, and A be the maximum

degree of G, the runtime of each step is listed as follows:

1. O(n) time to initialize all the nodes.

2. The complexity of Merge Sort algorithm to sort edges by weight in Step 2 is
O(mlog m) [17].

3. In Step 3, for each new internal node u from merging subtrees, all its neighbors
need to be checked to see if there are any subtrees with only one node, which is
O(A) for each edge to process. However, only merging subtrees would be able to
convert leaf nodes into internal nodes, and the total number of merging process
takes place at most O(n). As a result, the overall complexity for Step 3 is O(nA).

4. Pruning all leaf nodes only takes linear time.

From the above analysis, the total running time complexity is dominated by Step 2.

That is, the runtime of this heuristic algorithm is at most O(n2 log n), where the graph is

dense enough (A s O(n) and m e n2).

Algorithm 10 MergeTwoSubtrees(e = (u, v), DT)
Input: (e = (u, v), DT)
if u has only one active link in DT then
Remove the active links from u in DT
Initialize a subtree Tsub(u) -- {u}
end if
if v has only one active link in DT then
Remove the active links from v in DT
Initialize a subtree Tsub(v) -- {v}
end if
Add e = (u, v) to DT as an inactive link /* Merge two different subtrees */
if u == internal and u has at least one inactive link then
for each neighbor node w of N(u) in G do
if I Tub(w)l == 1 then
Add e = (u, w) to DT as an active link
Tsub(u) Tsub(u) U Tsub(w)
end if
end for
end if
if v == internal and v has at least one inactive link then
for each neighbor node w of N(v) in G do
if I Tsub(w) == 1 then
Add e = (v, w) to DT as an active link
Tub(v) Tsub(v) U Tsub(w)
end if
end for
end if
Return DT

5.4 Performance Evaluation

In this section, the simulation experiments were conducted to verify the performance

of the heuristic algorithm against the optimal solution. In addition, it is easy to see that

a minimum spanning tree without leaf (MST-L) of G is also a DT of G, we would like to

compare our proposed heuristic to this simple MST-L solution. To evaluate how good the

DT is in the WSNs setting, instead of randomly assigning a weight w for each edge, we

will consider the energy consumption of each edge during the communication. That is,

we consider a disk graph G = (V, E) where each disk represents a transmission range

of each node. The weight of each edge (u, v) is defined as w(u, v) = Cv- d, where dv is

the Euclidean distance between two nodes, u and v, 7 is predefined value to 2 because

it is a typical value for an unobstructed environment, and Cv is a random constant. n

nodes with transmission range r = 25m are randomly deployed in a predefined area size

of 100m x 100m. n varies from 10 to 17 with increment of 1, and 20 network instances

were investigated for each value of n, and the results were averaged.

IP Optimal -..**..-.. .
HeurAlgo -..
MST-L Algo -- .... --


50 ..... .....

9 10 11 12 13 14 15 16 17 18
# of nodes

A DT Weight

IP Optimal ... .....'
S Heur Algo -
MST-L Algo --.- ....

) 6


0 ----------------------
9 10 11 12 13 14 15 16 17 18
# of nodes

B DT Size



IP Optimal .... .. .....'
0000 HeurAlgo -
MST-L Algo -- --


100 ----- -----

9 10 11 12 13 14 15 16 17 18
# of nodes

C Running Time

Figure 5-4. Simulation results for HeurDT, MST-L and optimal results

First of all, let us present the Integer Programming (IP) formulation of the DT

problem. We will use CPLEX to solve this IP and the optimal result will be compared

with that of our heuristic.

min Y WUvXuv
subject to yu+ yv > 2xv (u, v) E E

Sx < |S 1 ScV
u, vS,(u,v)EE
Xv = Yu- 1 (5-1)
(u,v)EE uEV
SYu > 1 v V
yv E {0, 1} ve V

xuv E {0,1} (u, v) E
1 if vertex v is selected in the optimal solution
yv = (5-2)
0 otherwise

1 if edge (u, v) is selected in the optimal solution
Xuv = (5-3)
0 otherwise

In the above IP Formulation, the first constraint shows the relation between vertices

and edges in optimal solution, that is, for each edge selected in optimal solution, the

end vertices has to be selected; The second and third constraints are similar to the

formulation in MINIMUM SPANNING TREE problem to guarantee that the solution is a

tree; The fourth constraint shows the constraint of the dominating set. Basically, for each

vertex v, at least one of its neighbors or itself has to be selected.

Comparing the Weight. Figure 5-4A illustrates the performance of those three

approaches in terms of the weight of DT. As shown in Figure 5-4A, the DT weights

from HeurDT are very close to the optimal solution, which shows HeurDT performs

extremely well. In particular, the DT weight from HeurDT has at most 8% of additional

weights than the optimal results when n = 15 according to the Figure 5-4A. In addition,

the gap in DT weights between the optimal solution and that of HeurDT does not show

growing trends even with increasing number of nodes in G. For example, DT from

HeurDT has 8% more weights than optimal DT when n = 15. However, only 7% more

weights than optimal weight when n = 17. As expected, the weight from MST-L is

much larger than that of HeurDT. This is due to that fact that HeurDT converts all the

unnecessary edges into leaf edges except the inactive edges connecting subtrees

whereas the typically MST does not consider this.

Comparing the Size. As the number of nodes in DT may also affects the

performance of any routing protocol based on this virtual backbone, we also would

like to compare the performance of these three approaches in term of the DT size. As

shown in Figure 5-4B, the difference in size between optimal size and the DT obtained

by HeurDT is very small. According to the Figure 5-4B, the DT built from HeurDT has

at most 1.2 nodes more than the DT from OptDT in the case of the network instance

with 15 nodes. Significantly, 5-4B indicates that the difference in DT size is not affected

by network size. However, the size of MST-L is much larger than that of HeurDT. It is

very clear to prove that HeurDT maximizing the number of leaves during the merging

can drastically reduce the DT size. As n increases, the difference in size of DT between

MST-L and the HeurDT significantly increases up, such as 33% additional nodes when

n = 4 and 42% more nodes in MST-L when n = 17 than the DT generated by HeurDT

This reveals substantial difference of DT size between them when we take the total

number of nodes in G into consideration.

Comparing the Running Time. Figure 5-4C presents the running time of all

three approaches. As expected, the running time for finding the optimal solution is

extremely high. One more time, it confirms that it is too expensive to find the optimal

solution, leading to the study of approximation solution. Interestingly, the running

time of HeurDT and MST-L is very close to each other. For example, HeurDT takes

around 37ms more in average than the MST-L approach. This is due to the time spent

on identifying active edges and removing them if they are placed between internal

nodes Additionally, converting leaf nodes to internal nodes during merging subtrees

necessitates a procedure to check all their neighbors in order to maximize the number of

leaf nodes. However, the difference between them is very subtle where as the size and

weight of DT obtained from HeurDT is much smaller than that of MST-L. In summary,

HeurDT obtains a very good dominating tree with very low time complexity.

5.5 Conclusion

In this chapter, we investigate a new NP-hard problem of how to construct a

dominating tree with minimum weight in WSN. We prove the inapproximability result and

provide the approximation framework to solve the DT problem. In addition, due to the

high runtime complexity of this approximation algorithm, a much more efficient heuristic

algorithm is also proposed.


Connected Dominating Set (CDS) has been a well known approach for constructing

a virtual backbone to alleviate the broadcasting storm in wireless ad-hoc networks.

Current research has focused on minimizing the CDS size, since computing a minimum

size CDS is NP-hard. However, little work on CDS with multiple factors constraints has

been found in literature. In this chapter, we investigate the trade-offs among multiple

factors in CDS construction, such as fault tolerance, size, diameter and running time.

To our best knowledge, no existing research has considered these important factors

together in a single model, so that we introduce the multi-factors model studying a joint

optimization problem in which the objective is to optimize the CDS size, network latency

or running time while keeping the fault tolerance. Building on this model, we provide

the approximation algorithms with constant ratios. In addition, we present improvement

techniques, inspired by the computational geometry and probability, that systematically

reduce running time or size of CDS. Simulation results show that our algorithms can

gain good trade-offs among these factors, which coincide with theoretical analysis.

6.1 Overview of Virtual Backbone

Many works [3-5, 18-20, 24, 28, 40, 41, 45, 54, 59, 65, 67, 68, 74, 75, 79, 80]

seek a minimum size CDS (MCDS),which is NP-hard [27], as their major design goal.

Minimizing the cardinality of CDS can help to decrease the control overhead since

broadcasting for route discovery [33, 51] and topology update [1] is restricted to a small

subset of nodes [13]. Therefore broadcast storm problem [73] inherent to global flooding

can be greatly decreased.

However, there are several important factors that need to be fully investigated. The

first important factor is the network latency, also represented as diameter of CDS, which

is the longest shortest path between any pair of nodes in CDS. Considering the situation

that the receiver is not within the transmission range of the sender, communicate


through multi-hop links by using some intermediate nodes to relay the messages is

needed. Since a CDS with large diameter often leads to an increase in propagation error

and transmission latency, a CDS with small diameter is certainly preferred for reliable

message delivery and short latency.

The second important factor is the running time. Due to the frequent link failures

and limited power supplies, CDS suffers the challenges from mal-function, hence

requiring a new CDS generated by system in a short time, in order to maintain the

routing operation in network. Thus, time complexity of the CDS construction is a key

factor in the remedy of CDS. Unfortunately, little previous work has measured the

running time of their proposed algorithms in simulation. Since low running time of CDS

construction is highly preferred in wireless ad-hoc network, time complexity becomes

more important, especially in time-sensitive environment.

The third important factor is the fault tolerance. As CDS is often very vulnerable

due to frequent node failure and link failure, which is inherent in wireless networks,

constructing a fault tolerant CDS that continues to function during node or link failure is

another issue. The previous work [68, 75, 81, 82] have addressed this issue. However,

they only considered the size of CDS together with the fault tolerance, without the

diameter of CDS and running time.

The main contribution of this work is the multi-factors model for a fault tolerant

MCDS with bounded network latency (diameter) and the low running time for a feasible

solution is expected as well. The characterization of this model is that (1) a variable is

involved in this algorithm as an input to make the performance tunable. (2) trade-offs

among multiple factors are shown through analysis, which has not been addresses in

related works.

More specifically, the proposed progressive algorithm, which is the input of our

model, allows for systematic improvement. Taking inspiration from computational

geometry and probability, we devise improvement techniques for systematically reducing

the running time on locating the center with sacrificing a little performance. In addition,

we also present the techniques to remove the redundant nodes for further reducing

the size of CDS. In the end, we do simulation to verify of the improvement techniques.

The results indicate that the techniques are effective in either reducing the size or

the running time. Besides that, we also compare against other recently proposed

algorithms, CDS-BD-D [34], CDS-BD [38] and BDA [88] under the same parameters.

The results demonstrate our algorithm outperforms CDS-BD-D, CDS-BD and BDA in

most testing cases.

6.2 Related Work

Algorithms on constructing a CDS can be divided into two categories based on

their algorithm designs: centralized algorithms and decentralized algorithms. The

centralized algorithms usually yield a CDS with a better performance ratio than that of

decentralized algorithms. The decentralized algorithms can be further divided into two

categories: distributed algorithms and localized algorithms. In the distributed algorithms,

the decision process is decentralized and serialized. In the localized algorithms, the

decision process is not only distributed, but also requires only a constant number

of communication rounds. Based on the network models, these algorithms can be

classified into three types in undirected graph: general graph, Unit Disk Graphs

(UDG)[15], where all nodes have the same transmission ranges, and Disk Graphs
with Bidirectional Links (DGB) (we will introduce DGB in Section 6.3).

6.2.1 General Graph

Several work have been studied in general graph. In [28], two polynomial-time

algorithms to construct a CDS is proposed by the authors. The first algorithm has

performance ratio of 2(H(5) + 1), where H is a harmonic function and 6 is the maximum

degree of G. The idea of the first algorithm is to identify the node with a maximum

degree as the root. Then build a spanning tree T at the root, grow T until all nodes are

added to T. Then, all leaf nodes are cut off and the remaining nodes in T are a CDS.


The second algorithm is a progress of the first algorithm. The second algorithm consists

of two steps. The first step is to construct a dominating set and the second step is to

connect the dominating set with a Steinter tree. With such improvement, the second

algorithm has a better performance factor of H(6) + 2. Later, the two algorithms were

simulated by Das et al. in [19, 20, 59]. In [54], Ruan et al. introduced another centralized

and greedy algorithm of which the performance ratio is (2 + log 6).

Wu and Li [79] proposed an algorithm that can quickly generate a CDS based on

the connectivity information within the 2-hop neighbors. This approach uses a marking

process. In particular, each node is marked true if it has two unconnected neighbors.

All the marked nodes form a CDS. The authors also introduced some dominant pruning

rules to reduce the size of the CDS. In [74], the authors showed that the performance

ratio of [79] is within a factor of O(n) where n is the number of nodes in a network.

6.2.2 Unit Disk Graph

In UDG, most of proposed algorithms are to find an MIS and then connect the

MIS with minimum number of nodes. In [3, 5, 74], the authors presented a distributed

algorithm with a constant performance ratio of 8. Later, Cardei et al. presented another

distributed algorithm in [11]. This algorithm has the same performance ratio as previous

work. However, the message complexity is lower than that of [74].

As we know that distributed algorithm has a better performance than localized

algorithms. In the localized algorithms, in [4], Alzoubi et al. proposed a localized

algorithms with a performance ratio of 192. Although the performance of [4] can not

compete with that of [74] and [11]. Their algorithm only need one hop neighbors

information. Therefore, once a node knows that it has the smallest ID among it

neighbors, it becomes a dominator. Then, the dominators can be connected by

the intermediate nodes in the next step. In [41], Li et al. proposed another localized

algorithm with a performance ratio of 172, which is better than [4].


6.2.3 Disk Graphs with Bidirectional Links

Since the specific geographical characteristics of DGB, not all CDS construction

algorithms that are applicable in UDG can be applied to DGB. As far as we know,

the algorithms in [11, 74] are applicable in DGB. In [67], Thai et al. first proposed the

performance ratio of CDS on size in DGB and the two proposed algorithms can be

implemented by distributed ways. However, the only difference between two algorithms

is the strategy to select MIS, the first algorithm employed Wan's algorithm [74] to choose

the nodes in MIS, while the second algorithm used the greedy strategy, that is to include

the minimum number of nodes in MIS, thus leading to a better performance than the first


6.2.4 Other Results in CDS

Mohammed et al. mentioned the problem of constructing CDS with small diameter

[45]. However, they did not give a guaranteed performance in their model. In [38], Li et

al. studied the CDS problem with bounded diameter in UDG and proposed a constant

approximation algorithm, called CDS-BD. However, their algorithm is centralized and no

experimental results are provided. As an extended work of [38], Kim et al. first made

their centralized algorithm to be distributed, then added energy consideration when

constructed the CDS. Simulation results and comparison against other recent algorithms

were reported at the end. The problem in [34] is that they emphasized that the UDG

cannot be used as network models, since the transmission ranges of all nodes may

be different. However, they still used UDG as their model through their whole work. In

contrast, we will employ a new network model, DGB, to study our model in this work.

In summary, none of the previous work have addressed the following issues.

First, the performance of our model is tunable, it can be adjusted in a range by an

user-defined input. Second, we find out the trade-offs among CDS size, diameter,

running time through theoretical analysis and simulation, that is, it is hard to optimize

these factors at the same time. Third, running time is firstly introduced as a metric

into the CDS construction and simulation. Fourth, the importance of the center of

network is highlighted, since building a CDS rooted at the center will greatly improve the


6.3 Wireless Communication Model and Preliminaries

As we described in the above section, in this work, we model the wireless network

using a Disk Graph with Bidirectional links (DGB) G = (V, E), which is much more

general than UDG. The nodes in V are located in the two dimensional Euclidean

plane and each node vi e V has a transmission range r, e [rmi,, rax]. A directed

edge (v,, vj) c E if and only if d(v,, vj) < r, where d(v,, vj) denotes the Euclidean

distance between vi and vj. Such graphs are called Disk Graphs (DG). An edge (vi, vj)

is bidirectional if both (vi, vj) and (vj, vi) are in E, i.e., d(vi, vj) < min{ri, rj}. In this work,

we study the multi-factors model in disk graphs where all the edges in the network are

bidirectional. In this case, G is undirected.

Now we give some notations, terminologies and definitions throughout this work.

6.3.1 Notations

* r: a root node.

* dru: the number of hops in the shortest path between r and u.
R: the transmission range ratio, i.e. R = ma
K: the number of independent neighbors of a node u in DGB, if R = 1, then K = 5,
otherwise, K = 10([ i( ) + 1)[67], where the independent neighbors of a node
u are defined as a set of nodes that adjacent to u satisfying that any two nodes in
the set are independent.

6.3.2 Terminologies

* u is v's 2-hops away neighbor if u and v are not adjacent and they are connected
via only one intermediate node.

Two nodes x and y are siblings if they are adjacent and dry = dr,.

Node u is the parent of node v and v is the child of u such that u and v are
connected and drv = dru+1.


*Given a root r, node u is a terminal in graph if it has no child.

Figure 6-1 shows an example for the introduced terminologies.

Figure 6-1.

Given node r as the root, node a, b, f, g are terminals. r is the parent of c
and e. Node a, b are siblings, f, g are siblings. Node a, b, f, g are r's 2-hops
away neighbors

6.3.3 Definitions

Definition 2. Dominating Set: A Dominating Set (DS) of graph G is a subset
C c V such that each node either belongs to C or is adjacent to at least one node
in C. A CDS is a DS which induces a connected subgraph. The size of a CDS is
the number of nodes in CDS.

Definition 3. Diameter: The diameter of a graph G is equal to the maximum
value of dv, where u and v are any nodes in G. Likewise, the diameter of a CDS,
normally denoted as d(CDS), is equal to the maximum value of d,, where i,j are
any nodes in CDS.

Definition 4. Fault Tolerant MCDS (km-CDS) with Bounded Diameter: Given a
DGB G = (V, E) representing a network and two positive integers k and m, find a
subset Ckm C V with minimum size, such that: (1) the subgraph induced by Ckm,
i.e., G[Ckm], is k-connected, (2) each node not in Ckm is dominated (adjacent) by at
least m nodes in Ckm, and (3) the diameter of Ckm is bounded.

6.4 Multi-Factors Model and Solutions

In this section, we provide a solution for km-CDS with bounded diameter 1 < k <

m + 1. First, we need to give the following definitions in graph theory: A graph G is

k-connected if it is connected and removing any k 1 nodes from G will not partition

G. A separating set or cut-vertex of a graph G

(V, E) is a set S c V, such that


G S has more than one component. When IS| = 1, S is a cut vertex. A k-block of a

graph is a maximal k-connected subgraph of G that has no separating set. If G itself is

k-connected and has no separating set, then G is a k-block.

The multi-factor model considers three factors (size, diameter and fault tolerance)

together. Some recent work [68, 81, 82] has addressed the general fault tolerant MCDS

problem. However, none of them mentioned how to bound its diameter.

In our previous work[68], we have proposed a solution for km-CDS problem, where

1 < k < m + 1, as illustrated in Algorithm 11. In this chapter, we still use this algorithm

to solve our multi-factor model. However, a new analysis is proposed for the diameter of

km-CDS. The main idea of Algorithm 11 is that merging all the k'-blocks in 1-Connected

m-Dominating Set (Im-CDS) into only one k'-block by adding extra nodes, where k'= 2

initially. Then, we increase k' by 1 and repeat the above operation until k'= k. We can

use any 1-CDS with bounded size and diameter as the input of Algorithm 11. However,

in order to make the solution adjustable by the user, an (a, 3)-CDS, to be introduced in

Section 6.6, is preferred to be an input of Algorithm 11.

Algorithm 11 The Solution for Multi-factors Model [68]
1: INPUT: A connected DGB G = (V, E) and a CDS C11 with bounded diameter and
2: OUTPUT: A km-CDS Ckm with bounded diameter
3: Step 1: Based on the input C11, construct a Im-CDS Cim by using CDSMIS
Algorithm in [68]
4: Step 2: Compute all the k'-blocks in Cim, initially k'= 2.
5: Step 3: If there is more than one k'-block in Cim, find the shortest path in the
original graph that satisfies the two requirements: (i) the path can connect two
k'-blocks sharing a same separating set to be one k'-block of Cim. (ii) the path does
not contain any nodes in Cim except the two end points. Then add all intermediate
nodes in this path to Cim.
6: Step 4: Repeat Step 2 and 3, until there is only one k'-block in Cim.
7: Step 5: Increase k' by 1 and then repeat Step 2, 3 and 4, until k'= k. The resultant
Cim will be Ckm.


Theorem 6.1. If the input CDS has an approximation ratio of a on size (a > 1), then
Algorithm 11 produces a km-CDS with (2K + 2m + l)a-approximation on size, where

Ci~ and Cmn are the Im-CDS and km-CDS with optimal solution on size respectively.

