energy efficient fault tolerant coverage in wireless...

Research ArticleEnergy Efficient Fault Tolerant Coverage inWireless Sensor Networks

Shagufta Henna

Department of Computer Science Bahria University Islamabad Pakistan

Correspondence should be addressed to Shagufta Henna shinnabuicbahriaedupk

Received 2 November 2016 Revised 18 February 2017 Accepted 19 February 2017 Published 3 April 2017

Academic Editor Alberto J Palma

Copyright copy 2017 Shagufta Henna This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Energy efficiency and fault tolerance are two of the major concerns in wireless sensor networks (WSNs) for the target coverageDesign of target coverage algorithms for a large scale WSNs should incorporate both the energy efficiency and fault tolerance Inthis paper we study the coverage problem where the main objective is to construct two disjoint cover sets in randomly deployedWSNs based on relay energy (119864relay) Further we present an approximation algorithm called Energy Efficient Maximum DisjointCoverage (EMDC) with provable approximation ratios We analyze the performance of EMDC theoretically and also performextensive simulations to demonstrate the effectiveness of EMDC in terms of fault tolerance and energy efficiency

1 Introduction

WSN is a random or deterministic deployment of massivenumber of sensor nodes in a monitored area WSNs haveextensive applications including military surveillance [1]target tracking wild life monitoring fire prevention rescueoperations and air quality monitoring [2ndash4] The primarygoal of sensor nodes is to sense and collect raw data by moni-toring particular environment target and barrier and reportthat event to some sink node after some local processing oraggregation [5 6]

Target coverage and network life time are two of therecent research trends in WSNs Deployment of a set ofsensors to cover a particular area targets or barrier iscalled coverage problem [7] The main purpose of targetcoverage [8] is to continuously monitor a set of targets byusing a subset of sensors These sensor nodes are subjectto failures due to various reasons One of the commonreasons is battery failure Other reasons may include radiointerference software or hardware faults and environmentalchanges Sensor node failures may affect the coverage andconnectivity adversely which in turn degrades the sensornetwork performance with higher network delays and higherenergy consumption [9]

Sensor nodes are equippedwith limited capacity batteriesRecently it has been investigated whether it is possible

to conserve energy by using duty cycle protocols wherenodes switch their radio on and off periodically prolongingthe life time of a WSN Due to one time battery life anddifficulty of replacing it sensor nodes are densely deployedto increase connectivity and target coverage However if allthe nodes are constantly on it may quickly deplete theirbattery and may affect the network life time Therefore it isimportant to tune these sensors to duty-cycled mode wherethey alternate between the active and sleep periods Furthersensor hardware or software may fail due to weather or otherphysical conditions in a WSN affecting coverage of targetnodes If coverage of the target nodes is achieved by a singleset of covering nodes they may soon deplete their energyaffecting the network life time Therefore it is important forWSNs to use redundant or disjoint covering sensors to coverparticular area targets or barriers to construct a fault tolerantnetwork which may still cover the targets area or barrierdespite the failure of some covering sensors

In order to effectively utilize the sensor nodes somestudies have selected a number of cover sets to providecoverage to some target setsThese studies organize the coversets [7 10] into disjoint or nondisjoint cover sets [11 12] Theselection of such disjoint or nondisjoint cover sets is proved tobeNP-complete problem [9 11] Disjoint or nondisjoint coversets monitor the targets in a cooperative way Compared tonondisjoint cover sets disjoint cover sets are better at fault

HindawiJournal of SensorsVolume 2017 Article ID 7090782 11 pageshttpsdoiorg10115520177090782

2 Journal of Sensors

tolerance because all the cover sets have exclusive sensornodes among their sets Each cover set can alternatively workto maximize the network lifetime

A number of studies have addressed the issue of targetcoverage however only fewer of them considered the disjointtarget coverage based on minimum relay energy In thisarticle our key focus is on the fault tolerant target coverageproblem with minimum relay energy We formulate thedisjoint target coverage problem based on 119864relay energy Thisproblem differs from the target coverage which is based ondisjoint covering sets since coverage ensures that the 119864relayenergy of each sensor from each of the disjoint sets is kept atminimum We aim to select two disjoint covering sets withminimum 119864relay to cover the targets that is each sensor hasminimum 119864relay energy It is crucial to select sensor nodeswhich consume minimum energy to report an event to thesink node Therefore our primary objective is to maximizethe network lifetime by selecting two disjoint covering setswith minimum overall 119864relay energy In order to fulfil boththe fault tolerance and energy efficiency requirements wepropose an efficient approximation algorithm Energy Effi-cient Maximum Disjoint Coverage (EMDC) with provableapproximation bound Our key contributions in this paperare summarized as follows