Proof: Ckm is the union of Cim and the nodes added into Cim, in order to make Cim

k-connected. The number of nodes we added to make Cim k-connected is at most

2(k 2)(| C1m 1)+ 2(K 1)(| C1m 1) [68]. Therefore,

|Ckm =ICm +2(k- 2)( Cm 1) 2(K+ 1)( Cm -1)
< (2K+ 2k- )1 Cim
However, in our previous work [68], we already concluded the following inequality,

I Cim
I Ckm < (2K 2k- 1) Cim
<(2K + 2k- 1)(K+ m+ a- 1)Cm

< (2K +2m+ 1)(K m + 1)1 Cml

Lemma 12. d(Clm) < d(Cii) + 2.

Proof: Since each node not in C11 is dominated by at least one node in C11.

Therefore, when we add more nodes into C11 in order to make it to be Cim, we only

increase d(C11) by at most 2 hops. o

Lemma 13. d(Ckm) < d(Cim) + 2.

Proof: Suppose two nodes u and v are in Ckm. The position of node u and v has

three possibilities: (1) u, v e C,,. (2) u e Ckm Clm, V Cim. (3) u, v e Ckm Cm.

For case (1), the number of hops between u and v is bounded by d(Cim). For case

(2), u must be dominated by a node in C,,. Therefore, u is only one hop away from its
dominator in Cim and the number of hops between u and v is bounded by d(Cim) + 1.


For case (3), u and v are dominated by different nodes in Cm. However, u and v are

only one hop away from their dominators. Thus, the number of hops between u and v is

bounded by d(Cim) +2. o

Theorem 6.2. If the diameter of input CDS is bounded by 3D*, the approximation ratio

of the constructed km-CDS on diameter is 3D + 4.

Proof: From Lemma 12 and 13, we have the following inequality:

d(Ckm) < d(Cim) +2 < d(Cn) + 2 + 2 < D* + 4 < D + 4

6.5 A Better Algorithm for CDS on Diameter

Before we introduce the progressive algorithm as the input of Algorithm 11, we

would like to introduce an algorithm to determine a CDS with a better approximation on

diameter than existing work. As we know, the authors in [38] presented a 3-approximation

algorithm on diameter, which was the best known result at that time. In this section, an

algorithm that guarantees CDS with 2-approximation on diameter of CDS is described

and the size of CDS is bounded as well. The difference between other existing work

[34, 68] and our algorithm is that they try to minimize the CDS size while the diameter is

bounded. In contrast, we want to minimize the CDS diameter while the size is bounded.

To construct a CDS, we often employ an Maximal Independent Set (MIS) which

is also a subset of all the nodes in the network. The nodes in MIS are pairwise

nonadjacent and no more nodes can be added to preserve this property. Therefore,

each node which not in MIS is adjacent to at least one node in MIS. Thus, an MIS is

indeed a DS. If the nodes in MIS are connected by adding more nodes to the MIS, a

CDS can be constructed. Here, our algorithm consists of the following three phases,

1. Root r is randomly chosen and we only select the nodes, e.g. node y, into MIS,
where dry is an even. Then, the nodes in MIS is colored blue or black, and all other
nodes are colored gray or red.


2. Swap the colors of blue and red nodes and change some nodes to black according
to the rules described in second phase of Algorithm 12. Consequently, the blue
nodes and black nodes may be adjacent, but they still dominate other nodes,
therefore the MIS with black and blue nodes is changed to a DS.

3. Connect the DS with some intermediate nodes, and DS will be a CDS finally.

The details of our algorithm are shown in Algorithm 12. For more clarification, we

show an example to illustrate the second phase.

Algorithm 12 Algorithm for CDS with 2-Approximation on Diameter
First Phase: MIS construction
1 : INPUT: A connected DGB G = (V, E) and all nodes are white initially.
2: Randomly choose a root r E V, let {Vk y e V1dry k} and Gk is the subgraph of G induced by Vk, y is in level k, suppose
k* is the maximum of k.
3: Find an MIS /2 of G2 by Wan's algorithm.
4: Color all nodes in /2 black and all other nodes gray in G2.
5: for each i, where i = 4, 6, 8, 10...n, if k* is an even, n = k*, otherwise, n = k* 1 do
6: while there exists a white node x in G do
7: if x has a black 2-hops away neighbor z in Gi-2 then
8: Color x black and all adjacent nodes gray.
9: else
10: Color x blue and all adjacent nodes red if white, otherwise, no color changes.
11: end if
12: end while
13: end for/* from line 5 to 13, we find an MIS with black and blue nodes in Gi, but the process of constructing MIS gives prefer-
ence to those nodes who has a black 2-hops away neighbors in Gi-2*
14: while a white node y exists in G do
15: Color y in black and color its adjacent write nodes in gray. /* Note that the node colored black in this loop belong to / for
some odd i*/
16: end while/* All the black and blue node form an MIS. In next phase, we swap the colors of blue and red nodes and change
some nodes to black, therefore, the MIS is changed to a DS*/
Second Phase: Swap the color
1: for i 2 to n, where n is an even do
2: for each blue node x in G; do
3: (1) swap the colors of x and x's neighbors only in G 1 (now x is in red and x's neighbor is in blue), (2) suppose in Gi, y
is the red node dominated by x, color one y's neighbor only in G_1 black if it is not black. (3) Suppose the red node z in
Gi+, is dominated by x, color z black if it is not black.
4: end for
5: end for
6: Color all the blue nodes in G black and all red nodes gray. /* Note: all black nodes at last are a DS, not necessarily an MIS. In
next phase we connect all black nodes to be a CDS */
Third Phase: Connect DS to CDS
1: Color r black.
2: for i 2 to k* do
3: for every black node x E G do
4: if x can find a black 2-hops away neighbor y in Gi-2 then
5: Connect x and y with exactly one node z in Gi1, color z black if it is not black.
6: end if
7: end for
8: end for
9: Let C be the largest black connected component. Note that other than C, each black connected component Ci in Gi for some
odd i is not connected with C. But, there must exist one node z in G 1 to connect Ci with C, color z black if it is not black. At
last, all Ci in Gi for some odd i are merged into C and only one black connected component exists in DGB finally.
10: The algorithm stops until there is no node changed from gray to black.
11: OUTPUT: All black nodes consist of a MCDS with bounded diameter.


Figure 6-2 presents an example that illustrates the procedure of swapping color

in second phase. In this example, we assume that level a + 1 is equal to k*, where a

is even, and the MIS with blue and black nodes is produced in first phase. Now, we

describe how to swap the colors step by step.

1. The initial situation is shown in Figure 6-2(a), where black and blue nodes are in

2. In line 3 of second phase, step (1) is shown in Figure 6-2(b), the two red nodes in
level a 1 are changed to blue, and node x is changed to red.

3. For step (2), in Ga, y is the red node dominated by x, color one y's neighbor p in
Ga,_ black. This situation is shown as in Figure 6-2(c).

4. For step (3), the red node z in Ga+I is dominated by x, color z black. This is shown
in Figure 6-2(d).

5. In line 6, all gray nodes are colored black and all red nodes are colored gray, see
Figure 6-2(e).

At this moment, there are only black and gray nodes in the graph and for each black

node, we can always find exactly one node that make it connected with other black

nodes in upper level within 2 hops, so the number of black node for connecting the DS is

at most |DSI 1.

Theorem 6.3. If TCDS is the CDS determined by Algorithm 12, then I TCDSl < 2(K -

1)K|CDS*I 1 and d(TcDs) < 2D* + 6 in a DGB.

Proof: It is known that for an MIS / in DGB, I/I < K CDS* [67]. However, when we

swap the colors of nodes, the MIS is changed to a DS, so, |DSI < (K 1)|/| since in

the worst case, in G,, for even i, if we change the color for each blue node x, we have to

change at most K non-black nodes to black to maintain the whole network dominated

by all black nodes, such that x is in MIS and each node in MIS can be adjacent at

most K independent neighbors [67]. Therefore, the difference in size between MIS

and DS is DSI < (K 1)/ Thus, ITCDSI <_ DSI+ the size of connecting nodes

< 21DS 1 < 2(K- 1)1/ 1 < 2(K 1)K CDS* 1. For diameter of CDS, suppose

black g


red blue


black gi



red red


rey grey black

- red


black g
level a-2

level a-1


level a+1


grey black

blue blue



level a-2

level a 1

level a

level a+1

black grey

black blh

1 7

rey grey black
level a-2

blue blue
~ level a-1

F level a

red level a+1

grey black

ue blue



level a-2

level a-1

level a

level a+1

grey black


level a-2

level a-1

level a


lb1 k

Oa" level a+1

Figure 6-2. An example for second phase in algorithm 12

G has diameter D, then D = k* and the diameter of a CDS is at least D 2 = k* 2.

For each black node x in G,, where / is even, x can reach the root with exactly k* hops in

TcDS. For odd i, each black node x in G, can reach the root with at most k* + 1 hops in

TCDS. Therefore, d( TCDS) < 2k* +2 = (2k* 4)+ 6 = 2D +6.





6.6 Progressive Algorithm (PA) and Analysis

Although several work [34, 38] can guarantee the CDS size and diameter, their

performance ratios are fixed. Considering the flexibility of wireless ad-hoc network, we

introduce (a, 3)-CDS into our model so that first, its performance ratios are tunable

based on the input. Second, the center of network is involved in the CDS construction to

enhance the performance. Third, it can construct a CDS with approximately satisfying

the size constraint and diameter constraint. As we intent to balance the size and

diameter, the definition of (a, 3)-CDS in given in wireless ad-hoc networks as follows:

Definition 5. (a, 3)-CDS: Forp/ > 1, a CDS C of G meeting the following two require-

ments is called an (a, 3) -CDS.

1(Size) The size of C is at most a times the minimum CDS size.

2(Diameter) For any pair of vertex u and v in C, d(C) is at most 3 times the mini-
mum diameter of CDS plus a constant number.

In (a, 3)-CDS, 3 is an user-defined input, and usually a is a function of 3.

Therefore, the value of a depends on the user-defined input P. In the following, we

will describe how to generate an (a, 3)-CDS, analyze the time complexity and present

the trade-off between the size and diameter through analysis. The general idea of PA is

as follows.

1. Root r should locate at the center of network, which is the mid-point of the longest
shortest path between two nodes in G.

2. Construct a CDS TcDs rooted at r by using BDA [88] in our previous work, where
BDA is an approximation algorithm for CDS with 2K-approximation on size and
4-approximation on diameter.

3. Construct a Shortest Path Tree (SPT) TSPT rooted at r, which only includes all the
shortest paths from r to every other node in TCDS-

4. Traverse TCDS in a depth-first manner. When visiting a node u, if the number
of hops from r to u in TCDS is larger than a user-defined threshold 3 times the


number of hops from r to u in TSPT, then a new path from r to u in TSPT is added
in TCDS.

If we denote DCDS(U, v) as the number of hops from u to v in TCDS and DSPT(U, v)

as the number of hops from u to v in TSPT. The details of PA is as follows:

Algorithm 13 Progressive Algorithm (PA)
PA (0)
1: Locate the center of network and choose r at the center
2: Build a TCDs by BDA rooted at r
3: Use the algorithm in [46] to construct an SPT TSPT
4: C = FIND (TCDS, TSPT, r, 3)
5: return C
2: DFS (r)
3: return a desired CDS C
1: for each vertex v e TCDs do
2: d[v] oo
3: r[v] -- NIL
4: end for
5: d[r] -- 0
RELAX (u,v)
1: if d[v] > d[u] + DCDS(U, v) then
2: d[v] = d[u] + DCDS(U, v)
3: [v] u
4: end if
DFS (u)
1: if d[u] > /DsPT(r, u) then
2: ADD-PATH (u)
3: end if
4: for each child v of u in TCDS do
5: RELAX (u, v)
6: DFS (v)
7: RELAX (v, u)
8: end for
1: if d[v] > DsPT(r, v) and parentspT(v) != NIL then
2: ADD-PATH (parentspT(v))
3: RELAX (parentspT(v), v)
4: end if

1. Root Selection and CDS Tree Construction: With Distributed SPT algorithm [46],
each node maintains a global variable, which stores the current longest shortest
path in the graph G, if a longer shortest path is found, the global variable of each
node will be updated. At the end, we could find the mid-point of global longest
shortest path. While constructing TCDS rooted at r by BDA [88], each node u
needs to maintain a pointer 7[u] for its parent on the tree TcDs and an upper bound
d[u] for the number of hops to r. We use the INITIALIZE and RELAX algorithms in
[39] to initialize and maintain both of these attributes.

2. Shortest Path Tree Construction: TsPT rooted at r is constructed by using
Distributed SPT algorithm. It only contains all the shortest paths from the root
r to every other node in TCDS.

3. Depth First Search (DFS): Traverse the TCDS in a DFS manner beginning from
the root r along the paths from r to all the other nodes in TCDS. When node u is
reached for the first time, if d[u] is greater than 3 DSPT(r, u), then the shortest Pr,
in TSPT is added to TCDS and d[u] and 7[u] are updated. After this, node u's parent
v needs to be checked if the updated path from r to u will result in reducing the
number of hops from r to v. If so, then v's parent will be checked and so on until
the root r is reached.

With the execution of BDA, distributed SPT (dSPT) (e.g.[46]), and distributed DFS

(dPFS) (e.g.[57]), TCDS, TSPT and a DFS traversal order could be achieved. The details

of PA are illustrated in Algorithm 13.

To evaluate the correctness of the PA, we examine whether the two constraints

in the definition has been satisfied. Taking 3 as an user-defined input, we derive a

relationship between a and 3, which shows the relationship between the size of the

constructed CDS and the optimal solution of CDS on size. We also analyze the time

complexity of the PA.

Define w(TcDs) as the total weight of TCDS in G, where we assume each edge

has been assigned the unit weight of 1. Then DSPT(U, V) and DCDS(U, v) are equal

to the weight of TSPT(U, v) and TcDS(U, v) respectively. Another observation is that

STCDS = w( TCDS) + 1, since the number of node in a tree equals to the total number of
edges plus 1, which also equals to w(TCDS) + 1. Meanwhile, as we mentioned before,

the lower bound of minimum diameter of CDS is D 2. Actually, the upper bound for the

minimum diameter of CDS is D, i.e., all the nodes in G are in CDS, therefore, D* = D.


Due to the specific structures of CDS, we will classify the following proofs into two

cases. case (1): the diameter of SPT T rooted at r that spans all nodes in G is equal to

D and all other situations are classified into case (2).

Lemma 14. For any pair of nodes u and v in C, the number of hops between u and v is

atmost/3(D* +2), when d(T) = D.

Proof: When a vertex v is visited, if d[v] > 3DspT(r, v), then shortest path between

r and v is added into TCDS by calling ADD PATH. Also, we know that the maximum

value for DSPT(r, v) is the height h of TSPT, we will prove that 2h < D* + 2 in the

following. After v is visited, d[v] is at most 3DsPT(r, v), which is less or equal to ph and

subsequently never increases. For u, the same analysis can also be applied. Therefore,

the total number hops between v and u in C is at most 23h, therefore at most 3(D* + 2).

Now, we prove that 2h < D* + 2. First, it is easy to see that 2h < d(T) and

d(T) = D. Then we have the following:

2h 2 < d(T) 2 < D- 2 < D*

Therefore, we prove that 2h < D* + 2.

Lemma 15. In case (2), for any pair of nodes u and v in C, the number of hops between

u and v is atmost2/3(D* + 1).

Proof: If d(T) / D, the worst case is that d( T) = 2D*. A simple example to

illustrate that is a ring, the degree of each node in the ring is only 2 and all the nodes

in G are included in CDS, see Figure 6-3. Therefore, h < D* + 1, then the maximum

number of hops between u and v is at most 2h, that is 23(D* + 1). E

In real wireless ad-hoc network, case (2) rarely happens, since it requires that all

nodes are uniformly deployed as a ring. However, in most cases, they are deployed

randomly. Therefore, the diameter of CDS returned by PA is bounded by 3(D* + 2) in

most cases.


Figure 6-3. All the nodes in the ring are a CDS with diameter of 8

Lemma 16. The total number of nodes on the added shortest paths is at most
(5-)K CDS* 3.
Proof: Let vo = r and v, v2 .....vk be the vertices that caused shortest path to be

added during the traversal, in the order they were encountered. When the shortest

path from r to v,(i > 1) was added, the number of hops of the added path was

DsPT(r, v,). Also, the nodes on the path to vi has been relaxed in order, so that

d[vi] < DsPT(r, vi-1) + DCDS(Vi-1, i). The shortest path to vi was added because

/DsPT(r, vi) < d[v,]. Combining the inequalities,

3DsPT(r, vi) < DspT(r, vi-1)+ DCDS(Vi-1, Vi)

Summing over i bounds from 1 to k, the number of hops of the added paths:

k k
3 E DsPT(r, v,) < (DsPT(r v, i-) DCDS(Vi-1, Vi))
i= 1 i= 1
and therefore

k k
(3 1) Z DSPT(r, v,) < DCDS(Vi-1, v,)
i= 1 i= 1


The DFS traversal traverses each edge exactly twice, and hence the sum on the

right-hand side is at most twice w(TcDS), since one hop corresponds to a unit weight of

1, i.e.,

SDCDS(Vi-1, V) < 2w(TcDs)
i= 1
We note that the number of new nodes on the added shortest path is exactly equal

to DspT(r, vi) 1 and I TCDS = w(TCDS) +1. Therefore,

(3- 1) (DsPT 1)(r, vi) k(3 1) < 2(w(TcDs) 1)- 2

(3 1) Z(DSPT 1)(r, vi) + k(3 1) < 2| TCDSI 2
i= 1
Here, we intend to maximize k in order to have a tighter bound on Yi(DSPT -

1)(r, vi), which is the total number of new nodes on the added shortest paths, Let

denote ~1(DSPT 1)(r, i) as Psize for clear representation.

Intuitively, k is at most I|/, where I is the MIS in TCDS, since all black nodes in MIS

of TCDS may cause shortest paths to be added during the traversal. However, the root

r and at least two black nodes at level 2 will not cause shortest paths to be added.

Therefore, k is at most I|/ 3.

(/3- 1)Psze < 2 TcDS 2 (1/- 3)( 1)

< 2(21/| 1) 2 (1 3)( 1)

< (5- 3)/I + 3/- 7

Since I/I < K CDS* [67], we have:

(5 O) K
Ps <(5 )KCDS + 3



Theorem 6.4. Given the value of 3, the approximation ratio a on the size of CDS is
( +3)K
Proof: From the above analysis, C is the union of TCDs and the added shortest

paths. Therefore, combining the Theorem 3 in [88] and Lemma 16,

SC = TCDS + Psize

<2K CDS* -1 (5)KCDS*+ 3

< (+3) K CDS* +2

From the above theorem, we know that the performance ratios depend on the input

3. As the ratio on diameter increases, the ratio on size drops down and vice versa. From

a theoretical point of view, we show the trade-off between size and diameter.

Theorem 6.5. The time complexity of the PA algorithm is O(n2), and the message

complexity of the PA algorithm is O(n2).

Proof: The time complexity and message complexity for BDA are O(n) and

O(n log n) respectively [88] and dSPT and dDFS run at most O(n2) time complexity

and send O(n2) messages [46] [57]. Now, we analyze the procedure of finding the

center of network. The dSPT algorithm is executed at each node x simultaneously, after

that, x needs to broadcast the longest path in SPT rooted at x and compare it with the

longest paths returned by other nodes. Therefore, this procedure needs 0(n2) time

complexity and O(n2) message complexity. Since all other operation only take at most

O(n) time complexity and O(n) message complexity, the overall message complexity

and time complexity of PA are O(n2) and O(n2).


6.7 Further Improvements for The Progressive Algorithm

The PA in Section 6.6 allows a CDS to be constructed with guaranteed and tunable

performance, while the center of network greatly helps to improve the performance, e.g.

reducing the size and diameter of CDS, which will be verified in simulation. However, the


CDS construction comes at a cost: in PA, we include some redundant nodes that are

unnecessary in CDS, and the procedure of locating the center of network is very time

consuming, which will be clearly shown in simulation.

In this section, we present a set of improvement techniques that systematically

remove the redundant nodes and reduce running time with scarifying a little performance.

Taking inspiration from probability and computational geometry [44], we present three

distinct improvements: reducing multiple paths, removing redundant terminals and

locating central area. The first and second techniques reduce the size, whereas the last

technique reduces the running time.

6.7.1 Reducing Multiple Paths

In PA, after we locate the center r of network, a CDS TCDS rooted at r is determined

by BDA, then we test each node, e.g. v, in TCDS to see whether d[v] > /DsPT(r, v), if

true, then the shortest path between r and v is added into TcDs by calling ADD PATH.

However, there are at least two paths from r to v, one is over TCDs and another one is

the shortest path. Now, we can eliminate the path over TCDS to remove the redundant

nodes. The technique is: suppose v is at level b, we remove the intermediate node u

in TCDS that connects v with the black node in MIS at level b 1. A simple example

is illustrated in Figure 6-4. In Figure 6-4(a), the black and blue nodes are in TcDs and

black nodes represent the MIS. Suppose we set 3 = 1, the red nodes that consist of the

shortest path from r to v is added into TCDS. The redundant node in TCDS is u, since v

can be connected to the root via shortest path. In Figure 6-4(b), the redundant node u is

removed from TCDS, and the new CDS is smaller than the original one.

By doing this, we are able to reduce the CDS size, leading to the low message

overhead and transmission error without interfering with CDS diameter. We will show the

effectiveness of this technique in simulation.


grey red black red grey

red black black red
x blue


black blue blue black
grey red black red grey

red black black red
x blue

v u

black grey gre black

Figure 6-4. An example for reducing multiple path

6.7.2 Removing Redundant Terminals

Besides reducing multiple paths, we are still able to reduce the CDS size by

applying the second technique. Normally, a CDS generated by PA contains some

redundant terminals that if we remove them, the modified CDS still respects to the

definition of CDS. The main idea of this technique is to remove each terminal in CDS

to test if the resultant CDS will violate the definition. If not, then remove the terminal,

otherwise, no change is made. Algorithm 14 is shown to implement this technique.

For easy understanding, Figure 6-5 show the situations before and after applying

the technique. In Figure 6-5(a), the black nodes are in TCDS, while the redundant

terminal in TCDS is u, since, besides u, x is also dominated by v. In Figure 6-5(b), the

Algorithm 14 Removing Redundant Terminals
1: INPUT: A CDS TCDS with some redundant terminals
2: Color the nodes in TCDS in black and all other nodes in white
3: for each terminal x in TcDs do
4: for each node u e TCDS x do
5: for each u's neighbor v, v TCDs do
6: Color v in red
7: end for
8: end for
9: if all nodes not in TCDs are red then
10: Remove x from TCDS
11: end if
12: Reset all red node to white
13: end for
14: OUTPUT: A CDS with smaller size

redundant terminal u is removed from TCDS, and the new CDS is smaller than the

original one.


1 U V



Figure 6-5. An example for removing redundant terminals


6.7.3 Locating Central Area

In PA, we run dSPT on each node in order to locate the center of network. However,

the running time is extremely high, and in simulation, we will see the running time

increase of two orders of magnitude comparing with BDA. In time-sensitive network, this

is not acceptable due to the long time consumed on generating a new CDS if the original

one fails. Therefore, we present the third technique achieving the comparable running

time without sacrificing a lot performance.

Before we introduce our third technique, we note that this technique uses the link

based disk-union model proposed in [44], each link between two nodes is assigned a

weight. Considering a link (u, v) in network, the measure of weight on link (u, v) is given

by the number of nodes within the transmission range of nodes u and v (other than u

and v). Let D(u, v) denote the disk centered at u and radius Iu, v|. Then the weight

w(u, v) of the link is defined in term of the number of nodes in disks D(u, v) and D(v, u)

as defined below.

Definition 6. Weight w(u, v): The weight corresponding to a link (u, v) is given by the

count of the nodes in the region given by the union of disks D(u, v) and D(v, u)

From the view point of probability, given a randomly generated network, it is highly

possible that the center of network is located at the central area of network. In order

to have better performance on diameter and size, we usually expect the root of CDS

located at the central area, not in the boundary of network. Therefore, we introduce the

concept of convex hull in computational geometry [50] to approximate the central area of

the given network.

We employ a tree and its leaf nodes are defined as the convex hull of the given

network. Suppose the root of the tree is in the convex hull, more internal link and

very few boundary links are included in the tree. This approach has the drawback of

decreasing the probability of the root of CDS located at the central area. To overcome


this problem, we can consider the structure of Minimum Spanning Tree (MST), where

the weight on each link is defined in Definition 6.

Observation: The weight on boundary link is very likely less than the weight on

internal link.

From the above observation, it is not difficult to see that the central area is more

dense (the number of node per area) than the boundary of network. Therefore, the

weight on boundary link is normally less than that on internal link.

In [44], an O(n2 Ig n) algorithm for constructing Minimum Interference Tree (MIT),

which is based on the structure of MST, is reported. This algorithm is a modification

of the well known Kruskal's algorithm for constructing MST [17] that increases the

probability of boundary links included in MIT. We can use this algorithm to construct our

tree and the leaf nodes are defined as the node set of convex hull. Finally, we pick up

one node in convex hull as the root of CDS. We can also observe from the tree in Figure

6-6 that, as expected, most of the links near the boundary of network are presented in

our tree, causing most of leaf nodes located at the central area.

Figure 6-6. An example of leaf nodes located at central area. The black nodes consist of
the tree.

Since there is still small probability that the leaf node is at the boundary, not in

central area, if we select such node as the root of CDS, then our technique will fail at

the end. In order to minimize the probability of this unexpected situation, we may sort

the the leaf nodes based on the degree of each node and then pick up the node with

maximum degree as the root of CDS. If there is a tie, a root is selected randomly among

those nodes with maximum degree. The reason to do that is the leaf node in central

area often has more neighbors than the one at the boundary.

To verify the effectiveness of this idea, Figure 6-7 gives a good example. In Figure

6-7, the weight of each link is assigned by Definition 6, and the dotted links denote the

constructed tree, where a and b are the leaf nodes. If we select b as the root of CDS,

then the diameter of CDS will be 5. On the other hand, if a is the root, the diameter will

be only 4, since a is in central area, but b is not. Based on our above idea, we will only

pick up a as the root since the degree of a is larger than that of b.

4 4.
4 4 4
O 5 5,b
4 '.. 6 4
4 5 ..

Figure 6-7. An example of selecting the node with maximum degree as the root of CDS

6.8 Performance Evaluation

In this section, we conducted the simulation experiments to measure multiple

factors of CDS, e.g. size, diameter, fault tolerance and running time, constructed by our

proposed algorithms. First of all, we are interested in comparing the CDSs returned

by CDS-BD-D [34], CDS-BD [38], BDA [88] and PA. As far as we know, CDS-BD-D,

CDS-BD and BDA are the existing algorithms that guarantee the constant performance

ratios on size and diameter, and we will show that PA outperforms CDS-BD-D, CDS-BD

and BDA in most testing cases. Second, we also would like to verify the importance

of locating the center of network and test the running time of BDA and PA to show

the trade-off between performance and running time. Third, we do experiments by


adjusting the user-defined parameter 3 in PA, in order to see how the CDS size and

diameter could be balanced. Furthermore, we evaluate the three proposed improvement

techniques by comparing PA with improvement against PA without improvement. At

last, we test the performance of Algorithm 11 by comparing with PA so that the trade-off

between the fault tolerance and size could be systematically discovered.

In [34], the author first proposed the Average Backbone Path Length (ABPL) as

another factor to evaluate the CDS. ABPL of a CDS has been defined as the sum of

hop distance between any pair of two nodes in CDS divided by the number of all pair of

nodes. In our simulation, we evaluate ABPL in addition to diameter and size, since the

diameter only represents the worst case path length of CDS, ignoring the average path

length, while ABPL captures average path length for message delivery. Therefore, it is

our interests to measure the ABPL of CDS.

To simulate the network, we randomly deployed n nodes to a fixed area of 1,000m x

1,000m. n changed from 10 to 100 with an increment of 5. Each node vi randomly chose

the transmission range r, e [rmi, rmax] where rin = 100m and rmax = 200m. For each

value of n, 1,000 network instances were investigated and the results were averaged.

6.8.1 Performance for CDS-BD-D, CDS-BD and PA

We conducted simulations to compare the performance of CDS-BD-D, CDS-BD and

PA. CDS-BD is a centralized algorithm proposed in [38]. It selects a root randomly and

spans a CDS from the root. The approximation ratios of CDS-BD are 11.4 and 3 on size

and diameter respectively. On the other hand, the authors in [34] proposed CDS-DB-D

that can be implemented in distributed way, however, it only guarantees 4-approximation

on diameter, but 6.906-approximation on size. For the purpose of fairness, we set3 = 3

(the approximation ratio of PA on diameter) in PA.

Figure 6-8A shows that the diameters of CDS built by the three algorithms are easy

to distinguish, since the gap is clear to observe. Also, we notice that PA outperforms


CDS-BD / 60 CDS-BD -*-
12 PA 50 PA -

0 10 1 40

Number of nodes in the network Number of nodes in the network
8 0
8) 30
E 6 (Cl
PA --20
2 10
0 0
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Number of nodes in the network Number of nodes in the network
A Compare the diameter of CDS B Compare the size of CDS

performs better than CDS-BD-D


10 20 30 40 50 60 70 80 90 100
Number of nodes in the network
C Compare the ABPL of CDS

Figure 6-8. Performance for CDS-BD, CDS-BD-D and PA

CDS-BD-D because of the lower approximation on diameter in PA, and CDS-BD also

performs better than CDS-BD-D.

Figure 6-8B provides the performance comparison of the three algorithms on the

size of CDS. It shows PA always constructs a CDS with smaller size than CDS-BD and

CDS-BD-D, which is much better than theoretical analysis we gave in Section 6.6. As

expected, it is reasonable that CDS-BD-D performs better than CDS-BD, since CDS-BD

adds more nodes in CDS to shorten the diameter, which will cause the increase on size,

but the gap between the two curves is not large. Therefore, the performance of PA is

satisfactory on CDS size.

In Figure 6-8C, as the number of nodes in network increases, the CDS returned

by PA always has a lower ABPL than other two CDSs determined by CDS-BD-D and


CDS-BD. Since the better performance of PA on diameter and size, PA is superior to

other algorithms in terms of ABPL.

6.8.2 Performance for BDA and PA

5 BDA BDA ---

3 5 40

6 303
E 2
i:5 20
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Number of nodes in the network Number of nodes in the network
A Compare the diameter of CDS B Compare the size of CDS

3 5 BDA-Mid
3 PA -
2 25
2 2

1 15
10 20 30 40 50 60 70 80 90 100
Number of nodes in the network
C Compare the ABPL of CDS

Figure 6-9. Performance for BDA and PA

The purpose of this simulation is to verify the importance of root selection and

the trade-off between performance and running time at the same time. In order to

highlight the root selection, we use a variation of BDA, called BDA-Mid, as a reference.

Compared to BDA, BDA-Mid selects the center of network as the root instead of

choosing randomly. Also, we include PA in this simulation and is set to 1.

Figure 6-9A compares the diameter of CDS constructed by the three algorithms.

It is shown that, under different number of nodes deployed in networks, the CDS built

by PA has the smallest diameter. We observe that the gap between BDA and BDA-Mid


is shown clearly, which indicates that the CDS could achieves smaller diameter with

locating at the center of network. On the other hand, the difference between BDA-Mid

and PA is small, which highlights an important fact that if the center of network is

detected, the diameter of CDS rooted at the center will be nearly optimal, even using an

algorithm that only guarantees a loose bound on diameter, such as BDA. In order to see

how far the diameter of CDS returned by BDA-Mid from the optimal solution, we set 3 to

1 in PA. Since with P = 1, PA will produce a CDS with minimum diameter in most cases.

In Figure 6-9B, we present the size of CDS obtained from all three algorithms,

depending on the number of nodes deployed. The sizes of CDSs returned by the three

algorithms are close to each other and they all increase with the number of nodes. Also,

considering the same number of nodes, BDA returns a larger size of CDS than PA and

BDA-Mid, although the gaps between these algorithm look small in Figure 6-9B. This

illustrates that the size of CDS can be reduced by choosing the center of network as the


As shown in Figure 6-9C, PA achieves a CDS with smallest ABPL, whereas

BDA-Mid still performs better than BDA. Overall, PA leads the performance on size,

diameter and ABPL due to the center of network. Therefore, it appears to be an

important issue in the construction of CDS.

Table 6-1 summarizes the running time under different number of nodes. As the

complexity analysis indicates, the runtime of BDA-Mid and PA is much longer than that

of BDA. This is due to the long time spent on detecting the center of network. Moreover,

we show in Table 6-1 that the BDA-Mid still runs faster than PA, since PA needs to

compute TSPT to shorten the diameter. When the number of nodes increases, PA and

BDA-Mid spend more time on detecting the center of network. Therefore, it is a tradeoff

between the size/diameter of CDS and running time.


Number BDA BDA-Mid PA PA 3rd Tech.
of Node Runtime Runtime Runtime Runtime
10 0.0001 0.0003 0.0006 0.0003
15 0.0002 0.0012 0.0014 0.0003
20 0.0003 0.0044 0.0046 0.0004
25 0.0004 0.0108 0.0132 0.0032
30 0.0006 0.0236 0.0280 0.0056
35 0.0007 0.0442 0.0536 0.0108
40 0.0012 0.0768 0.0980 0.0232
45 0.0012 0.1222 0.1558 0.0352
50 0.0013 0.1836 0.2372 0.0556
55 0.0014 0.2812 0.3742 0.0956
60 0.0030 0.4016 0.5418 0.1438
65 0.0036 0.5414 0.7378 0.2010
70 0.0040 0.7552 1.0332 0.2832
75 0.0046 0.9842 1.3488 0.3712
80 0.0046 1.3050 1.8086 0.5110
85 0.0050 1.6676 2.3030 0.6450
90 0.0045 2.1294 2.9578 0.8400
95 0.0048 2.6672 3.6630 1.0078
100 0.0060 3.7564 5.2224 1.4856
Table 6-1. Runtime(ms)

10 20 30 40 50 60 70 80 90 100
Number of nodes in the network
A Compare the diameter of CDS

10 20 30 40 50 60 70 80 90 100
Number of nodes in the network
B Compare the size of CDS

Figure 6-10. Performance based on different 3

6.8.3 Performance Based on Different 3

In the above simulations, 3 is fixed. Now we conduct the simulations with different

values of 3. We study the relationship between 3 and the size of CDS and the

relationship between 3 and diameter of CDS. Results are shown in Figure 6-10.


In Figure 6-10A, each line represents the diameter of CDS based on one of different

values of 3. When 3 is set to 1, PA adds a shortest path from v to r if DcDs(r, v) is larger

than DSPT(r, v). Therefore, PA with 3 = 1 returns a CDS with the smallest diameter.

When P is set to 4, PA only adds the path from v to r in TCDS under the condition that

DcDs(r, v) is greater than 4 times of DSPT(r, v). Thus, the CDS by PA with 3 = 4 has the

largest diameter. For 3 = 2, the corresponding line is in the middle. Therefore, as we

expected, the diameter of CDS built by PA could be controlled by adjusting the values of


In Figure 6-10B, each line represents the size of CDS based on one of different

values of 3. When 3 is set to 1, if DcDs(r, v) is larger than DsPT(r, v), PA adds a

shortest path from v to r. This strategy will incur more nodes to be added. On the

opposite, when 3 is set to 4, PA results in a CDS with smaller size. For 3 = 2, the

corresponding line is in the middle, the same situation as in Figure 6-10A. In conclusion,

the performance of PA can be balanced depending on the value of 3 and the tradeoff

between size and diameter is clear.

6.8.4 Performance for Improvement Techniques

5 50

4 40

3 30

2 2 20

PA with 1st and 2nd tech PA with 1st and 2nd tech -
PA without 1st and 2nd tech PA without 1st and 2nd tech
0 0
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Number of nodes in the network Number of nodes in the network
A Compare the diameter of CDS B Compare the size of CDS

Figure 6-11. Performance for the first and second improvement techniques

In this section, we are interested in evaluating the effectiveness of the presented

improvement techniques. Since the first and second techniques are devoted into

reducing the size of CDS, we would like to test them together, whereas the third

technique is performed alone.

Figure 6-11A describes the performance in terms of the diameter of CDS. As we

expected, the diameter is not affected by the first and second techniques. Meanwhile,

as observed from Figure 6-11 B, the size of CDS is reduced when the two techniques

apply. Clearly, we believe that the first and second improvement techniques are effective

in reducing the size of CDS.

5 50

S4 40
3 30
2 N .
.) 20

1 10
PAwith3rdtech PA with 3rd tech -0--
PA without 3rd tech PA without 3rd tech
0 0
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Number of nodes in the network Number of nodes in the network
A Compare the diameter of CDS B Compare the size of CDS

Figure 6-12. Performance for the third improvement techniques

Table 6-1 also summarizes the comparison of runtime by PA with and without the

third improvement technique. Incredibly, the third technique achieves the reduction of

running time greatly, although here it sacrifices a little performance on size and diameter,

as shown in Figure 6-12A and 6-12B, which indicates the trade-off between running time

and size/diameter. However, it is still promising to find the central area in network, in

order to achieve the fast construction of CDS.

6.8.5 Performance for Multi-Factors Model

We are also interested in evaluating the performance of Algorithm 11. We intend to

illustrate that Algorithm 11 improves the fault tolerance of CDS by adding marginal

overhead (in terms of the number of nodes added into CDS). We take the CDS

generated by PA as the input of Algorithm 11, and we set k = 2, m = 1 and 3 = 2.


0 3 / 30
2 320

1 10
Algorithm 1 Algorithm 1 -
0 0
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Number of nodes in the network Number of nodes in the network
A Compare the Diameter of CDS B Compare the Size of CDS

Figure 6-13. Performance for multi-factors model

Figure 6-13A compares the performance of Algorithm 11 and PA in terms of the

diameter of CDS. As we expected, there is little difference on the diameter of CDS

based on the two algorithms, which perfectly matches our theoretical analysis for the

diameter of km-CDS. Therefore, Algorithm 11 enhances the fault tolerance of CDS

without affecting its diameter greatly.

Meanwhile, as observed from Figure 6-13B, the size of km-CDS obtained from

Algorithm 11 is certainly larger than CDS by PA. Specifically, the performance of the

two algorithms is relatively proportional. As observed from our experiments, the size of

km-CDS obtained from Algorithm 11 is almost 1.1 times the size of CDS returned by

PA. The results indicate that considering the fault tolerance will increase the size of the

CDS at the same time. However, the increase in size is still bounded and predictable.

Therefore, it is clear to see the trade-off between the fault tolerance and size.

6.9 Conclusions

In this chapter, we introduce the multi-factors model studying a joint optimization

problem in which the objective is to reduce the CDS size, network latency and running

time while keeping the fault tolerance of CDS as well. Building on this model, we

provide an approximation algorithm with constant ratios as the solution. After that, an

algorithm for CDS construction that guarantees the best approximation on diameter


is provided. More importantly, the progressive algorithm, featured with a tunable and

outstanding performance, is addressed in details as an input of our model. In addition,

we present improvement techniques for progressive algorithm that systematically reduce

running time or size of CDS. Simulation results show that our algorithms can gain good

trade-offs among these factors, which coincide with theoretical analysis.

Many research problems remain open. Our simulation is preliminary, and stronger

results may allow us to better predict and find out the trade-offs among the factors

of CDS. A better understanding of probability and graph theory may yield localized

algorithms and better performance. But, even with our current model, theoretical

analysis and simulation show large improvements over previous solutions.


This dissertation investigates a novel approach against the reactive jamming attack

by identifying triggers and building virtual backbone based on the detection. In other

words, the proposed approach consists of two main parts including identification of

all trigger nodes to quarantine jammed areas and construction of virtual backbone to

de-route the region.

First of all, two identification schemes are introduced, centralized and decentralized

algorithms. The proposed centralized identification procedure shows several benefits

of detecting trigger nodes in practical multiple-radio WSNs. By utilizing nonadaptive

group testing scheme, disjoint disk cover method, and clique-based clustering, this

countermeasure achieves low overhead in terms of time and message complexity, thus

is practical for general WSNs. Also this work proposed the first localized algorithm

to identify triggers in networks. Due to its localization and simplicity the algorithm is

well-scalable. In addition, to against more sophisticated jammers that randomly react to

signal we also devise an efficient fault-tolerance algorithm in both algorithms.

Secondly, in order to construct effective virtual backbone not only for jamming

resistant routing protocol but also for efficient broadcasting/multicasting routing, this

dissertation investigates dominating tree and multi-factor model with approximation

algorithms in wireless ad-hoc networks. DT problem can help each node in the

network to construct its own broadcast tree with small amount of message overhead.

Furthermore, since there are several important factors that need to be fully investigated

for broadcast latency and fault-tolerant routing protocol in the networks, this dissertation

designed multi-factor models for a fault minimum size CDS with bounded network

latency and the low running time for a feasible solution.


Theoretical analysis and simulation results endorse the scalability and efficiency

of our new approach against reactive jamming attack in terms of latency and message




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Incheol Shin was born in 1977, in Seoul, Republic of Korea. He received Bachelor

of engineering degree at computer engineering in 2002 from Hansung University, Seoul,

Republic of Korea. In 2006, he received his Master of Engineering degree from the

Department of Computer and Information Science and Engineering at the University of

Florida. His major research area is computer networks.