(i) We present a comprehensive comparison of wellknown target coverage area coverage and barriercoverage schemes

(ii) We formulate disjoint coverage problem with mini-mum 119864relay energy

(iii) Wepropose an efficient bounded approximation algo-rithm the EMDC to the minimum 119864relay energy cov-erage problem and present an appropriate theoreticalanalysis of the EMDC approximation ratio

(iv) We perform simulations under different scenarios toestablish the effectiveness of EMDC

The remaining article is organized as follows Section 2gives a comprehensive background of the coverage andpresents a comparison of different coverage schemes inWSNs Section 3 summarizes the relatedwork followed by theformulation of minimum energy disjoint coverage problemin Section 4 Section 5 presents EMDC algorithm designSection 6presents the theoretical analysis of EMDC Section 7presents the EMDC simulation results and finally Section 8concludes the paper

2 Coverage in WSNs

Asensor is a devicewith the capability of responding to differ-ent physical stimuli including sound heat smoke pressureand any other event and transforming it into correspondingelectrical or mechanical signal [13]These signals are mappedto sensor information A sensor node consists of one or moresensing units batterymemory data processing unit and datatransmission unit AWSN consists of different sensing nodesplaced in an area to detect or monitor certain activity Oneof the most recent trends in WSNs research is the coverage

question which reflects how well a particular area target orbarrier is monitored Coverage problems in WSNs can ariseduring the network design deployment or operation [14]During the design of the network coverage questions canbe addressed by deciding the number of sensors to cover aparticular area In WSN deployment sensors are deployedto achieve the coverage of desired targets barriers or areasin a geographical region During the operational phase of asensor network a schedule is decided to conserve energy andincrease network life time Sensor coverage problems can bedivided into three categories

(i) Area coverage [15ndash18] where the primary objective isto continuously observe or cover some particular areaor whole sensor field

(ii) Target coverage [19] where the key objective is tomonitor some particular points also termed as targets

(iii) Barrier coverage [20] a barrier coverage is a circulararea where the presence of any intruder can bedetected by a set of sensor deployed in this area

Table 1 summarizes different coverage approaches with typeof coverage and objectives in WSNs Our work in this paperfocuses on targeting coverage only

21 Target Coverage Problems In target coverage the pri-mary objective is to cover some particular set of pointsor targets deployed in a sensor field for example missilelaunchers in a battlefield These targets can be covered byusing a random or deterministic placement of sensors

Optimal Placement of Sensors In the deterministic approachto node placement nodes are placed at predetermined loca-tions to cover targets The deterministic approach to nodeplacement is convenient to use for reachable and friendlysensor fields The main objective of this approach is tocover optimal locations by using a minimum number ofcovering nodes In this technique it is assumed that thelocations of targets to be monitored are fixed known andare limited In some cases coverage of all the targets is notnecessary when the number of covering sensors is limited orit is expensive to cover them Most of the problems relatedto sensor placement are optimization problems and it ispossible to formulate them as mathematical programmingproblems However greedy solutions may not produce thebest possible placementThe problem to construct minimumnumber of disjoint sensors to cover targets is a well-knownset cover problem [37] Covering sensors can be representedas set covers used to cover particular deployed targets or areaTo place a covering sensor it must be placed on a locationto cover at least one target and it is possible to cover allthe targets if the covering sensors are deployed on all theavailable locations Different variants of the greedy approachfor set cover arewell documented in literature to solve variousproblems related to optimal node placement [38ndash41] Apart

Journal of Sensors 3

Table 1 Coverage approaches used in WSNs

Method Type of coverage Main objectivesDisjoint dominating sets [21] Area coverage Maximize lifetime and energy of a WSNCoverage configuration protocol (CCP)[15] Area coverage Improve connectivity and energy efficiency

Coverage based on CDS [22] Area coverage Enhance network lifetime and energy of a WSN

Placement algorithm for nodes [19] Area coverage andTarget coverage Coverage and connectivity

Disjoint set cover algorithm [23] Target coverage Energy efficient strong coverageDensity control algorithm based onprobing [24] Area coverage Energy efficient strong coverage

Optimal geographical density control(OGDC) algorithm [25] Area coverage Energy efficient strong coverage

Self-scheduling algorithm for nodes [16] Area coverage Energy efficient strong coverageOSRCEA Algorithm [26] Area coverage Improved coverage and connectivityVoronoi-based coverage improvementapproach [27] Area coverage Improved coverage ratio

Localized algorithm for hole detectionand healing [28] Area coverage Coverage hole detection and healing

Optimal angular coverage in video sensornetworks [29] Area coverage Improved angular area coverage

Approximation algorithm for surfacecoverage [30] Surface coverage Improved surface coverage