Mostofall,IwouldliketoacknowledgemychairadvisorDr.MyTraThai.FromthemomentIstartedtoworkwithher,shehasencourageme,guidedmethroughalltheresearches,andgavemeinvaluableadvices,suggestionsandsupportstopursuethisdegree.Iamheartilythankfultothemembersofmysupervisorycommittee,Dr.RandyY.C.Chow,Dr.TamerKahveci,Dr.PrabhatMishraandDr.PanosM.Pardalos,fortheirguidanceandmentoring.Finally,Iwouldliketoshowmygratitudetomyfamilymembers. 3


page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INTRODUCTION ................................... 12 1.1ReactiveJammingAttacksinWSNs ..................... 12 1.2IdenticationofTriggerNodes ......................... 13 1.3ConstructionofRoutingBackbone ...................... 14 1.4Organization .................................. 15 2JAMMINGATTACKS ................................. 16 2.1EffectivenessofJammers ........................... 16 2.1.1PacketSendRatio(PSR) ....................... 16 2.1.2PacketDeliveryRatio(PDR) ...................... 18 2.2JammingAttackModels ............................ 19 2.2.1ConstantJammer ............................ 19 2.2.2RandomJammer ............................ 21 2.2.3DeceptiveJammer ........................... 22 2.2.4ReactiveJammer ............................ 23 2.3ExistingSolutions ............................... 25 2.3.1PhysicalLayerApproaches ...................... 25 2.3.2LinkLayerApproaches ......................... 31 2.3.3NetworkLayerApproaches ...................... 35 2.4Conclusion ................................... 36 3CENTRALIZEDIDENTIFICATIONOFTRIGGERNODES ............ 37 3.1NetworkModelandProblemDenition .................... 37 3.2Preliminaries .................................. 39 3.2.1MaximumCliqueProblem ....................... 39 3.2.2Non-AdaptiveGroupTesting ...................... 39 3.3CentralizedTriggerNodeIdentication(CTNI) ................ 40 3.3.1GroupVictimNodesBasedonMinimumCollectionofDisjointDiskCovers(GVN-MCDDC)Algorithm ................... 41 3.3.2DetectionofTriggerNodesBasedonNon-AdaptiveCombinatorialGroupTesting(DTN-NCGT)Algorithm ................ 41 3.4TheoreticalAnalysis .............................. 45 4


45 3.4.2Correctness ............................... 47 3.4.3PerformanceAnalysis ......................... 48 3.4.4RandomReactiveJammingModel .................. 50 3.5TheTNLT-CDSRoutingAlgorithm ...................... 51 3.6PerformanceEvaluation ............................ 52 3.6.1SimulationSetup ............................ 52 3.6.2ResultsandAnalysis .......................... 55 55 55 56 ........ 56 ... 57 3.7Conclusion ................................... 57 4LOCALIZEDIDENTIFICATIONOFTRIGGERNODES .............. 59 4.1NetworkModelandProblemDenition .................... 59 4.2OverviewandFundamentalResults ..................... 60 4.2.1OverviewofIdenticationProcedure ................. 61 4.2.2HexagonTilingColoring ........................ 62 4.2.3Thek2-ColoringAlgorithm ....................... 63 4.3LocalizedTriggerNodeIdentication(LTNI) ................. 65 4.3.1PartitionofNodesBasedonHexagonTilingandColoring ..... 65 4.3.2TriggerNodesDetectionProcedure .................. 68 ............. 68 .. 69 4.4TheoreticalAnalysis .............................. 70 4.4.1UpperboundonTestingRounds .................... 70 4.4.2MessageComplexity .......................... 72 4.4.3RandomReactiveJammingModel .................. 73 4.5TheTNLT-CDSRoutingAlgorithm ...................... 74 4.6PerformanceEvaluation ............................ 74 4.6.1TestingRoundsT 76 4.6.2Messagecomplexity .......................... 78 4.6.3Runtime ................................. 81 4.6.4Thenumberofnodesinquarantineareas .............. 83 4.6.5Randomreactivejammers ....................... 83 4.7Conclusion ................................... 84 5CONSTRUCTIONOFDOMINATINGTREE .................... 86 5.1OverviewofDominatingTree ......................... 86 5.2HardnessandApproximation ......................... 87 5.2.1Inapproximability ............................ 87 5


.................... 89 5.3HeuristicAlgorithmandAnalysis ....................... 91 5.3.1AlgorithmDescription ......................... 92 5.3.2RuntimeComplexity .......................... 94 5.4PerformanceEvaluation ............................ 95 5.5Conclusion ................................... 99 6CONSTRUCTIONOFVIRTUALBACKBONEWITHMULTIPLEFACTORS .. 100 6.1OverviewofVirtualBackbone ......................... 100 6.2RelatedWork .................................. 102 6.2.1GeneralGraph ............................. 102 6.2.2UnitDiskGraph ............................. 103 6.2.3DiskGraphswithBidirectionalLinks ................. 104 6.2.4OtherResultsinCDS ......................... 104 6.3WirelessCommunicationModelandPreliminaries ............. 105 6.3.1Notations ................................ 105 6.3.2Terminologies .............................. 105 6.3.3Denitions ................................ 106 6.4Multi-FactorsModelandSolutions ...................... 106 6.5ABetterAlgorithmforCDSonDiameter ................... 109 6.6ProgressiveAlgorithm(PA)andAnalysis ................... 113 6.7FurtherImprovementsforTheProgressiveAlgorithm ............ 119 6.7.1ReducingMultiplePaths ........................ 120 6.7.2RemovingRedundantTerminals ................... 121 6.7.3LocatingCentralArea ......................... 123 6.8PerformanceEvaluation ............................ 125 6.8.1PerformanceforCDS-BD-D,CDS-BDandPA ............ 126 6.8.2PerformanceforBDAandPA ..................... 128 6.8.3PerformanceBasedonDifferent 130 6.8.4PerformanceforImprovementTechniques .............. 131 6.8.5PerformanceforMulti-FactorsModel ................. 132 6.9Conclusions ................................... 133 7CONCLUSION .................................... 135 REFERENCES ....................................... 137 BIOGRAPHICALSKETCH ................................ 145 6


Table page 3-1Notations ....................................... 38 6-1Runtime(ms) ..................................... 130 7


Figure page 2-1Constantjammingattack .............................. 19 2-2Randomjammingattack ............................... 21 2-3Deceptivejammingattack .............................. 22 2-4Reactivejammingattack ............................... 23 3-1Sinceitem6(6thcolumn)isatriggernode(positiveitem),onlythe2ndand6thgroups(rows)returnnegativeoutcomes.Onthecontrary,allotherfourgroupsproducepositiveoutcomes. ........................ 44 3-25Possiblejammersactivatedbyatriggernodet 46 3-3Experimentalresultsbyvarioussizeofjammers ................. 52 3-4Experimentalresultsbyvarioussizeofchannels ................. 53 3-5Experimentalresultsbyvarioussizeofnodes ................... 53 3-6Experimentalresultsbyvariousnetworkdensities ................ 54 3-7Experimentalresultsbyvarioussizeof 54 4-1Theminimumdistancebetweentwonodeswithsamecolor ........... 64 4-2Thecoloringpatternfork=4 65 4-3Triggernodesinahexagon ............................. 71 4-4Roundsbyvariousparameters ........................... 76 4-5Messagesbyvariousparameters .......................... 77 4-6Runtimebyvariousparameters ........................... 78 4-7Nodesinquarantineareasbyvariousparameters ................ 79 4-8ThenumberofroundsTinrandomreactivejammingmodelwithdifferentvaluesofjammingprobabilityP. .............................. 80 5-1ReductionfromWDSGtoDTG0 89 5-2AnexampleofreductionfromGtoG' ....................... 90 5-3TheexecutionofHeurDTalgorithm ......................... 93 5-4SimulationresultsforHeurDT,MST-Landoptimalresults ............ 96 8


....................................... 106 6-2Anexampleforsecondphaseinalgorithm 12 ................... 112 6-3AllthenodesintheringareaCDSwithdiameterof8 .............. 117 6-4Anexampleforreducingmultiplepath ....................... 121 6-5Anexampleforremovingredundantterminals ................... 122 6-6Anexampleofleafnodeslocatedatcentralarea.Theblacknodesconsistofthetree. ........................................ 124 6-7AnexampleofselectingthenodewithmaximumdegreeastherootofCDS .. 125 6-8PerformanceforCDS-BD,CDS-BD-DandPA ................... 127 6-9PerformanceforBDAandPA ............................ 128 6-10Performancebasedondifferent 130 6-11Performancefortherstandsecondimprovementtechniques .......... 131 6-12Performanceforthethirdimprovementtechniques ................ 132 6-13Performanceformulti-factorsmodel ........................ 133 9






8 ].Jammingattacks,oneoftheDoSattacks,especiallyarelightweighted,butthemostfatalthreatstoWSNs,becausetheyattackthecoreofwirelessbroadcastadvantageevenwithoutmodifyingcommunicationpacketsandcompromisingwirelesssensordevices.Duetotheexcessivehardwarerequirementonexistingmethods,threatscannotbeneutralizedandnulliedwithconventionalsecuritysolutions. 12


78 ].Secondly,incasetriggernodesneedstosendmessages,they 13




2 describestheevolutionofjammingstrategiestoreactivejammersandexistingcountermeasureagainsttheattacks.Fortheidenticationphase,Chapter 3 providesthesolutionforcentralizedidenticationoftriggernodes,meanwhilethelocalizedalgorithmforthedetectionoftriggernodesispresentedinChapter 4 .OurproposednewproblemofdominatingtreestudiedinChapter 5 followedbythemulti-factormodelinChapter 6 soastoprovidetheefcientconstructionofjammingresistantroutingprotocol.Chapter 7 concludesthisdissertation. 15


52 55 69 84 86 ]describingjammingattacksbasedonthesemeasurements.Inthissection,theimportanceofjammingattacksandhowpowerfultheyarewillbeintroducedastheyapplytoPSRandPDR. IntendedToBeSentPacketsInmostMAClayersinWSNs,carriersensingmultipleaccess(CSMA)controlhastobeperformedbeforelegitimatecommunicationsinsendernodes.Thatis,senderdevicesarerequiredtosenseactivityinthechannelforacertaindurationoftimebefore 16




ReceivedPacketsACyclicRedundancyCheck(CRC)isasimplenon-securehashfunctionfordetectionoferrorsincommunicationmessages.UsuallytheCRCcomputationwouldbedoneinthelinklayerbyalongdivisionoperationwherequotientsarediscardedandremaindersfromtheoperationbecomestheresultsoftheCRC,whichareappendedtotheendoflinklayerframes.ReceiverswouldbeabletodecodeandvalidatereceivedpacketswitheasebyutilizingtheCRCcheck.ThePDRratiodropsifjammersinjectinterferencesignalsintocommunicationmessages.Ajammerwouldbeabletodecreasethenumberofpacketsthataresuccessfullydeliveredtodestinationnodesbycorruptingongoingcommunicationpackets.Duetothebroadcastingnatureofwirelesscommunications,collisionsamongpacketsareconsideredacriticalproblem,andthejammersattackthePDRfromtheviewpointofthisweaknessbycorruptinginterferencesignals.AttackingthePDRnotonlydropsthePDR,butalsowastestheenergyofsensornetworksduetothefactthatcollidedmessagesrequireretransmission.Thesensornetworksareresource-limitednetworks,andenergyconsumptionhasbeenmuchstudiedbecauseitdominatesthenetworklifetime.Inotherwords,invalidationofpacketsbyCRCcheckingimplyretransmissionsinsendernodesafternoticationsfromreceivers,whichwastessignicantlyenergyandresultsinashorternetworklifetime.Asaresult,wecansaythatattackingthePDRfromjammerscausesmoreseriousproblemsthanattackingthePSR.Inaddition,intermsofstealth,itwouldbebetterforjammerstodropPDR.ItwouldnotbenecessaryforjammersattackingPDRtoexposethemselvestolegitimatenodes 18


Constantjammingattack AccordingtotheFig. 2-1 ,theconstantjammer,atrivialjammer,isthemostintuitivestrategytoimplement,butithastheleastenergyefciencyamongalljammerssinceitdoesnotfollowtheprotocolsinWSNs,justemittingaseriesofnoisesignalsintothe 19




Randomjammingattack 2-2 ,therandomjammerhasevolvedfromtheconstantjammertoconserveenergy.Liketheconstantjammer,itemitsjammingsignalsforacertainamountofthetime,butsleepsafterturningitsradiooffinordertoconserveenergyforalongerlifetimeofjamming.Whiletheswitchingmechanismbetweensleepingmodeandjammingmodecansaveasignicantamountofenergy,itwoulddroptheefciencyofattacktoPSR.Because,duringitsjammingphase,normalsenderswouldnotbeabletotransmitmessagesforchannelactivitiesunderjammingsignalsandwouldhavetowaituntilitssleepingphasebegins.Theycouldsendoutthestalledmessagesduringthejammingphase,andmostofthemessageswouldbesuccessfullydeliveredwithoutinterferenceduringthejammers'sleepingmode.Thisbecomesatrade-offbetween 21


Deceptivejammingattack BymonitoringtheprotocolsinWSNs,thisisthersttypeofjammerthattakesthestealthofjammersintoconsideration.ThedeceptivejammerinFig. 2-3 doesnotsendoutrandombitsorwaveformsbyagenerator,butregularpacketsinordertocapturethechanneloflegitimatecommunicators.Thedeceptivejammersemittingregularpacketsforceslegitimatecommunicatorsintothereceivingstateandpreventsthemfromconvertingtheirstateintosendmode.Thismethodwasinitiallyimplementedbycontinuouslysendingoutpreamblemessages,sothatitishardtodetectandisaneffectivemethodtodisableaCSMA.ThedeceptivejammernotonlywoulddropthePSR,butalsoincreasethestealthagainstthedetectionsystembytransmittingregularframesintoaMAC-layerchannel. 22


2 ]alsomentionsaperiodicjammer,anotheradaptationofdeceptivejammer.Insteadofsendingoutcontinuouspreamblemessages,itgeneratesaseriesofshortpulsesineveryDIFSinterval(50nanosec),sonormalnodesndthenetworkalwaysbusy. Reactivejammingattack Reactivejammingattacksareconsideredoneofthemostintelligentjammingstrategiesduetotheirreactivebehavior.ThereactivejammingattackinFig. 2-4 is 23


2 ]withknowledgeoftheprotocolsisoneoftheimplementationsofareactivejammeranditcanhaveseveraldifferentstrategiestocorruptmessages,includingcontrolmessagesanddatamessages.Importantly,itwouldbeabletodistinguishbetweencontrolmessagesanddatamessagesbasedonthelengthofeachcommunicationmessageortheintervalsbetweentheminWSNs.Accordingtothejammingstrategies,therecouldbefourtypesofintelligentjammingattacks,suchasCTScorruptionjamming,Acknowledgecorruptionjamming,datacorruptionjamming,andDIFSwaitjamming. 24


7 26 31 32 35 37 43 47 61 70 78 83 85 87 ],butthehighcomputationaloverheadofthesemethodsbadlyreducestheeffectinresource-limitednetworkenvironments,suchasWSNs.Forexample,inthechannelsurngmethodsfrom[ 7 35 37 47 78 83 85 87 ]andfrequencyhoppingmethodsfrom[ 26 31 32 36 43 58 61 70 ],thetransmissionfrequencyorchannelischangedtoarangewherethereisnointerferencefromtheadversaries.ThesestrategiesarenotquitesuitableforWSNs,especiallyinmulti-channelWSNs,sincethesensorshavetoscanallthechannelstodetectthejammingattacksandhoptonewfrequenciesallthetime,eveninthemiddleofacommunication.Duetothefactthatmostofthesensornodeshaveahalf-duplextransceiveronthem,scanningthechannelsduringtransmissioncausescommunicationstallstochecktheavailabilityofthecurrentchannel.Frequentcommunicationstallsresultinalongertransmissiondurationandmoreenergyconsumption.Consequently,thesemethodscannotavoidhighoverheadandresourceconsumption. 25


26 31 32 36 43 58 61 70 ]andcodedivisionmultipleaccess(CDMA)[ 14 21 30 53 76 89 ],formsofdirectsequencespread-spectrumcommunication.Sincemostjammingattacksarecategorizedintophysicallayerattacks,thebeginningofthedefensemechanismsstartinthephysicallayer.Thissectionwillintroduceexistingphysicallayercountermeasuresagainstthejammingattacks.Thefrequencyhoppingtechniquewasdesignedasakindofsecuresolutionagainstjamming,eavesdropping,tempering,etc,inwirelesscommunication.JammingattacksareabletoattackWSNswithpartial-bandnoiseatthebeginningstageofjammingattacks,andthefrequencyhoppingsolutionisutilizedtodefendagainstthejammerswithpartial-bandnoiseatthattime.TheinitialoutlineoftheconventionalFHmethodistouseeachfrequencyslottotransmitpacketsthroughoneoforthogonalsignalsduringacertainperiodoftime,signalinginterval.Thatis,thetransmitterhopsbetweensafefrequenciesbasedonapredenedalgorithms.However,themostimportantissuetoexploitfrequencyhoppingtechniqueishowtosecretlyestablishswitchingsequencesbetweentwocommunicationpartiesinordertofoilathirdparty.Thatis,reducingtheprobabilityofinferenceisthekeyofthistechniqueagainstjammingattacks.Apre-sharedsecretcodeforFHisnotfeasibleinwirelesscommunicationnetworksduetothedynamicbehaviorofsensornodesandthescalabilityofthenetworks.SincethemainissuesofFHapproacharehowtoassignthehoppingsequencesforshiftingfrequenciesandhowtosynchronizethemamongthenodes,therehasbeenmuchresearchregardingthosecriticalissuesinFHmechanisms.Toremovetheburdenofdistributingsequences,[ 61 ]proposedtheuncoordinatedfrequencyhopping(UFH)techniqueforananti-jammingpoint-to-pointschemetoestablishasecretekeybetweentwocommunicationparties.Thispaperintroduced 26


42 ]hasbeenintroducedtoachieveamorespectralefciencythananyotherexistingFHdesigns.Inthetraditionalmodels,FHtechniquesrequireamuchwiderspreadbandwidththantheyactuallyusetotransfermessages,whichmeansthespectralefciencyfromthetotalnumberofavailablecarrierfrequenciesistoolowinpracticalnetworkenvironments.[ 42 ]presentedaninnovativeformofMDFHthatexploitedmessagestreamsasapseudo-randomsequenceforFHselection.Thedatastreamisdividedintomultipleblocks,andeachblockconsistsofadditionalcarrierbitvectorstodeterminethehoppingfrequenciesandordinarybitvectorsthatareactualdatatotransmit.AcarrierbitvectorhasBctospecifyahoppingfrequencytotransferthedataandNhthenumberofhopswithinasymbolperiod.Thedatablocksarefedintoaserial-to-parallel(S/P)converterinordertosplittwocarrierbitsandordinarybitsintotwoparalleldatastreams.Inaddition,thispaperpresentedenhancedMDFHtoutilizemultipletransmissionsateachhopbyexploitingalltheavailablecarriers.Thissolutionhelpstoincreasetheresistanceagainstjammingattacksusinganunpredictablemessage-drivenhopping 27


26 31 32 36 70 ],nocompletesolutiontotheproblemoffollowerjammingattackshassofarbeenreached.Thefrequencyhoppedm-aryfrequencyshiftkeyed(FH/MFSK)wasdesignedasacountermeasureagainstapartial-bandnoisejammer[ 36 ].TheimplementationofFH/MFSKutilizesMnon-overlappingfrequencysynthesizersineachtransmitterandreceivertohopeachMFSKsignalsincetheperformancefromconventionalFH/MFSKimplementationisgreatlyeffectedbythedeviationofasinglecarrier.However,thisapproachrequirescomplicatedhardwaretorealizeinapracticalsystem,whichisnotinfeasibleforresource-limitedsensornetworks.[ 31 32 ]introducedadifferentapproachasacountermeasureevolvedfromFH/MFSKagainstfollowerjammers.Themultipleorthogonalsignalsduringacertaintimeperiod,signalinginterval,wouldbeemittedineachfrequencyslotthatisdividedfromtotalspreadbandwidth.Furthermore,thereisconventionalmodeandunconventionalmodeinordertosynchronizecommunicators.Inthecaseofconventionalmodefrompseudo-randomprobabilityofpcinbothsendersandreceivers,areceiverwoulddeterminethe 28


89 ]wasdesignedtobeimmunetoaninterferencesignal,butthisrequiressophisticatedmodulatinghardwareinthesensors.ThemainissueoftheDSSStechniqueisalsosecretkeysharingduetothefactthattheperformanceofsuppressioncapabilityislimitedbythepseudorandomgeneratorwiththekeysamongcommunicators.Thekeyestablishmenttodriveidenticalspreadingcodesamongthecommunicatorsisacriticalissueforthewirelessad-hocnetworksintermsofscalability.ThesecretsfortheDSSScommunicationbetweenthesenderandthereceivershavetobeinagreementbeforethestartoflegitimatecommunications,butthispre-sharedsecretkeyhasbeenconsideredadifcultproblemtosolveduetothedynamicbehaviorofsensors.[ 53 ]proposedasolutioncalledUncoordinatedDSSS(UDSSS)forauthenticspreadspectrumanti-jammingcommunicationinordertosolvethekeysharingproblem.ThisapproachenablestheimplementationofDSSSwithoutpriorestablishmentofsecretkeysamongthecommunicators,andreceiverskeepacerticateofthesender'spublickeyinsteadofsharingsecretkeys. 29