Particle swarm optimization (PI-BPSO)algorithm [31] Camera coverage Improved homogeneous camera network

coverageDelaunay-based coordinate-freemechanism (DECM) [32] Area coverage Coverage hole detection and healing

Full-view coverage detection [33] Area coverage Full view coverage detectionDetection accuracy algorithm [34] Target coverage Achieve detection accuracyMinimum weight barrier algorithm(MWBA) [26] Barrier coverage Increase detection probability of barriers

Strong barrier coverag algorithm [35] Barrier coverage Strong barrier coverage with minimumdirectional sensors

A greedy solution for 119896-barrier coverage[36] Barrier coverage To construct minimum size 119896-barrier coverage

from greedy algorithms several approximation solutionshave also been proposed for node placement [42 43]

Coverage Lifetime Maximization In a random placementsensors are randomly scattered to cover targets In a randomdeployment a single sensor node may cover multiple fixedtargets and a fixed target may be covered by multipledeployed sensors Deployment of sensors in a random place-ment may be dense The coverage lifetime maximizationproblem which is a distinct version of the target coverageproblem is to partition the sensors into more than oneset covers subject to certain coverage requirements and toactivate these set covers alternately to increase the networklifetime An example of random deployment of target cov-erage is illustrated in Figure 1(a) where 6 sensing devices aredeployed to cover 4 targets in a random setting In Figure 1(a)the 1198792 and 1198794 targets are covered by two sensors and 1198791and 1198793 are covered by three sensor nodes The coveragerelationship between the sensors and targets can be depictedby a bipartite graph as illustrated in Figure 1(b)

To achieve target coverage all the sensors can be activatedwhich is not very energy efficient andmay reduce the networklifetime However alternatively activating the sensors mayprolong the network lifetime Assume that if all the sensorsare activated for one unit of time it will consume one unit ofnetwork lifetime In Figure 1 we have two disjoint set covers1198781 = 1199041 1199043 1199046 and 1198782 = 1199042 1199044 1199045 to cover all the targetsFor one time unit set 1198781 can cover targets and for the other1198782 increase the network lifetime to two time units Usingan optimal number of set covers and alternatively activatingthem may increase the network lifetime

Another version of the target coverage is Maximum SetCover (MSC) in which the primary objective is to coverall the specified targets all the time The MSC problemis known to be NP-complete [44] Target coverage at alltimes is a strict requirement for the coverage The 119896-setcover forminimum coverage breach problem allows coveragebreach and relaxes the strict coverage requirement [45] Abreached target is not covered by any sensor or in otherwordsbreach coverage requires partial target coverage only In this


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Figure 1 (a) Random deployment of sensor nodes (b) Corresponding bipartite graph for (a)

problem set covers are computed to cover only a fraction offixed targets and are activated alternatively for short durationThe main objective of the 119896-set cover problem is to increasethe lifetime of a WSN by constructing maximum 119896 set covers[45ndash47] In [45] a problem called disjoint set covers (DSC)has been proposed for complete target coverage which issimilar to the MSC problem with disjointness constraintsEnergy efficiency using disjoint set covers to alternativelyperform the coverage task has been discussed in [18 44]

Slijepcevic and Potkonjak [18] proposed a centralizedsolution for the 119896-coverage problem where points enclosedin a particular area called fields are monitored by 119896 set ofsensors The algorithm [18] covers the most critical fieldsby using maximum possible set covers In this algorithmthe set covers which can cover a high number of uncoveredpoints in an area are given priorityThis algorithm also avoidsfield coverage redundancy There exist several distributedsolutions which can achieve 1-coverage that is can cover thetarget or area by using only one set cover In [16] a pruningmethod is presented where each node switches off its radioto conserve energy if its area can be covered by some of itsneighbours Unlike a centralized solution for the 119896-coverageproblem in [18] a distributed solution for the same problemhas been proposed in [46]

In our work we formulate a decision version of the targetcoverage problem called EMDC The EMDC problem is toachieve themaximumdisjoint coverage using two disjoint setcovers1198631 and1198632 with minimum 119864relay energy Our problemaims to find a set cover 1198632 with minimum 119864relay energy tomaximize the target coverage in such a way that disjoint setcover 1198631 with minimum 119864relay still completely covers all thetargets Further 119864relay of 1198631 is less than or equal to 119864relayenergy of1198632

3 Related Works

Recently there is a trend in WSNs to discover set covers thatare disjoint and are connectedwith a sink for target reportingThese disjoint sets can be activated alternatively to conserveenergy or can be activated simultaneously to ensure reliable

coverage I Cardei andM Cardei [48] addressed the problemknown as Connected Set Covers (CSC) problem which com-putes the maximum possible set covers connected to a sinknode and proved this problem as an NP-complete problemTo address this problem authors proposed two differentheruistics based on integer programming and breadth-firstsearch Ostovari et al presented an edge-cost based approachfor the connected point coverage [49] In this approach anode can decide to act as a relay node by evaluating its edgecost in the Minimum Spanning Tree (MST) [50 51]