14 ]relatedtoutilizingthedirectsequenceCDMA(DS-CDMA),resortstohigh-powerdynamictree-remergingschemestomaintainthesmallnumberoforthogonalcodesinuseandtoavoidre-calculationofthecodes.SpreadspectrumcommunicationhasbeenstudiedtoresistjammingattacksinunicastcommunicationbecausethenumberofcodesgreatlyeffectstheperformanceofDSSS.[ 14 ]developedabroadcastingtechniquewithaDSSSschemewithfewernumberofcodesbyusingabinarykeytree.Duetothevariationinnodesindynamicenvironments,thismethodsuffersfromtheadditionalmaintenanceoverheadofjoin-inandleavingbehaviors,especially,socomputationoforthogonalcodestakesmuchtime.Inaddition,becauseoftheprobabilisticnatureofpacketreception,italsohasaproblemoffalsealarms,andasasolutionforfalsealarms,networksareperiodicallyrequiredtoresettheircodeineachsensorandbuildthecodetreerepeatedly.Thisseriesofreconstructionproceduresnecessitateshighmessagecomplexityandadditionalcomputationoverheadonthenetworksaswell.Intheserespects,aschemewithcryptographickeymanagementhasascalabilityproblemandastabilityproblemwhenappliedtovariousdynamicnetworks. 30


30 ]aswellsincetherepeaterjammerstrytoacquirethecodebymonitoringtheon-goingtrafcandgarblethecommunicationmessagesbasedontheacquisitionofthecode.[ 76 ]haveanalyzedDSSStechniquesattackedbyrepeaterjammersindetail,butsofartherehasbeennocompletesolutionforrepeaterjammingattack.Duetothenatureofajammingattack,mostdefenseschemesstartfromthephysicallayer,FHandDSSS.FHmethodsfrom[ 26 31 32 36 43 58 61 70 ]hopcommunicationfrequenciesseekingasafeoneinordertoavoidthejammedcommunicationsbasedontheswitchingsequences.Howtodistributethehoppingsequenceandsynchronizecommunicationpartnerswiththenewsequencesarethemainissuestoovercomelowspectralefciency.CodeDivisionMultipleAccess(CDMA)schemecommunication[ 14 21 30 53 76 89 ],aformofdirectsequencespreadspectrumisalsooneofthemostcommonwaytoresistjammingattacks.However,theproblemofhowtomanagesecretkeysforefcientsuppressioncapabilityhastobesolvedforbetterperformanceofimmunityagainstattackinresource-limitednetworks. 7 35 37 47 78 83 85 87 ]regardingtheinvestigationofjammingattackfromtheviewpointoflinklayers.Inthissection,wedescribevarioustypesofevasiontechniquesinthelinklayer.EventhoughthechannelsurngmethodintheMAClayerwasmotivatedbyFH,itisthemostreactiveapproachbecauseitswitcheschannelsondemandaftervericationof 31


83 ]introducedthechannelsurngstrategy,suchthatwhenthenodeswithdetectionsensorsarejammed,theyswitchtheircommunicationchannelintoanotherorthogonalchannelinordertoreconnecttotherestofanetwork.Theboundarynodesthatlosetheirneighborsfromajammingattackcandiscoverlostneighborsinnewchannelsandtrytorebuildtheconnectivityoftheentirenetwork.Therearetworeasonsnodeslosetheirneighbors,poorconnectivityandjammingattacks,andtheyprovidesimpleprotocoltoidentifythereasonforthelostneighborsbyanalyzingthechannelbeingusedforreconstructionbythelostneighbors.However,thisprotocolforcesnetworksintoanunstablestateduringconnectivityrebuildingduetofrequentlinkqualitydegradationsorthedynamicbehaviorofnetworks.Twomethodshavebeenproposedinordertorestorenetworkconnectivityafterattacks.Therstisthecoordinatedchannelswitchingtechniquewhenanentirenetworkswitchesitscurrentchanneltoanewchannelsoastoreconstructnetworkconnectivity.Thistechniquesuffersfromunreliablelinks,sothatsomenodesmightmissthenoticationtoshifttheirchanneltoanewone.Thesecondapproachisthespectralmultiplexingtechniquewhereboundarynodesactasbridgestoconnectthenodesofoldchanneltothenodesofnewchannel.Thisapproachenablesthenetworkstomaintainmultiplechannels,sothattheentirenetworkdoesnotneedtonotifyallnodes,justsome,toswitchtoanewchannel.Thereare,however,severalchallengingproblemstorealizingapracticalsystem,synchronization 32


87 ]alsodescribedaspatialretrievalmethod,calledaphysicalevasionmethod,byphysicalrepositioningofmobilenodesoutofjammedregions,butthenetworkswouldbeunbalancedandevenisolatedbytheattacks.Sincetheyassumestationaryjammerswithmobilenodes,thenodeswithinajammedregionwouldbeabletoescapefromthejammedregionafterthepresenceofjammerswasdetected.Thechallengingissuesofthephysicalevasionmethodarehowtodeterminewhichdirectionsnodesshouldretreatandhowfartheyshouldretreatfromtheircurrentpositions,becausethesedecisionsmaycausedisruptionofnetworkconnectivity.Inaddition,thispapermentionedjammednodesmovingintoradiorangeafterrelocations,butthiswouldresultinshorternetworklifetimeaswell.Asanothertypeofevasiontechnique,[ 85 ]designedatimingchanneltorecoverreliablecommunicationlinksafterjamming.Thetimingchannelisalow-ratelayeroverphysical/link-layersusedtodetectthetimingofinterferedpacketsinthereceiversbyutilizingCRCcheckormonitoringsignalstrength.Thisapproachisforpoint-to-pointcommunicationlinks,notforbroadcastcommunications.Thecriticaldependenciesofthetimingchannelschemearehowtodetecttheexacttimingofthefailurepacketreceptionsandhowtomaptheoccurrenceoffailedpacketstotheinformationtobedelivered.[ 7 ]proposedajamming-resistantMACprotocolthatadjuststheprobabilityforsuccessfultransmissionbymonitoringchannelactivities,andeachnodewouldbeabletotransmitmessagesbasedonprobability.Theprotocolalsodividesthetimeintosmallerorbiggertimeintervalsaccordingtosuccessfulmessagetransmissionsinordertoadapttransmissiontime.Themainideabehindthisisthatadversariesobservetheactivityofthecurrentchanneland,ifthereisnotenoughactivity,theywouldnotheavilyjamthechannel.However,thisprotocolshouldincludeamechanismtodeterminesuccessfultransmissionsofmessagesinremotenodes,whichmeansthatother 33


78 ]inordertoreducethedamagefromjammingattacksoncommunicationpackets.TheyintroducedseveralstrategiestodefendtheMAClayeraccordingtothetypeofattack.Forexample,framemaskingagainstaninterruptingjammingattack,channelhoppingagainstanactivityjammingattack,packetfragmentsagainstascanjammingattack,andaredundantencodingmethodagainstapulsejammingattack.FramemaskingisaDSSStechniqueusingsharedkeysbetweenwirelessnodes.Thepacketfragmentationmethodwouldbeusedtotransmitamessageinmultiplefragmentsduringajammer'schannelactivityscanning,andtheredundantencodingmethodisusefulforthereceivertorecovercorruptedmessagesduetojammingattacks.TheywanttocombineallthesetechniquesintoaMAClayerprotocoltodefeatjammingattacks.Thefundamentallimitationsoneachdefensemechanismareremained.Thatis,framemaskinghasaproblemofkeydistribution,andchannelsurnghasserioussynchronizationprobleminpracticalsystemasdescribebefore.Packetfragmentationmethodmightdivideapacketintotoosmallfragmentswithadditionalredundantencodingdataforrecovery,whichmakestheapproachunfeasibleinrealcommunicationsystems.Therehavebeentwomainapproachestojammingattacksinthelinklayer,channelsurngandmodicationoftheMACprotocol.Bothbelongtoacategorycalledevasionmethods,andutilizethejammers'scanningtimetotransmitlegitimatemessages.Channelsurngschemesfrom[ 83 85 87 ]arereactiveintermsofswitchingchannels,butsynchronizationisacriticalissuetoimplementinapracticalsystem.ModicationofMACprotocolschemesrequireadditionalcommunicationoverheadamongthe 34


77 ].Inthissystem,thejammednodescooperativelymapajammedregion.Jammednodesthatarewithinajammedareatransmitmultipleblindmessagestoannouncetheirjammedstatustothemappingnodesthatarenotinthejammedarea,buthavejammedneighbors.Themappingnodescommunicatewithothermappingnodestoisolatethejammedareaandtoidentifybridgenodes.Thebridgenodesparticipateinrelayingmessagesaroundthejammedarea.Onedeciencytothisapproachwouldbethepossiblyunnecessarilylargejammedregionbuiltagainstthereactivejammingattack.Asaresult,partsofthenetworkmightbeisolated.Thisisbecausemanynodesintheexaggeratedlylargejammedregionmaystillbeabletotransmitwithoutactivatingthejammers,yettheyareisolatedandthemessagedeliveriesareinterrupted.Duringthemappingprocedureamongthemappingnodes,theprotocolrequiresanexcessivenumberofcommunicationmessagestobuildadetourroutearoundthejammedregion.Themultipletrafctopologiesfrom[ 62 ]couldbeusedtoevadethejammednodesunderattackfrommobilejammers.Themobilejammersinthispaperwouldbeabletoidentifythecriticalbroadcastingpathsinordertopreventdownlinknodesfromreceivinganymessages.Thenodescooperativelyconstructthemultiplepathsandselectapath 35


63 ]designedalinearprogrammingmodelforaspecictypeofthejammingattack,butitfocusesmainlyonaow-basedattackwithoutconsideringofaprotocol-basedattackmodel.Unfortunately,thismightnotapplytogeneraljammingattacks.[ 16 ]investigateanefcientschedulingtechniqueforbroadcastingmessageswhenunderajammingattack.Thisapproachshowsgoodperformanceonlywhentherearepowerlimitationonjammers,whichmightnotbeapracticalassumptionsinceusuallythejammersaremuchstrongerthanthenormalnodesinWSNs. 36


22 23 ]couplingwithminimumcollectionofdisjointdiskcoverbasedgrouping,thissolutioncanidentifyallthetriggernodeswithlowoverheadintermsofrunningtime,computationandmessagecomplexity.Thetheoreticalanalysisandexperimentalresultsshowthatoursolutionperformswellintermsoftimeandmessagecomplexities,whichprovidesagoodapproachtodefendreactivejammingattacks. 37


3-1 Table3-1. Notations Meaning n ni nij U k H()


9 ].Sofar,thebestpolynomial-timeapproximationalgorithmforthemaximumcliqueproblemwasdevelopedbyBoppanaandHalldorsson[ 9 ],andachievedanapproximationratioofn(1o(1)).In[ 9 ],Hastadshowsthatthisisactuallythebestwecanachieveanditcannotbeapproximatedwithinafactorthatofn1forany>0.Therearesomeotherresultsintheliteratureconcerningtheapproximationofthemaximumcliqueproblemonarbitraryorspecialgraphs[ 9 10 29 ].Inthischapter,themaximumcliqueproblemisappliedtoobtaintheupperboundofthenumberoftriggernodesbasedonthenumberofreactivejammers.Sinceajammercanonlybeactivatedbythenodeswithinacertaindistance,wecanconstructaunitdiskgraphofallnodeswiththeradiustwicethedistancetoestimatetheupperboundofthenumberoftriggernodes. 22 23 ]methodsaretominimizethetestingperiodbysophisticatedlygroupingandtestingtheitemsinpoolssimultaneously,insteadofindividuallytestingthem.Thewayofgroupingisbasedona0-1matrixMtnwherethematrixrowsrepresentthetestinggroupandtheeachcolumnrefersanitem.M[i,j]=1impliesthatthejthitemparticipatesintheithtestinggroup,andthenumberoftestingisthenumberofrows.Theresultofeachgroupisrepresentedasanoutcome 39


23 ],wheretheunionofanydcolumnsdoesnotcontainanyothercolumn.Basedonthepropertiesofd-disjunctness,thedecodingalgorithmtoidentifythetriggersbasedonthetestingresultsbecomesverysimple.Wejustneedtoremovealltheitemsappearedinanynegativepoolsandtheremainingitemarepositive[ 23 ].Inthisway,onlyO(1)testingroundsandO(tn)decodingtimeareneeded.ToutilizeGTforourtriggerdetection,weneedtosolvethetwomostchallengingproblems:(1)Howtogroupthenodestoavoidinterferencebetweentheresultsamonggroupssoastotestthesegroupssimultaneously.(Anytwogroupsarecalledinterferencefreeifanyjammerstriggeredbyeithergroupcannotjamtheothergroup).(2)Howtoaccuratelyestimatethevalueofdwhichistheupperboundofthenumberoftriggernodes.Sinceddeterminesthenumberoftests,thetighterdis,thebettertimeandmessagecomplexitieswecanobtain. 60 ].Thenwetestthesevictimstoidentifythetriggernodesbycallingtwosub-procedures:1)WeusetheGVN-MCDDCalgorithmGroupVictimNodesBasedonMinimumCollectionofDisjointDiskCovertogroupasmanyasvictimnodeswithoutinterferencewitheachotherineachcover.Eachcoverincludesasetofdisjointdiskswherethecenterofeachdiskwillactasatestoutcomecollector.Eachofthedisjointdiskscanbetestedsimultaneously.2)Forasetofvictimsineachdisjointdisk,weusetheDTN-NCGT 40


2 .BasedonthisobtainedvalueDij,DTN-NCGTconstructs 41


3 .ConsiderFigure 3-1 asanexamplewherewehavetwojammernodesJ1andJ2.Nodesv1,v2,...,v9andv15,v16,...,v25arethevictims,andm=3.Accordingtoour 42




Sinceitem6(6thcolumn)isatriggernode(positiveitem),onlythe2ndand6thgroups(rows)returnnegativeoutcomes.Onthecontrary,allotherfourgroupsproducepositiveoutcomes. algorithm,twodisjointdiskswillbefoundandtwogroupsG11=fv1,v2,...,v9gandG12=fv15,v16,...,v25gareconstructedaccordingly.Testingwillbeconductedonthesetwogroupssimultaneously.Forsimplication,Figure 3-1 justshowsthedetailtestingofG11.AftertheestimationofDij=1,ouralgorithmwillconstructa1-disjunctmatrix.Basedonthismatrix,therstthreerowswilldoaone-hopbroadcastmessagetothree 44


3-1 wherethesecondandsixthrowshaveapositiveresult.Basedonasimpledecodingmethodmentionedearlier,wecaneasilydetectv6asatriggernode. 3.4.1EstimationofTriggerNodeUpperBoundDijInordertoconstructd-disjunctmatrixfortestingsintestinggroupGij,weneedtoobtainanupperboundontriggernodes.Weassumethattheinterferenceradiusislargerthanlegitimatetransmissionradius,R=rwhere>1sincejammershavemorecapabilitiesthannormalsensornodes.LetJbethesetofjammersthattriggernodetcouldactivate.WenotethatthedistancesfromjammersinJtotareatmostrwhilethedistancebetweenanytwojammersmustbelargerthanR=r.Otherwisejammerswillinvokeeachotherandrunoutofenergy.Wehavethefollowinglemma: 3-2 ,wherem=jJj.WehaveOJi(=(O,Ji))r8i=1...mandJiJj>R=r81i

Followingthelemma,wehave: jJj1when2. jJj2whenp jJj3whenp jJj4whenq 2. jJj5when1. 5Possiblejammersactivatedbyatriggernodet


Proof. ,thenodesingroupGijcantriggeratmostjJijjjammers.Intuitively,weknowthatasetoftriggernodestoactivatethesamejammerhaveadistancelessthan2r.Inalgorithm 2 ,weconstructaunitdiskgraphGij=(Wij,Eij)withdiskradius2rsothatthenodeswhichtriggerthesamejammermustformacliqueingraphGij.Ineachiteration,accordingtoAlgorithm 2 ,wechoosetherstJthijmaximumcliquesandunionallthesecliques.Thatis,SJijk=1ck(Gij).Thustheproofiscomplete. Lemma2. Proof. Proof. 47


Proof. 2 andthefactthateachdiskD1vhasaradius(Rr),allthevictimnodesinanytwodifferentdisjointdisksareinterference-free.Thusthetestingresultiscorrectlycollected. Lemma4. Proof. 48


Proof. 22 23 ].InWSNs,aswedenedtherearemradiossothatatmostmgroupscanbetestedatthesametime.AccordingtoTHEOREM ,dijareboundedbyDijandnijisthenumberofvictimnodes,wecompletetheproof. Proof. andCOROLLARY ,thecoversforallvictimnodesare(H)+1andthetestingtimeforeachcoveristhemaximumtestingtimeamongallgroups,thatis,maxjdminf(2+o(1))D2ijlog22nij


22 23 ]ford-disjunctmatrix,hasthelowestupper-boundforthematrixsize.Itistrivialtondthat,eachcolumnhasexactlys1-entriesinthematrixconstructedinthatway,wheres=(2+o(1))Dijlog2nij Wedonotconsiderthefalsenegativefromrandomdelayonemittingadversarialsignalfromjammerssinceaccordingtothedenitionofreactivebehavior,thejammerswouldonlyemitinterferencesignalsduringthelegitimateactivitiesonchannels. 22 23 ].Using(d,e)-disjunctmatrixhelpstocorrectatmosteerrorsinthetestingoutcomes,thuswearestillabletocorrectlyidentifyallthetriggers.Wewouldliketonotethatinordertousethementioned(d,e)-disjunctmatrix,weneedtoestimatetheupperboundofe.Inpracticalnetworkenvironmentsunderrandomreactivejammingattacks,wecouldestimatethisboundbyanalyzingthePacketDelivery 50


ReceivedPacketsThereactivejammerswouldbeabletodropPDReffectivelybythereactivestrategy,however,wecouldusethisratioagainstthemtoboundtheunreliabletestingoutcomesinthecaseofrandomreactivejammingbehaviorsbecausePr(1PDR)istheprobabilityofemittingadversarialsignalfromjammers,andPDRisalsooneofwell-knownprobabilisticmethodstodeterminethepresenceofjammingattacksbyasimplecalculation.InordertoachievehighlyaccuratePDR,Strasseretal.[ 60 ]introducedabit-erroridenticationtechniquetodifferentiatejammedpacketsfromerrorscausedbyweaksignal(e.g.,becauseoffastfadingorshadowing).Consequently,theupperboundoferrorsovertestscouldbederivedfrominvestigationofPDRandsentfromsensorstobasestationsoastoconstructerror-tolerantdisjunctmatrix. 64 ]onG0.Itiseasytoseethatthe 51


Experimentalresultsbyvarioussizeofjammers 52


Experimentalresultsbyvarioussizeofchannels Experimentalresultsbyvarioussizeofnodes basestation,weassume=rinthissimulation,whilelargerwouldmakethissolutionmoreefcient.Wehaveintotalsixbenchmarksinthesimulationswithdifferentinputparameterteams.Ononehand,westudytheaveragenumberofdiskcoverscintheGVN-MCDDCalgorithm,andthemaximumnodedegreetovalidatetheboundofcprovedinLEMMA .Ontheotherhand,weshowtheoveralltestlength(numberofroundsT)analyzedinTHEOREM3.Moreover,werecordthenumberofvictimnodesnandthetotalvolume


Experimentalresultsbyvariousnetworkdensities Experimentalresultsbyvarioussizeof 5.2.1 3.6 3.6 3.6 and 3.6 arethecorrespondingresultsandanalysis.Notethat 54

PAGE 55 5.2.1 (a)and(b)explainourprotocolperformancebasedonthevariousnumbersofjammersJinthenetwork.Inthistest,wehaveN=1000nodeswithm=3radios,ona15001500networkeld,whereJ2[1,10]jammersarerandomlydeployed.OurprotocolemploysasophisticatedtechniquetoperformasmanyparalleltestingaspossibleasshowninAlgorithm3,thereforethenumberoftestingrounds,T,canbestablewhilethenumberofjammersJandvictimnodesnincrease.AsshowninFigure 5.2.1 (a)and(b),Tincreasesalittlewhilencanvaryfrom50to450whenJincreasesfrom1to10.Morespecically,thenumberofdiskcoverscandmaximumnumberoftestingroundsperdisktaresmallerthan10,wherethelatterismuchsmallerthanmaximumnodedegree.ThiscontributestodramaticallysmallnumberofoverallroundsT,whichisnolargerthan30andstableforincreasingJ.Moreover,sinceeach(Rr)-diskinourtestsneedsonlyonesensornodetosendtheresultbacktothebasestation,themessagecomplexityMisalsomuchsmaller(lessthan100)thanthenumberofvictimnodesn.Notethatinindividualtestingmethod,MshouldbeashighasO(n).Therefore,oursolutioncanpromptlydefendajammingattackwithincreasingnumberofjammers,intermsoftimecomplexityandmessagecomplexity. 55


3.6 (a),themaximumtestingroundsperdiskdecreaseastheradiosizeincrease,whichassiststodropthetotalrounds,T,drastically.Especially,whenm=2fromm=1intheFigure 3.6 (a),theoveralltotalroundsdroprapidly.Inconclusion,welearnthattheradiosizecanhighlybenettheoveralltestlengthofourprotocol. 3.6 (a)and(b).AsshowninFigure 3.6 (a)and(b),thevictimquantityincreasesobviouslyasthenumberofnodesincreases,butthenumberofmessagesisquiteconstant.Moreover,thetotaltestingroundsincreaseslowly.ThisgureshowshowoursystemefcientlyoperateswhenthenumberofnodesincreasesfromN=500toN=1000withm=3andJ=5jammersina15001500networkarea.Fromthisevaluation,wecanconcludethatourmodelisalsoaverysuitablesecuritysolutionforthemajorityofsensornetworksinvariousareas. 56


3.6 (a)and(b)showsthevarioussimulationresultswiththeincreasingnetworkeldsizefrom15001500to25002500whereN=1000withm=3andJ=5jammers.Asthenetworkissparse,thenumberofvictimnodesdecreasesasgetssmallerinthisgureaswediscussed. 77 ]locksdownthewholejammedregionwhileoursystemminimizesthejammedregionsizebyidentifyingthesmallernumberoftriggernodes.InFigure 3.6 (a)and(b),asthegetslarger,thenumberofvictimnodesincreasessinceajammercantransmitfartherandcontaminatesmorenodesduringtheactivation.Moreover,morevictimnodesrequiresmoretestingroundstoculloutthetriggernodesamongthem.Inourresult,thenumberofroundsrisesasgetslarger.However,thenumberofroundsischangingveryslowly. 57


22 23 ]discussedinSection 3.4.4 58




60 ]proposedahighlyaccuratedetectionschemeofreactivejammingattack,andallinterferencesignalscanbecorrectlyidentiedasnoisebysensorsfromotherexternalinterferenceseveninlowerandunsteadyRSS.However,individualtestingistootime-consuming,thusweoftentestanumberofnodes,calledgrouptesting(GT).However,testingagroupofnodessimultaneouslyencounterseveraldifculties.Forexample,ifsomeNoisesensedafterperformingtesting,wemaynotknowwhichonesinthetestednodestriggeredthejammers.Moreover,schedulingnodesinatestinggrouptoperformthetestingsynchronouslymayresultinalotofcommunicationoverheadinthenetworkiftestednodesarefarfromeachother.Inaddition,iftwogroupofnodesaretestingatthesametimeandthejammertriggeredbytherstgroupcanjamnodesinthesecondgroup,the 60


1. Iftwonodesu,vareatthedistanceatleastR+rtheycannottriggerasamejammer.Thisenableustotestu,vinasameroundwithouthavingtheoutcomeoftestinguandthatofvinterferedeachother.Ingeneral,wecanperformtestinginparallelfortwosetsofnodesUandVthatareR+rfarawayfromeachother. 2. Ifu,v,wareidentiedtriggers,thenallnodesinsidethetrianglewhoseverticesareu,v,warealsotriggers.Furthermore,ifT=ft1,...,tkgisasetoftriggers,thenallthenodesinsidetheconvexhullofTarealsotriggers.ThisholdsaslongasR>2r. 61


4.3 tolocallypartitionsensornodesinagivenWSNintoasetoftestinggroups.Inordertostudythehexagontilingcoloring,weconsiderthefollowingnewproblem: Hexagontilingcoloringproblem:Givenadistanced2<+andahexagontilingHdividingthe2Dplaneintoregularhexagonsofsides1 2.FindtheminimumnumberofcolorsneededtocolorH,suchthatanytwohexagonsh1andh2inHwithsamecolorareatdistancegreaterthand.Thedistancebetweentwohexagonsh1andh2,denotedasd(h1,h2),isdenedastheEuclideandistancebetweenanytwoclosestpointsp1andp2,suchthatp1islocatedinh1andp2islocatedinh2.Thismakesthehexagontilingcoloringproblemdifferentfromthechannelassignmentproblem[ 56 ]incellularnetwork,wherethedistancebetweentwohexagoncellsismeasuredfromtheircenters.centersofallthehexagonsareplacedonatriangularlattice.Therefore,weconsideranewcoordinatesysteminthe2Dplane,withaxesinclinedat60o.Thisnewcoordinatessystemhastwounitsvectors!i(p 2,0)and!j(p 4,3 4)asshowninFigure 4-1 .Thecentersofeachhexagonhcoincidewiththeintegralcoordinatesinthis 62


2p 4-2 showsthecoloringpatterngeneratedbythek2-coloringalgorithmford=3p 2andk=4.Thek2-coloringalgorithmisusedbythesensornodesinourproposedlocalizedalgorithmtolocallyidentifythegrouptheybelongto. Lemma6. Proof. 2(k1)(wherek=l2d


Theminimumdistancebetweentwonodeswithsamecolor Letx=i1i2andy=j1j2.Itfollowsthatxandywillbemultipleofk.Thedistancebetweenthecentersofh1(i1,j1)andh2(i2,j2)isgivenbydc(h1,h2)=p 2p 4(x 16x2q 16(2k)2>p 2(k1)+1.Notethatforeveryhexagonthedistancefromapointinsideittoitscenterisatmost1 2.Hence,thedistancebetweentwohexagonsd(h1,h2)willbeatleastdc(h1,h2)2(1 2)>p 2(k1). 2)>q 4k21>p 2(k1).Otherwisethereareonlysixleftcasesofx,yasshowninFigure 4-1 .Thedistancebetweentwohexagonsinallofthesecasesisexactlyp 2(k1).Hence,thelemmaiscompletelyproved. 64


Thecoloringpatternfork=4 65


4 ,anodecanidentifythecolorofitshexagonandalsothetimeslotassignedtoitsgroupintheschedule.Weconsiderthatanodev2VknowsitsneighborsN(v)andusingsomeadhocpositioningmethod[ 48 49 ],itcanidentifyitslocationas(xv,yv)withrespecttosomereferencenode.Weconsiderthesinknodes2VintheWSNasthereferencenodesuchthat(xs,ys)=(0,0).Now,weshowthatifanodevknowsitscoordinates(xv,yv)intheCartesiansystemthenwithouthavingtheglobalviewofthehexagontiling,itcanlocallycomputeitscoordinates(xhv,yhv)innewcoordinatesystemonthehexagontilingandfurther,itcanidentifythehexagonitbelongsto.Forinstanceanodevatcoordinates(xv,yv)intheCartesiancoordinatescancomputeitscoordinates(xhv,yhv)inthenewcoordinatesystemas: Thecoordinatesofthehexagonh(i,j)inwhichnodevislocatedisgivenas: 2% 2% Now,usingthek2-coloringalgorithmandconsideringd=R+r,k=l(R+r)=p 2m=l2(+1) Inordertoshowthecorrectnessofourmethod,weprovethefollowinglemmas: 66


Proof. Proof. 4 tocolortheentirehexagontilingis: (2)+1)m2,whenDh=R2r. Proof. Dhp (2)+1)m2colors 67


7 ,basedontheconstraintondistancebetweenanytwojammersj1andj2,d(j1,j2)>Rinordertoavoidmutualinvocationbetweenthem,weprovedthatonlyonejammercanbeactivatedbynodeswithinahexagon.ReactiveJammingModel,byusingSGT,alltriggernodescanbeidentiedinO(jCTjlog)whereCTistheconvexhullofthesetoftriggernodeswithinahexagon(seeFigure 4-3 )andisthemaximumdegreeofallnodesinthenetwork,hence,therearenomorethan+1nodeswithinahexagon.WeuseamethodnamedQuickIdenticationinordertoreducethenumberoftestingrounds.AccordingtoLemma 7 ,alltriggerswithinahexagonactivateasamejammer.Thus,anodeisatriggeriffitbelongstotheintersectionofthehexagonwiththediskofradiusrwhosecenteristhejammer.Theconvexityoftheintersectionarea 68


5 .Ineverystep,Tdenotesthesetofidentiedtriggers,Udenotesthesetofunidentiednodes.WeuseISTNalgorithm(presentedshortlyafter)tondamongUasingletriggervtthathasthemaximumdistancetothetemporaryconvexhullofT.Weshowlaterthatvtmustbelongtothethe(nal)convexhullCTofalltriggersinsidethehexagon.WesafelyeliminateallnodeswhosedistancesfromtheconvexhullofTarelargerthanthatofvt.WealsouseQuickIdenticationtoincludealltriggersinsidethenewconvexhullofT[fvtg.Thealgorithmterminateswhenallnodeswithineachhexagonareclassiedintoeithertriggersornon-triggers. 6 .Thealgorithmworksinasamemannerwithbinarysearchalgorithmasitsequentiallydividesthesetintotwohalves.However,italwaystestsforthepresenceofthetriggersintherighthalfrstsothatifthereexisttriggersamongU,theonewiththemaximumindex(therightmosttrigger)willbereturned.ISTNterminatesassoonasonetriggernodeisidentied.Clearly,eachidenticationofatriggernodeamongasetUofnodesbyISTNtakesatmostlog2(jUj)rounds.RandomReactiveJammingModel:Incaseofjammerrandomlyreactswithprobabilityp,weproposeasimpleandeffectivealgorithmtoidentifytriggersinAlgorithm 7 .Asetofnodesareidentiedasnon-triggersonlyifafterftestingrounds,noNoiseissensed.Werstrevealiftherearetriggerswithinthehexagonasinlines5to15.Ifitisthecase,furtherindividualtestsareperformedtoidentifywhethernodesaretriggers. 69


sthen 4.4.1UpperboundonTestingRounds Lemma10. Proof. 5 requiresnomorethanO(jCTjlog)numberofroundswherejCTjisthenumberofverticesontheconvexhullofthesetoftriggers.


2(low+high)c stimethen Triggernodesinahexagon 71


sthen sthen 9 andmaxfctgisthemaximumsizeofconvexhullofasetoftriggerswithinahexagon.Althoughmaxfctgmaygoupto,thealgorithm'sperformanceisoftenfarbetterthanitsworstcase. Theorem4.2. 5 isO(T)whereTisthenumberoftestinground.


5 ,thenumberoftestingmessageswithinahexagonaltestinggroupcannotbemorethanineachtestinground.TheobservationunderliesonthefactthatthemaximumdiameterofahexagonisatmostrfromtheSection 4.3 .Consideringthecasethatalltriggernodesconsistofconvexhullwithinahexagon,eachiterationoftestingroundwillidentifyatleastatriggernode.Hence,themessagecomplexityofalgorithm 5 isatmostO(T). 7 is1(1p)f.Theprobabilitythatatriggernodesiscorrectlyidentiedisalso1(1p)f(lines17to25).Hence,theexpectednumberofidentiedtriggerswillbe(1(1p)f)(1(1p)f)d>(12(1p)f)d.Toobtainanexpectedfalse-negativeratei.e.thefractionoftriggersthatareincorrectlyclassiedasnon-triggers,weneedtosetf=dlog1p=2e.Forexample,ifp=3=4andthedesiredfalse-negativerate=0.01i.e.1%,weneedf=4.Notethat 73


7 alsoworksforReactiveJammingModel.Simply,settingp=1,f=1wehaveanalgorithmwiththenumberofroundsisatmostc(+2).Clearly,thenumberofroundsdoesnotdependsonthesizeofnetwork(thenumberofsensornodes)butontheratio=R=randthemaximumdegreethatisoftendecidedbythedensityofthenetwork.Hence,theproposedalgorithmisscalablefornetworksofarbitrarysize. 77 ]approachintermsoflatency,messageoverheadandsizeofjammedregions(quarantinearea)aswell.Thepurposeofthesesimulationsistovalidateourapproachinvariousnetworkenvironmentsviadifferentteamofparametersinnetworkdensity,quantityofjammers 74


r=3.Toinvestigatetheperformanceofourscheme,thenodesarevariedfromn=1000ton=5000inordertobesubjecteddensityofnetwork,atmostJ=10jammersareplacedforvarioussizeofjammers,andthetransmissionrangeofajammerisvariedfrom=R r=2.5to=R r=8.Experimentalimplementationofthesesimulationsdonotconsiderpacketlosses,link-congestionorMACmis-behaviorexceptjammingsignalsinordertoevaluatetheidenticationperformanceonly.Sinceweranthesimulationsforeachsetup100timesandaveragedtheresults,theresultssufcetoreecttheefciencyofLTNIalgorithms.Wemodeledthepracticalnetworkstovalidateouralgorithmagainstreactivejammers,oneimplementationofthereactivejammers,byutilizingZigBeeprotocol.AwiderangeofexperimentswasconductedbasedonsimpleZigBeeprotocolusingCarrierSenseMultipleAccess/CollisionAvoidance(CSMA/CA)channelaccessmechanism.RequestToSend(RTS)ofsize30bytesandClearToSend(CTS)ofsize30bytesareimplementedintheseexperiments.Theprocessingtimeforanytypeofmessagesisuniformly10mssincesensorshavelimitedresourcetogeneratecommunicationmessages,andthepropagationspeedis3108m/sinbothalgorithms,JAMandLTNI.Tocommunicatewithothers,everynodeneedstosendatleastthreemessages,apairofRTS/CTSandadatamessageandwaitthepredenedintervalsbetweenthosemessages,20msintheseexperimentsinordertosimulatepracticalWSNs.Wealsoassumethatthesizeofacommunicationmessageisbiggerthan2347bytes,sothatRTS/CTSshouldbesentbeforelegitimatecommunicationsbegin.ByimplementingarealprotocolZigBee,wecouldreportmorereliableevaluationofouralgorithmbasedonthat. 75


Roundsbyvariousparameters 4.6 (a),whichdirectlyreectsthelatencyofSGT-LTNIalgorithmsduetothepredenedlengthofatestinground.AsshowninFigure 4.6 (a),thetestingroundsrequiredtocompletetheidenticationofalltriggernodesgrowsteadily,comparedtotheincrementalsizeofsensorsindensernetworks.Duringthenodesinincrementsfrom1000until5000,thetestingroundsgraduallyascendonlyaround120additionalroundsinSGT-LTNI,butIT-LTNItestsatmost150additionalroundstodetectalltriggernodes.Thatis,thedesignofSGT-LTNIalgorithmwithQuick 76


Messagesbyvariousparameters IdenticationandQuickEliminationinordertoidentifyalltriggernodesonlyonconvexhullofeachhexagonproducesagreatbenetoverthetimecomplexity.Then,theimpacttoLTNIalgorithmsfromdifferentquantityofjammersaredepictedthroughFigure 4.6 (b)soastoshowtheeffectivenessofourlocalizedschemeinmassivejammingdisruption.Sincer=20and=R r=3withJ2[1,10]aresufcientconditionstoinvestigatemassivejammingattackovern=3000inWSNs,noadditionaljammersbeyondJ=10issimulated.Asjammersswellupto10timesofinitialsize,just130supplementarytestingroundstakeplaceinSGT-LTNI.Consequently,evenwithmassiveimpactscenariofromlargenumberofjammersagainstWSNs,thelocalizedidenticationalgorithmproducesgreatrobustnessandfeasibilityonpracticalsystems. 77


Runtimebyvariousparameters Finally,thetestingroundsshowsdiversityduetothedistanceamonginterference-freetestinggroupsaccordingtothesizeof=R r,whileparametervaluebiggerthan8wouldbeimpracticalscenarios.AsindicatedbyFigure 4-1 ,disjointinterference-freetestinggroupshavetobefarawayatleastR+r,thereforethedistancebetweenparalleltestinggroupsistightlyrelatedtothenumberofcolors.Duetothefactthatbiggerresultsinmorecolorswithsmallernumberofinterference-freetestinggroups,Figure 4.6 (c)disclosesincreasingtrendsoftestsinbothLTNIalgorithms. 78


Nodesinquarantineareasbyvariousparameters resultinlongernetworklifetimegenerally.ThegraphsinFigure 4.6 plotthenumbersofmessagespernodefromthreesolutions,JAM,IT-LTNIandSGT-LTNIsoastoreportcomparativemessagecomplexity.Figure 4.6 (a)providestheperformancecomparisonofthreeapproachesintermsofmessagespernodewhenchangingthenetworkdensity.ThemessagesfromJAMsolutionarehigherthanthosefrombothLTNIschemes.Inaddition,Figure 4.6 (a)showsthesuperiorityofmessagecomplexityinLTNIapproachesoverthatinJAMincreasesasmorenodesareplacedinnetworks.Thegraphexplainsthat40%moremessagesarerequiredtoconstructjammedareasinJAMwheren=1000,however,around47%lessmessagessufcetocompletetheclassicationofalltrigger 79


ThenumberofroundsTinrandomreactivejammingmodelwithdifferentvaluesofjammingprobabilityP. nodesfromSGT-LTNIintotalwheren=5000.Apartfromthenumberofmessagesbetweentwoapproaches,JAMsolutiondemandsinevitablymoreenergythanSGT-LTNIdoessinceJAMprotocolhasacoupleofdifferenttypesofcommunicationmessagesincludingBUILDandPROBEmessagesexceptblindmessageJAMMEDinordertoquarantinejammedregions,butSGT-LTNInecessitatesmainlysmallsizeoftestingmessagestoinvokejammersduringidenticationofalltriggernodes.Insummary,ourlocalizedalgorithmispromisingapproachtoapplyinpracticalnetworkswithaffordablemessagecomplexityandenergyconsumption.Simulationswerealsocarriedouttocomparetheperformanceofallthreeapproachesduringincreasingthenumberofattackers(jammers)aswellastoseehowthisaffectstheirperformances.AsrevealedinFigure 4.6 (b),bothLTNIalgorithmssignicantlyoutperformJAMapproach.Especially,thenumberofmessagesfromLTNIalgorithmsis32percentlessthanthatofJAMwhereasinglejammerJ=1,andLTNIschemesrequire45percentlessthanJAMdoeswhereJ=10.Inaddition,Whensizeofjammersisgreaterthan7,thenumbersofmessagespernodesobtainedfromthreeapproacheskeepconstanttrend,sincethejammerscoveredmostofnodesinnetworks. 80


4.6 (c)showsthemessagespernoderequiredtocompletethreealgorithmsandnotonlymoremessagesinJAMthaninLTNIalgorithmsbutalsogrowingsizeofmessagespernodesinJAMapproach.Consequently,eveninseverewidespreadreactivejammingagainstWSNs,ouridenticationapproachvalidatesgreatrobustnessandpracticality. 81


4.2.2 ,theoverallruntimeforcompleteidenticationofalltriggernodesdoesnotdrasticallygrowwiththesizeofjammersornodes.InFigure 4.6 (a),duringtheincrementsofnodesfromn=1000ton=5000,ourapproachdelayedonly2secondstoachievethetotalidenticationoftriggernodes,whereas,JAMtakes7timesaslongtimeasLTNIalgorithmsdo.Thatis,ouridenticationschemesintroduceoutperformanceonscalabilityovertheJAM.Asexpected,theruntimesobtainedfrombothLTNIalgorithmsshowssimilarincreasingtrendofcurves.Figure 4.6 (b)comparestheruntimebasedonvarioussizeofjammerswithxednumberofnodes,andSGT-LTNIisthebest.Particularly,theruntimeofSGT-LTNIisslightlybetterthanIT-LTNI,andthegapbetweenJAMandLTNIapproachesgetbiggerwhenjammersincrease.Asdescribedbefore,bigger=R rwithxednumberofjammersJ=3resultsinsmallernumberofinterference-freetestinggroups,whichimplieslessparallelismonidenticationconsequently.Figure 4.6 (c)plotsthetimeofquarantineprocedures,andduetothebiggerimpactofjammersfrombigger,JAMalgorithmrequiresconsiderablylongertimetoquarantinejammedregionswhenincreasing.Inparticular,SGT-LTNIandIT-LTNIshowsincreasingtrendofcurvesasgrowing.ConsideringtheruntimeofJAMapproach,thisvericationtimeofidenticationtriggernodesinLTNIalgorithmsisquitereasonable.Forexample,JAMdemands30secondstoblockjammedregions,butSGT-LTNIcompletestheidenticationoftriggernodeswithinonly15secondswhere=8.Inaddition,IT-LTNIalsoshowsgoodperformance,buthigherthanSGT-LTNIdoes.Consequently,overalllengthofruntimedependsonthesizeofnodesinjammedregions,however,hexagontilingcoloringschemehelpstokeepsmallincrementsofruntimebymaximizingparalleltestings. 82


77 ],andunreachabletriggernodesalsocannotreceiveanymessageeither.InFigure 4.6 ,thesizeofunreachabletriggernodesisalwayssubstantiallylessthenthesizeofjammednodesfromJAMalgorithm.Especially,inFigure 4.6 (a),onlylessthancoupleofnodesareunreachabletriggernodesandwouldnotbeabletoreceivemessageswheren2[1000,5000],butjammednodesgetsignicantlylargerashighernetworkdensity.InFigure 4.6 (b),aspredicted,thenumberofunreachabletriggernodeskeepsmallnumber,lessthan10,evenin10jammers,butjammednodessproutwithhigherpopulationfrommorejammersinWSNs.Withxednumberofjammersandsensornodes,largersizeofresultsinbiggerimpactagainstWSNs,whichimpliesthatmorejammednodesinJAMalgorithm.Yet,importantly,ouridenticationapproacheswillnotgetaffectedfromintermsofunreachabletriggernodes.Thatis,byutilizingthesuccessfulidenticationofalltriggernodes,actualjammedareasinwhichnonodewouldbeabletosendoutanymessagestoavoidreactivejammingsignalwouldbeverysmall,sothatsignicantlymorenodeswouldbeparticipatedinsecurecommunicationsthanJAMalgorithmdoes. 83


4.6 thefalse-negativerateoftheAlgorithm 7 inalogscale(Recallthatwedonothavefalse-positive).Thefalse-negativeratelinearlydecreasesinthelog-scalei.e.exponentiallydecreaseswhenthenumberofduplicatedtestingfincreases.Evenwiththep=0.6,thefalse-negativeratequicklydecreasesto1%withf=6.Thatis,weonlyneedtorepeatthetestfor6times.Whenwexthetargetedfalse-negativeratetobe1%,thenumberofroundsrequiredisshowninFigure 4.6 .Thenumberofroundsincreasesslightlytogetherwiththenumberofnodesinthenetworksinceputtingmorenodesinasamexedarearisethedensityi.e.degreeofnodes.However,therateofincreasecomesclosertozerowhenn=5000. 84




66 ].However,thisproblemonlyconsidersthesizeofthesetobtained,nottheweightofedges.Inotherwords,theweightisonlyassociatedwith 86


6 72 ]studyingthetreecoverproblemwhichisdenedasaconnectededgedominatingsetwithtotalminimumedgeweights.Arkinetal.rstsolvedthisproblemin[ 6 ].Later,in[ 71 ],thisproblemcanbeapproximatedwithinafactorof3+.In[ 72 ],theauthorpresentedafastcombinatorial2-approximationalgorithmforthetreecoverproblem.Incontrasttotheabovework,DTisdenedasnodedominatingsets,notedgedominatingsets.Usually,DTalwaysproducesasmallernumberoflinksandweightthantreecover,anditismoredifcultthantreecoverproblem. Theorem5.1. 25 ],WDSisshowntobeinapproximablewithin(1)lnjVjforany0,unlessNPDTIME(jVjloglogjVj).GivenaninstanceofWDS,thatis,agraphG=(V,E,w)andaweightfunctionw:V!Z+,theproblemistondaminimumweightsubsetofnodesthatdominatesallothernodes.WewillconstructaDTinstanceG'=(V',E',w')asfollows.Foreachnodevi2V,weintroducetwonewnodesxiandyishownasgraynodesandblacknodesinFigure 5-1B .LetX=fxigandY=fyig.LetV'=V[X[Y.ThesetE'andw' 87




ReductionfromWDSGtoDTG0 89


12 ]andthuswecanobtainanDTofG.Itisclearthatthereductioniscompletedinlineartime.ThisreductionisshownasanexampleinFigure 5-2 AnexampleofreductionfromGtoG' 90


12 ],theauthorsprovidedapolylogarithmicapproximationfortheDSTprobleminquasi-polynomialtime.ThenwehaveanalgorithmtoobtainthisratiofortheDTproblemaswell: 12 ]inG'andmakevastherootrtogetaDT Algorithm 8 isbasedontheideaoftransformingtheDTproblemtotheDSTproblem,andthenusethealgorithmin[ 12 ]tosolveDSTproblem,thusobtainingthesolutionforDT.Notethatafterthetransformation,weneedtondtherightrootforapplyingthatalgorithm,sincetheratioforDSTismaintainedifandonlyifrisintheoptimalDT.Thiscanbedonebyenumeratetheneighborsofthenodewiththeminimumdegree,sinceatleastoneoftheneighborsshouldbeinoptimalDT.Therefore,fromLemma 11 ,wecanobtainthesameapproximationratioforDT.Finally,sincetheterminalnodesinG'arethosedummyverticeswhichhavenooutgoingedges,wecansimplyremovethesedummyverticesandthoseedgesincidenttothemtoobtainaDT.Bysettingi=lgn,thealgorithmwillobtainanO(lg2n)approximationinquasi-polynomialtimewhichisnO(lgn). 91


9 .Fromthehighlevel,thealgorithmconsistsofthefollowingmainsteps: 1. Initializeatree,whereeachvertexinagivengraphisaseparatesubtree. 2. CreateasortedlistofalledgesinGbyweights. 3. WhileallthesubtreesarenotmergedintoatreeDT Removeanedgewithminimumweightfromthesortedasaninactiveedge. (b) Whentheedgefromthelistconnectstwodifferentsubtreeswithoutanycircles. i. MergethemintoasubtreebyaddingtheinactiveedgetoDT. ii. Ifnewinternalnodesconvertedfromleafnodesduringmergingsubtreeshavesomesingle-nodesubtreeneighbors,thenlinktheseinternalnodeswiththembyactiveedgessoastomaximizethesizeofleafnodesinDT. iii. Ifthenewinactiveedgeconnectingtoanodewhichalreadyhasanactiveedgeincidenttoit,removethisactiveedge. 4. PrunealltheleafedgesoftheresultantDT.ThedetailsofmergingtwosubtreesareshowninAlgorithm 10 .TheonlypurposeofactiveedgesistomaximizethenumberofleafnodeswithoutconsideringtheirweightsduetothefactthatthetotalweightofDTdoesnotincludetheweightsfromleafedges. 92


5-3 whichdepictstheexecutionofheuristicalgorithm.IntheFigure 5-3 (b)and(c),sinceleafnodegisanewinternalnodewithsingle-nodesubtreeiaftermerging,glinksitogetherbyactiveedge.However,activeedge(i,g)hastoberemovedwhennewinactiveconnection(c,i)occursconnectingsubtreectoi.Becauseallinternalnodeshavetobeconnectedbyinactiveedges,andifwedonotremoveactiveedge(i,g),iwillbeinternalnodewithanexistingactiveedge(i,g)andthusincreasingtheweightofDT. Figure5-3. TheexecutionofHeurDTalgorithm 93


endwhile 1. 2. ThecomplexityofMergeSortalgorithmtosortedgesbyweightinStep2isO(mlogm)[ 17 ]. 3. InStep3,foreachnewinternalnodeufrommergingsubtrees,allitsneighborsneedtobecheckedtoseeifthereareanysubtreeswithonlyonenode,whichisO()foreachedgetoprocess.However,onlymergingsubtreeswouldbeabletoconvertleafnodesintointernalnodes,andthetotalnumberofmergingprocesstakesplaceatmostO(n).Asaresult,theoverallcomplexityforStep3isO(n). 4. Pruningallleafnodesonlytakeslineartime.Fromtheaboveanalysis,thetotalrunningtimecomplexityisdominatedbyStep2.Thatis,theruntimeofthisheuristicalgorithmisatmostO(n2logn),wherethegraphisdenseenough(O(n)andmn2). 94


ifvhasonlyoneactivelinkinDTthen foreachneighbornodewofN(u)inGdo ifjTsub(w)j==1then endfor endif ifv==internalandvhasatleastoneinactivelinkthen foreachneighbornodewofN(v)inGdo ifjTsub(w)j==1then endfor endif 95


BDTSize CRunningTime SimulationresultsforHeurDT,MST-Landoptimalresults Firstofall,letuspresenttheIntegerProgramming(IP)formulationoftheDTproblem.WewilluseCPLEXtosolvethisIPandtheoptimalresultwillbecomparedwiththatofourheuristic. 96


5-4A illustratestheperformanceofthosethreeapproachesintermsoftheweightofDT.AsshowninFigure 5-4A ,theDTweightsfromHeurDTareveryclosetotheoptimalsolution,whichshowsHeurDTperformsextremelywell.Inparticular,theDTweightfromHeurDThasatmost8%ofadditionalweightsthantheoptimalresultswhenn=15accordingtotheFigure 5-4A .Inaddition,thegapinDTweightsbetweentheoptimalsolutionandthatofHeurDTdoesnotshow 97


5-4B ,thedifferenceinsizebetweenoptimalsizeandtheDTobtainedbyHeurDTisverysmall.AccordingtotheFigure 5-4B ,theDTbuiltfromHeurDThasatmost1.2nodesmorethantheDTfromOptDTinthecaseofthenetworkinstancewith15nodes.Signicantly, 5-4B indicatesthatthedifferenceinDTsizeisnotaffectedbynetworksize.However,thesizeofMST-LismuchlargerthanthatofHeurDT.ItisverycleartoprovethatHeurDTmaximizingthenumberofleavesduringthemergingcandrasticallyreducetheDTsize.Asnincreases,thedifferenceinsizeofDTbetweenMST-LandtheHeurDTsignicantlyincreasesup,suchas33%additionalnodeswhenn=4and42%morenodesinMST-Lwhenn=17thantheDTgeneratedbyHeurDT.ThisrevealssubstantialdifferenceofDTsizebetweenthemwhenwetakethetotalnumberofnodesinGintoconsideration.ComparingtheRunningTime.Figure 5-4C presentstherunningtimeofallthreeapproaches.Asexpected,therunningtimeforndingtheoptimalsolutionisextremelyhigh.Onemoretime,itconrmsthatitistooexpensivetondtheoptimalsolution,leadingtothestudyofapproximationsolution.Interestingly,therunningtimeofHeurDTandMST-Lisveryclosetoeachother.Forexample,HeurDTtakesaround37msmoreinaveragethantheMST-Lapproach.Thisisduetothetimespentonidentifyingactiveedgesandremovingthemiftheyareplacedbetweeninternal



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3 5 18 20 24 28 40 41 45 54 59 65 67 68 74 75 79 80 ]seekaminimumsizeCDS(MCDS),whichisNP-hard[ 27 ],astheirmajordesigngoal.MinimizingthecardinalityofCDScanhelptodecreasethecontroloverheadsincebroadcastingforroutediscovery[ 33 51 ]andtopologyupdate[ 1 ]isrestrictedtoasmallsubsetofnodes[ 13 ].Thereforebroadcaststormproblem[ 73 ]inherenttoglobaloodingcanbegreatlydecreased.However,thereareseveralimportantfactorsthatneedtobefullyinvestigated.Therstimportantfactoristhenetworklatency,alsorepresentedasdiameterofCDS,whichisthelongestshortestpathbetweenanypairofnodesinCDS.Consideringthesituationthatthereceiverisnotwithinthetransmissionrangeofthesender,communicate 100

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68 75 81 82 ]haveaddressedthisissue.However,theyonlyconsideredthesizeofCDStogetherwiththefaulttolerance,withoutthediameterofCDSandrunningtime.Themaincontributionofthisworkisthemulti-factorsmodelforafaulttolerantMCDSwithboundednetworklatency(diameter)andthelowrunningtimeforafeasiblesolutionisexpectedaswell.Thecharacterizationofthismodelisthat(1)avariableisinvolvedinthisalgorithmasaninputtomaketheperformancetunable.(2)trade-offsamongmultiplefactorsareshownthroughanalysis,whichhasnotbeenaddressesinrelatedworks.Morespecically,theproposedprogressivealgorithm,whichistheinputofourmodel,allowsforsystematicimprovement.Takinginspirationfromcomputationalgeometryandprobability,wedeviseimprovementtechniquesforsystematicallyreducing 101

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34 ],CDS-BD[ 38 ]andBDA[ 88 ]underthesameparameters.TheresultsdemonstrateouralgorithmoutperformsCDS-BD-D,CDS-BDandBDAinmosttestingcases. 15 ],whereallnodeshavethesametransmissionranges,andDiskGraphswithBidirectionalLinks(DGB)(wewillintroduceDGBinSection 6.3 ). 28 ],twopolynomial-timealgorithmstoconstructaCDSisproposedbytheauthors.Therstalgorithmhasperformanceratioof2(H()+1),whereHisaharmonicfunctionandisthemaximumdegreeofG.Theideaoftherstalgorithmistoidentifythenodewithamaximumdegreeastheroot.ThenbuildaspanningtreeTattheroot,growTuntilallnodesareaddedtoT.Then,allleafnodesarecutoffandtheremainingnodesinTareaCDS. 102

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19 20 59 ].In[ 54 ],Ruanetal.introducedanothercentralizedandgreedyalgorithmofwhichtheperformanceratiois(2+log).WuandLi[ 79 ]proposedanalgorithmthatcanquicklygenerateaCDSbasedontheconnectivityinformationwithinthe2-hopneighbors.Thisapproachusesamarkingprocess.Inparticular,eachnodeismarkedtrueifithastwounconnectedneighbors.AllthemarkednodesformaCDS.TheauthorsalsointroducedsomedominantpruningrulestoreducethesizeoftheCDS.In[ 74 ],theauthorsshowedthattheperformanceratioof[ 79 ]iswithinafactorofO(n)wherenisthenumberofnodesinanetwork. 3 5 74 ],theauthorspresentedadistributedalgorithmwithaconstantperformanceratioof8.Later,Cardeietal.presentedanotherdistributedalgorithmin[ 11 ].Thisalgorithmhasthesameperformanceratioaspreviouswork.However,themessagecomplexityislowerthanthatof[ 74 ].Asweknowthatdistributedalgorithmhasabetterperformancethanlocalizedalgorithms.Inthelocalizedalgorithms,in[ 4 ],Alzoubietal.proposedalocalizedalgorithmswithaperformanceratioof192.Althoughtheperformanceof[ 4 ]cannotcompetewiththatof[ 74 ]and[ 11 ].Theiralgorithmonlyneedonehopneighborsinformation.Therefore,onceanodeknowsthatithasthesmallestIDamongitneighbors,itbecomesadominator.Then,thedominatorscanbeconnectedbytheintermediatenodesinthenextstep.In[ 41 ],Lietal.proposedanotherlocalizedalgorithmwithaperformanceratioof172,whichisbetterthan[ 4 ]. 103

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11 74 ]areapplicableinDGB.In[ 67 ],Thaietal.rstproposedtheperformanceratioofCDSonsizeinDGBandthetwoproposedalgorithmscanbeimplementedbydistributedways.However,theonlydifferencebetweentwoalgorithmsisthestrategytoselectMIS,therstalgorithmemployedWan'salgorithm[ 74 ]tochoosethenodesinMIS,whilethesecondalgorithmusedthegreedystrategy,thatistoincludetheminimumnumberofnodesinMIS,thusleadingtoabetterperformancethantherstalgorithm. 45 ].However,theydidnotgiveaguaranteedperformanceintheirmodel.In[ 38 ],Lietal.studiedtheCDSproblemwithboundeddiameterinUDGandproposedaconstantapproximationalgorithm,calledCDS-BD.However,theiralgorithmiscentralizedandnoexperimentalresultsareprovided.Asanextendedworkof[ 38 ],Kimetal.rstmadetheircentralizedalgorithmtobedistributed,thenaddedenergyconsiderationwhenconstructedtheCDS.Simulationresultsandcomparisonagainstotherrecentalgorithmswerereportedattheend.Theproblemin[ 34 ]isthattheyemphasizedthattheUDGcannotbeusedasnetworkmodels,sincethetransmissionrangesofallnodesmaybedifferent.However,theystillusedUDGastheirmodelthroughtheirwholework.Incontrast,wewillemployanewnetworkmodel,DGB,tostudyourmodelinthiswork.Insummary,noneofthepreviousworkhaveaddressedthefollowingissues.First,theperformanceofourmodelistunable,itcanbeadjustedinarangebyanuser-denedinput.Second,wendoutthetrade-offsamongCDSsize,diameter,runningtimethroughtheoreticalanalysisandsimulation,thatis,itishardtooptimizethesefactorsatthesametime.Third,runningtimeisrstlyintroducedasametric 104

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ln(2cos( 67 ],wheretheindependentneighborsofanodeuaredenedasasetofnodesthatadjacenttousatisfyingthatanytwonodesinthesetareindependent. 105

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6-1 showsanexamplefortheintroducedterminologies. Figure6-1. Givennoderastheroot,nodea,b,f,gareterminals.ristheparentofcande.Nodea,baresiblings,f,garesiblings.Nodea,b,f,garer's2-hopsawayneighbors 106

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68 81 82 ]hasaddressedthegeneralfaulttolerantMCDSproblem.However,noneofthemmentionedhowtobounditsdiameter.Inourpreviouswork[ 68 ],wehaveproposedasolutionforkm-CDSproblem,where1km+1,asillustratedinAlgorithm 11 .Inthischapter,westillusethisalgorithmtosolveourmulti-factormodel.However,anewanalysisisproposedforthediameterofkm-CDS.ThemainideaofAlgorithm 11 isthatmergingallthek'-blocksin1-Connectedm-DominatingSet(1m-CDS)intoonlyonek'-blockbyaddingextranodes,wherek'=2initially.Then,weincreasek'by1andrepeattheaboveoperationuntilk'=k.Wecanuseany1-CDSwithboundedsizeanddiameterastheinputofAlgorithm 11 .However,inordertomakethesolutionadjustablebytheuser,an(,)-CDS,tobeintroducedinSection 6.6 ,ispreferredtobeaninputofAlgorithm 11 68 ] 68 ] 107

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11 producesakm-CDSwith(2K+2m+1)approximationonsize,whereC1mandCkmarethe1m-CDSandkm-CDSwithoptimalsolutiononsizerespectively.Proof:CkmistheunionofC1mandthenodesaddedintoC1m,inordertomakeC1mk-connected.ThenumberofnodesweaddedtomakeC1mk-connectedisatmost2(k2)(jC1mj1)+2(K+1)(jC1mj1)[ 68 ].Therefore, 68 ],wealreadyconcludedthefollowinginequality,jC1mjjCDSj+(K+m1)jC1mjThus, 108

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12 and 13 ,wehavethefollowinginequality:d(Ckm)d(C1m)+2d(C11)+2+2D+4Dkm+42 11 ,wewouldliketointroduceanalgorithmtodetermineaCDSwithabetterapproximationondiameterthanexistingwork.Asweknow,theauthorsin[ 38 ]presenteda3-approximationalgorithmondiameter,whichwasthebestknownresultatthattime.Inthissection,analgorithmthatguaranteesCDSwith2-approximationondiameterofCDSisdescribedandthesizeofCDSisboundedaswell.Thedifferencebetweenotherexistingwork[ 34 68 ]andouralgorithmisthattheytrytominimizetheCDSsizewhilethediameterisbounded.Incontrast,wewanttominimizetheCDSdiameterwhilethesizeisbounded.ToconstructaCDS,weoftenemployanMaximalIndependentSet(MIS)whichisalsoasubsetofallthenodesinthenetwork.ThenodesinMISarepairwisenonadjacentandnomorenodescanbeaddedtopreservethisproperty.Therefore,eachnodewhichnotinMISisadjacenttoatleastonenodeinMIS.Thus,anMISisindeedaDS.IfthenodesinMISareconnectedbyaddingmorenodestotheMIS,aCDScanbeconstructed.Here,ouralgorithmconsistsofthefollowingthreephases, 1. Rootrisrandomlychosenandweonlyselectthenodes,e.g.nodey,intoMIS,wheredryisaneven.Then,thenodesinMISiscoloredblueorblack,andallothernodesarecoloredgrayorred. 109

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SwapthecolorsofblueandrednodesandchangesomenodestoblackaccordingtotherulesdescribedinsecondphaseofAlgorithm 12 .Consequently,thebluenodesandblacknodesmaybeadjacent,buttheystilldominateothernodes,thereforetheMISwithblackandbluenodesischangedtoaDS. 3. ConnecttheDSwithsomeintermediatenodes,andDSwillbeaCDSnally.ThedetailsofouralgorithmareshowninAlgorithm 12 .Formoreclarication,weshowanexampletoillustratethesecondphase.

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6-2 presentsanexamplethatillustratestheprocedureofswappingcolorinsecondphase.Inthisexample,weassumethatlevela+1isequaltok,whereaiseven,andtheMISwithblueandblacknodesisproducedinrstphase.Now,wedescribehowtoswapthecolorsstepbystep. 1. TheinitialsituationisshowninFigure 6-2 (a),whereblackandbluenodesareinMIS. 2. Inline3ofsecondphase,step(1)isshowninFigure 6-2 (b),thetworednodesinlevela1arechangedtoblue,andnodexischangedtored. 3. Forstep(2),inGa,yistherednodedominatedbyx,coloroney'sneighborpinGa1black.ThissituationisshownasinFigure 6-2 (c). 4. Forstep(3),therednodezinGa+1isdominatedbyx,colorzblack.ThisisshowninFigure 6-2 (d). 5. Inline6,allgraynodesarecoloredblackandallrednodesarecoloredgray,seeFigure 6-2 (e).Atthismoment,thereareonlyblackandgraynodesinthegraphandforeachblacknode,wecanalwaysndexactlyonenodethatmakeitconnectedwithotherblacknodesinupperlevelwithin2hops,sothenumberofblacknodeforconnectingtheDSisatmostjDSj1. 12 ,thenjTCDSj2(K1)KjCDSj1andd(TCDS)2D+6inaDGB.Proof:ItisknownthatforanMISIinDGB,jIjKjCDSj[ 67 ].However,whenweswapthecolorsofnodes,theMISischangedtoaDS,so,jDSj(K1)jIjsinceintheworstcase,inGi,foreveni,ifwechangethecolorforeachbluenodex,wehavetochangeatmostKnon-blacknodestoblacktomaintainthewholenetworkdominatedbyallblacknodes,suchthatxisinMISandeachnodeinMIScanbeadjacentatmostKindependentneighbors[ 67 ].Therefore,thedifferenceinsizebetweenMISandDSisjDSj(K1)jIj.Thus,jTCDSjjDSj+thesizeofconnectingnodes2jDSj12(K1)jIj12(K1)KjCDSj1.FordiameterofCDS,suppose 111

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B C D E Anexampleforsecondphaseinalgorithm 12 112

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34 38 ]canguaranteetheCDSsizeanddiameter,theirperformanceratiosarexed.Consideringtheexibilityofwirelessad-hocnetwork,weintroduce(,)-CDSintoourmodelsothatrst,itsperformanceratiosaretunablebasedontheinput.Second,thecenterofnetworkisinvolvedintheCDSconstructiontoenhancetheperformance.Third,itcanconstructaCDSwithapproximatelysatisfyingthesizeconstraintanddiameterconstraint.Asweintenttobalancethesizeanddiameter,thedenitionof(,)-CDSingiveninwirelessad-hocnetworksasfollows: 1. (Size)ThesizeofCisatmosttimestheminimumCDSsize. 2. (Diameter)ForanypairofvertexuandvinC,d(C)isatmosttimesthemini-mumdiameterofCDSplusaconstantnumber.In(,)-CDS,isanuser-denedinput,andusuallyisafunctionof.Therefore,thevalueofdependsontheuser-denedinput.Inthefollowing,wewilldescribehowtogeneratean(,)-CDS,analyzethetimecomplexityandpresentthetrade-offbetweenthesizeanddiameterthroughanalysis.ThegeneralideaofPAisasfollows. 1. Rootrshouldlocateatthecenterofnetwork,whichisthemid-pointofthelongestshortestpathbetweentwonodesinG. 2. ConstructaCDSTCDSrootedatrbyusingBDA[ 88 ]inourpreviouswork,whereBDAisanapproximationalgorithmforCDSwith2K-approximationonsizeand4-approximationondiameter. 3. ConstructaShortestPathTree(SPT)TSPTrootedatr,whichonlyincludesalltheshortestpathsfromrtoeveryothernodeinTCDS. 4. TraverseTCDSinadepth-rstmanner.Whenvisitinganodeu,ifthenumberofhopsfromrtouinTCDSislargerthanauser-denedthresholdtimesthe 113

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46 ]toconstructanSPTTSPT

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RootSelectionandCDSTreeConstruction:WithDistributedSPTalgorithm[ 46 ],eachnodemaintainsaglobalvariable,whichstoresthecurrentlongestshortestpathinthegraphG,ifalongershortestpathisfound,theglobalvariableofeachnodewillbeupdated.Attheend,wecouldndthemid-pointofgloballongestshortestpath.WhileconstructingTCDSrootedatrbyBDA[ 88 ],eachnodeuneedstomaintainapointer[u]foritsparentonthetreeTCDSandanupperboundd[u]forthenumberofhopstor.WeusetheINITIALIZEandRELAXalgorithmsin[ 39 ]toinitializeandmaintainbothoftheseattributes. 2. ShortestPathTreeConstruction:TSPTrootedatrisconstructedbyusingDistributedSPTalgorithm.ItonlycontainsalltheshortestpathsfromtherootrtoeveryothernodeinTCDS. 3. DepthFirstSearch(DFS):TraversetheTCDSinaDFSmannerbeginningfromtherootralongthepathsfromrtoalltheothernodesinTCDS.Whennodeuisreachedforthersttime,ifd[u]isgreaterthanDSPT(r,u),thentheshortestPruinTSPTisaddedtoTCDSandd[u]and[u]areupdated.Afterthis,nodeu'sparentvneedstobecheckediftheupdatedpathfromrtouwillresultinreducingthenumberofhopsfromrtov.Ifso,thenv'sparentwillbecheckedandsoonuntiltherootrisreached.WiththeexecutionofBDA,distributedSPT(dSPT)(e.g.[ 46 ]),anddistributedDFS(dPFS)(e.g.[ 57 ]),TCDS,TSPTandaDFStraversalordercouldbeachieved.ThedetailsofPAareillustratedinAlgorithm 13 .ToevaluatethecorrectnessofthePA,weexaminewhetherthetwoconstraintsinthedenitionhasbeensatised.Takingasanuser-denedinput,wederivearelationshipbetweenand,whichshowstherelationshipbetweenthesizeoftheconstructedCDSandtheoptimalsolutionofCDSonsize.WealsoanalyzethetimecomplexityofthePA.Denew(TCDS)asthetotalweightofTCDSinG,whereweassumeeachedgehasbeenassignedtheunitweightof1.ThenDSPT(u,v)andDCDS(u,v)areequaltotheweightofTSPT(u,v)andTCDS(u,v)respectively.AnotherobservationisthatjTCDSj=w(TCDS)+1,sincethenumberofnodeinatreeequalstothetotalnumberofedgesplus1,whichalsoequalstow(TCDS)+1.Meanwhile,aswementionedbefore,thelowerboundofminimumdiameterofCDSisD2.Actually,theupperboundfortheminimumdiameterofCDSisD,i.e.,allthenodesinGareinCDS,therefore,D=D. 115

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6-3 .Therefore,hD+1,thenthemaximumnumberofhopsbetweenuandvisatmost2h,thatis2(D+1).2Inrealwirelessad-hocnetwork,case(2)rarelyhappens,sinceitrequiresthatallnodesareuniformlydeployedasaring.However,inmostcases,theyaredeployedrandomly.Therefore,thediameterofCDSreturnedbyPAisboundedby(D+2)inmostcases. 116

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67 ],wehave:Psize(5)K

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88 ]andLemma 16 88 ]anddSPTanddDFSrunatmostO(n2)timecomplexityandsendO(n2)messages[ 46 ][ 57 ].Now,weanalyzetheprocedureofndingthecenterofnetwork.ThedSPTalgorithmisexecutedateachnodexsimultaneously,afterthat,xneedstobroadcastthelongestpathinSPTrootedatxandcompareitwiththelongestpathsreturnedbyothernodes.Therefore,thisprocedureneedsO(n2)timecomplexityandO(n2)messagecomplexity.SinceallotheroperationonlytakeatmostO(n)timecomplexityandO(n)messagecomplexity,theoverallmessagecomplexityandtimecomplexityofPAareO(n2)andO(n2).2 6.6 allowsaCDStobeconstructedwithguaranteedandtunableperformance,whilethecenterofnetworkgreatlyhelpstoimprovetheperformance,e.g.reducingthesizeanddiameterofCDS,whichwillbeveriedinsimulation.However,the 119

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44 ],wepresentthreedistinctimprovements:reducingmultiplepaths,removingredundantterminalsandlocatingcentralarea.Therstandsecondtechniquesreducethesize,whereasthelasttechniquereducestherunningtime. 6-4 .InFigure 6-4 (a),theblackandbluenodesareinTCDSandblacknodesrepresenttheMIS.Supposeweset=1,therednodesthatconsistoftheshortestpathfromrtovisaddedintoTCDS.TheredundantnodeinTCDSisu,sincevcanbeconnectedtotherootviashortestpath.InFigure 6-4 (b),theredundantnodeuisremovedfromTCDS,andthenewCDSissmallerthantheoriginalone.Bydoingthis,weareabletoreducetheCDSsize,leadingtothelowmessageoverheadandtransmissionerrorwithoutinterferingwithCDSdiameter.Wewillshowtheeffectivenessofthistechniqueinsimulation. 120

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B Anexampleforreducingmultiplepath 14 isshowntoimplementthistechnique.Foreasyunderstanding,Figure 6-5 showthesituationsbeforeandafterapplyingthetechnique.InFigure 6-5 (a),theblacknodesareinTCDS,whiletheredundantterminalinTCDSisu,since,besidesu,xisalsodominatedbyv.InFigure 6-5 (b),the 121

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redundantterminaluisremovedfromTCDS,andthenewCDSissmallerthantheoriginalone. B Anexampleforremovingredundantterminals 122

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44 ],eachlinkbetweentwonodesisassignedaweight.Consideringalink(u,v)innetwork,themeasureofweightonlink(u,v)isgivenbythenumberofnodeswithinthetransmissionrangeofnodesuandv(otherthanuandv).LetD(u,v)denotethediskcenteredatuandradiusju,vj.Thentheweightw(u,v)ofthelinkisdenedintermofthenumberofnodesindisksD(u,v)andD(v,u)asdenedbelow. 50 ]toapproximatethecentralareaofthegivennetwork.Weemployatreeanditsleafnodesaredenedastheconvexhullofthegivennetwork.Supposetherootofthetreeisintheconvexhull,moreinternallinkandveryfewboundarylinksareincludedinthetree.ThisapproachhasthedrawbackofdecreasingtheprobabilityoftherootofCDSlocatedatthecentralarea.Toovercome 123

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6 .Observation:Theweightonboundarylinkisverylikelylessthantheweightoninternallink.Fromtheaboveobservation,itisnotdifculttoseethatthecentralareaismoredense(thenumberofnodeperarea)thantheboundaryofnetwork.Therefore,theweightonboundarylinkisnormallylessthanthatoninternallink.In[ 44 ],anO(n2lgn)algorithmforconstructingMinimumInterferenceTree(MIT),whichisbasedonthestructureofMST,isreported.ThisalgorithmisamodicationofthewellknownKruskal'salgorithmforconstructingMST[ 17 ]thatincreasestheprobabilityofboundarylinksincludedinMIT.Wecanusethisalgorithmtoconstructourtreeandtheleafnodesaredenedasthenodesetofconvexhull.Finally,wepickuponenodeinconvexhullastherootofCDS.WecanalsoobservefromthetreeinFigure 6-6 that,asexpected,mostofthelinksneartheboundaryofnetworkarepresentedinourtree,causingmostofleafnodeslocatedatthecentralarea. Figure6-6. Anexampleofleafnodeslocatedatcentralarea.Theblacknodesconsistofthetree. Sincethereisstillsmallprobabilitythattheleafnodeisattheboundary,notincentralarea,ifweselectsuchnodeastherootofCDS,thenourtechniquewillfailattheend.Inordertominimizetheprobabilityofthisunexpectedsituation,wemaysortthetheleafnodesbasedonthedegreeofeachnodeandthenpickupthenodewith 124

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6-7 givesagoodexample.InFigure 6-7 ,theweightofeachlinkisassignedbyDenition 6 ,andthedottedlinksdenotetheconstructedtree,whereaandbaretheleafnodes.IfweselectbastherootofCDS,thenthediameterofCDSwillbe5.Ontheotherhand,ifaistheroot,thediameterwillbeonly4,sinceaisincentralarea,butbisnot.Basedonouraboveidea,wewillonlypickupaastherootsincethedegreeofaislargerthanthatofb. Figure6-7. AnexampleofselectingthenodewithmaximumdegreeastherootofCDS 34 ],CDS-BD[ 38 ],BDA[ 88 ]andPA.Asfarasweknow,CDS-BD-D,CDS-BDandBDAaretheexistingalgorithmsthatguaranteetheconstantperformanceratiosonsizeanddiameter,andwewillshowthatPAoutperformsCDS-BD-D,CDS-BDandBDAinmosttestingcases.Second,wealsowouldliketoverifytheimportanceoflocatingthecenterofnetworkandtesttherunningtimeofBDAandPAtoshowthetrade-offbetweenperformanceandrunningtime.Third,wedoexperimentsby 125

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11 bycomparingwithPAsothatthetrade-offbetweenthefaulttoleranceandsizecouldbesystematicallydiscovered.In[ 34 ],theauthorrstproposedtheAverageBackbonePathLength(ABPL)asanotherfactortoevaluatetheCDS.ABPLofaCDShasbeendenedasthesumofhopdistancebetweenanypairoftwonodesinCDSdividedbythenumberofallpairofnodes.Inoursimulation,weevaluateABPLinadditiontodiameterandsize,sincethediameteronlyrepresentstheworstcasepathlengthofCDS,ignoringtheaveragepathlength,whileABPLcapturesaveragepathlengthformessagedelivery.Therefore,itisourintereststomeasuretheABPLofCDS.Tosimulatethenetwork,werandomlydeployednnodestoaxedareaof1,000mx1,000m.nchangedfrom10to100withanincrementof5.Eachnodevirandomlychosethetransmissionrangeri2[rmin,rmax]wherermin=100mandrmax=200m.Foreachvalueofn,1,000networkinstanceswereinvestigatedandtheresultswereaveraged. 38 ].ItselectsarootrandomlyandspansaCDSfromtheroot.TheapproximationratiosofCDS-BDare11.4and3onsizeanddiameterrespectively.Ontheotherhand,theauthorsin[ 34 ]proposedCDS-DB-Dthatcanbeimplementedindistributedway,however,itonlyguarantees4-approximationondiameter,but6.906-approximationonsize.Forthepurposeoffairness,weset=3(theapproximationratioofPAondiameter)inPA.Figure 6-8A showsthatthediametersofCDSbuiltbythethreealgorithmsareeasytodistinguish,sincethegapiscleartoobserve.Also,wenoticethatPAoutperforms 126

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BComparethesizeofCDS CComparetheABPLofCDS PerformanceforCDS-BD,CDS-BD-DandPA CDS-BD-DbecauseofthelowerapproximationondiameterinPA,andCDS-BDalsoperformsbetterthanCDS-BD-D.Figure 6-8B providestheperformancecomparisonofthethreealgorithmsonthesizeofCDS.ItshowsPAalwaysconstructsaCDSwithsmallersizethanCDS-BDandCDS-BD-D,whichismuchbetterthantheoreticalanalysiswegaveinSection 6.6 .Asexpected,itisreasonablethatCDS-BD-DperformsbetterthanCDS-BD,sinceCDS-BDaddsmorenodesinCDStoshortenthediameter,whichwillcausetheincreaseonsize,butthegapbetweenthetwocurvesisnotlarge.Therefore,theperformanceofPAissatisfactoryonCDSsize.InFigure 6-8C ,asthenumberofnodesinnetworkincreases,theCDSreturnedbyPAalwayshasalowerABPLthanothertwoCDSsdeterminedbyCDS-BD-Dand 127

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BComparethesizeofCDS CComparetheABPLofCDS PerformanceforBDAandPA Thepurposeofthissimulationistoverifytheimportanceofrootselectionandthetrade-offbetweenperformanceandrunningtimeatthesametime.Inordertohighlighttherootselection,weuseavariationofBDA,calledBDA-Mid,asareference.ComparedtoBDA,BDA-Midselectsthecenterofnetworkastherootinsteadofchoosingrandomly.Also,weincludePAinthissimulationandissetto1.Figure 6-9A comparesthediameterofCDSconstructedbythethreealgorithms.Itisshownthat,underdifferentnumberofnodesdeployedinnetworks,theCDSbuiltbyPAhasthesmallestdiameter.WeobservethatthegapbetweenBDAandBDA-Mid 128

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6-9B ,wepresentthesizeofCDSobtainedfromallthreealgorithms,dependingonthenumberofnodesdeployed.ThesizesofCDSsreturnedbythethreealgorithmsareclosetoeachotherandtheyallincreasewiththenumberofnodes.Also,consideringthesamenumberofnodes,BDAreturnsalargersizeofCDSthanPAandBDA-Mid,althoughthegapsbetweenthesealgorithmlooksmallinFigure 6-9B .ThisillustratesthatthesizeofCDScanbereducedbychoosingthecenterofnetworkastheroot.AsshowninFigure 6-9C ,PAachievesaCDSwithsmallestABPL,whereasBDA-MidstillperformsbetterthanBDA.Overall,PAleadstheperformanceonsize,diameterandABPLduetothecenterofnetwork.Therefore,itappearstobeanimportantissueintheconstructionofCDS.Table 6-1 summarizestherunningtimeunderdifferentnumberofnodes.Asthecomplexityanalysisindicates,theruntimeofBDA-MidandPAismuchlongerthanthatofBDA.Thisisduetothelongtimespentondetectingthecenterofnetwork.Moreover,weshowinTable 6-1 thattheBDA-MidstillrunsfasterthanPA,sincePAneedstocomputeTSPTtoshortenthediameter.Whenthenumberofnodesincreases,PAandBDA-Midspendmoretimeondetectingthecenterofnetwork.Therefore,itisatradeoffbetweenthesize/diameterofCDSandrunningtime. 129

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BDA BDA-Mid PA PA3rdTech. ofNode Runtime Runtime Runtime Runtime 10 0.0001 0.0003 0.0006 0.0003 15 0.0002 0.0012 0.0014 0.0003 20 0.0003 0.0044 0.0046 0.0004 25 0.0004 0.0108 0.0132 0.0032 30 0.0006 0.0236 0.0280 0.0056 35 0.0007 0.0442 0.0536 0.0108 40 0.0012 0.0768 0.0980 0.0232 45 0.0012 0.1222 0.1558 0.0352 50 0.0013 0.1836 0.2372 0.0556 55 0.0014 0.2812 0.3742 0.0956 60 0.0030 0.4016 0.5418 0.1438 65 0.0036 0.5414 0.7378 0.2010 70 0.0040 0.7552 1.0332 0.2832 75 0.0046 0.9842 1.3488 0.3712 80 0.0046 1.3050 1.8086 0.5110 85 0.0050 1.6676 2.3030 0.6450 90 0.0045 2.1294 2.9578 0.8400 95 0.0048 2.6672 3.6630 1.0078 100 0.0060 3.7564 5.2224 1.4856 Table6-1. Runtime(ms) BComparethesizeofCDS Performancebasedondifferent 6-10 130

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6-10A ,eachlinerepresentsthediameterofCDSbasedononeofdifferentvaluesof.Whenissetto1,PAaddsashortestpathfromvtorifDCDS(r,v)islargerthanDSPT(r,v).Therefore,PAwith=1returnsaCDSwiththesmallestdiameter.Whenissetto4,PAonlyaddsthepathfromvtorinTCDSundertheconditionthatDCDS(r,v)isgreaterthan4timesofDSPT(r,v).Thus,theCDSbyPAwith=4hasthelargestdiameter.For=2,thecorrespondinglineisinthemiddle.Therefore,asweexpected,thediameterofCDSbuiltbyPAcouldbecontrolledbyadjustingthevaluesof.InFigure 6-10B ,eachlinerepresentsthesizeofCDSbasedononeofdifferentvaluesof.Whenissetto1,ifDCDS(r,v)islargerthanDSPT(r,v),PAaddsashortestpathfromvtor.Thisstrategywillincurmorenodestobeadded.Ontheopposite,whenissetto4,PAresultsinaCDSwithsmallersize.For=2,thecorrespondinglineisinthemiddle,thesamesituationasinFigure 6-10A .Inconclusion,theperformanceofPAcanbebalanceddependingonthevalueofandthetradeoffbetweensizeanddiameterisclear. BComparethesizeofCDS Performancefortherstandsecondimprovementtechniques Inthissection,weareinterestedinevaluatingtheeffectivenessofthepresentedimprovementtechniques.Sincetherstandsecondtechniquesaredevotedinto 131

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6-11A describestheperformanceintermsofthediameterofCDS.Asweexpected,thediameterisnotaffectedbytherstandsecondtechniques.Meanwhile,asobservedfromFigure 6-11B ,thesizeofCDSisreducedwhenthetwotechniquesapply.Clearly,webelievethattherstandsecondimprovementtechniquesareeffectiveinreducingthesizeofCDS. BComparethesizeofCDS Performanceforthethirdimprovementtechniques Table 6-1 alsosummarizesthecomparisonofruntimebyPAwithandwithoutthethirdimprovementtechnique.Incredibly,thethirdtechniqueachievesthereductionofrunningtimegreatly,althoughhereitsacricesalittleperformanceonsizeanddiameter,asshowninFigure 6-12A and 6-12B ,whichindicatesthetrade-offbetweenrunningtimeandsize/diameter.However,itisstillpromisingtondthecentralareainnetwork,inordertoachievethefastconstructionofCDS. 11 .WeintendtoillustratethatAlgorithm 11 improvesthefaulttoleranceofCDSbyaddingmarginaloverhead(intermsofthenumberofnodesaddedintoCDS).WetaketheCDSgeneratedbyPAastheinputofAlgorithm 11 ,andwesetk=2,m=1and=2. 132

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BComparetheSizeofCDS Performanceformulti-factorsmodel Figure 6-13A comparestheperformanceofAlgorithm 11 andPAintermsofthediameterofCDS.Asweexpected,thereislittledifferenceonthediameterofCDSbasedonthetwoalgorithms,whichperfectlymatchesourtheoreticalanalysisforthediameterofkm-CDS.Therefore,Algorithm 11 enhancesthefaulttoleranceofCDSwithoutaffectingitsdiametergreatly.Meanwhile,asobservedfromFigure 6-13B ,thesizeofkm-CDSobtainedfromAlgorithm 11 iscertainlylargerthanCDSbyPA.Specically,theperformanceofthetwoalgorithmsisrelativelyproportional.Asobservedfromourexperiments,thesizeofkm-CDSobtainedfromAlgorithm 11 isalmost1.1timesthesizeofCDSreturnedbyPA.TheresultsindicatethatconsideringthefaulttolerancewillincreasethesizeoftheCDSatthesametime.However,theincreaseinsizeisstillboundedandpredictable.Therefore,itiscleartoseethetrade-offbetweenthefaulttoleranceandsize. 133

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IncheolShinwasbornin1977,inSeoul,RepublicofKorea.HereceivedBachelorofengineeringdegreeatcomputerengineeringin2002fromHansungUniversity,Seoul,RepublicofKorea.In2006,hereceivedhisMasterofEngineeringdegreefromtheDepartmentofComputerandInformationScienceandEngineeringattheUniversityofFlorida.Hismajorresearchareaiscomputernetworks. 145