Zhao and Gurusamy formulated the connected targetcoverage problem as maximum cover tree (MCT) problem[52]They provedMCT problem as an NP-complete problemand established an upper bound for the network lifetimeZorbas et al [53] also considered the target coverage problemand proposed a power efficient coverage algorithm to selectdisjoint and nondisjoint cover sets with particular focuson weakly monitored targets Yu et al [54] presented a119896-coverage working set construction (CWSC) algorithmCWSC algorithm is able to produce different degrees ofcoverage according to the application selected In [55] Shihet al modelled the target coverage problem by consideringmultiple sensing units They reduced it to a connectedset cover problem Further they presented two distributedheuristics the energy efficiency first scheme (EEFS) andremaining energy first scheme (REFS) In [56] authorshave proposed a centralized algorithm called CCTC119896 and adistributed algorithm called DCTC119896 for connected target 119896-coverage problem in heterogeneous WSNs Both algorithmsconstruct connected cover sets to achieve connectivity andcoverage in an energy efficient way

Zhao and Gurusamy [52] proposed a distributed approx-imation algorithm known as Communication WeightedGreedy Cover (CWGC)The primary objective of the CWGCis to maximize the covering sets by considering minimumtotal weight from each node to the sink node CWGCalgorithm maximizes network lifetime compared to someexisting work however it does not take into account poorlycovered targets Yang et al considered the special instance of119896-connected coverage and designed two distributed solutions


based on clustering and pruning [57] In [58] authors haveconsidered the target coverage problem by considering twotypes of sensor nodes including resource rich sensors andenergy-constrained sensors

Zorbas and Razafindralambo [34] proposed OptimizedConnected Coverage Heuristic (OCCH) to compute setcovers and each node is assigned a weight which exemptsthe critical nodes from acting as relay nodes OCCHprolongs network lifetime by conserving the energy ofenergy-constrained node Experiments reveal that OCCHhas better lifetime compared to CWGC Some other popularapproaches which satisfy the energy and connectivity havebeen discussed in [34 59]

Henna and Erlebach [60] formulate a problem calledMaximum Disjoint Coverage Problem (MDC) Main objec-tive of MDC is to construct two disjoint set covers 1198781 and 1198782where 1198781 completely covers all the targets and 1198782 covers themaximum of these targets Authors proved the problem asan NP-complete problem and presented an efficient approx-imation algorithm called DSC-MDC to solve it HoweverDSC-MDC just computes the disjoint set covers but does notconsider the relay energy of the sensor nodes DSC-MDCtherefore is not an energy efficient fault tolerance solution totarget coverage

Coverage connectivity and fault tolerance are primaryobjectives for most of the target tracking sensor networksHowever in order to achieve connectivity and coverage wecannot ignore critical nodes especially nodes with criticalenergy Hence it is necessary to select disjoint set coverswhich take into account 119864relay energy of nodes to reportan event to a particular sink However as discussed inthe aforementioned work most of the existing schemesdiscussing target coverage problem to compute cover setsignore the issue of critical nodes as relay nodes In this studywe propose an approximation Energy Efficient MaximumDisjoint Coverage (EMDC) algorithm to construct two dis-joint cover sets to achieve both the fault tolerance and energyefficiency We establish that approximation ratio of EMDC isradic119898 where119898 denotes the number of fixed targets

4 Preliminaries

41 Set Cover Problem Let 119880 denote the set of elements and119862 be a collection of subsets of set119880 Given both119880 and 119862 theset cover problem targets to cover all the elements of set 119880by selecting the minimum number of sets from 119862 Basicallyset cover problem aims to cover all the elements of set 119880The set cover problem is illustrated below with the help of anexample

Let 119880 = 119886 119887 119888 119889 be the universal set Given thefollowing collection of sets 119878 119878 = 1198781 1198782 1198783 1198784 where 1198781 =119886 119887 1198782 = 119887 119888 1198783 = 119888 119889 and 1198784 = 119889 119886 Both 1198781 and1198783 together form a minimum set cover that is 119878119890119905_119888119900V1198901199031 =1198781 1198783 Another possible minimum set cover is 119878119890119905_119888119900V1198901199032 =1198782 1198784 Both minimum set covers have size 2

42 Disjoint Set Covers (DSC) Given a finite set of sensornodes119882 to cover a finite set of targets 119879 the DSC problem

is to construct disjoint set covers from 119882 to cover all theelements of 119879 [23] A set cover119882119894 sub 119882 is selected such that119905119895 isin 119879 is covered by at least one of the elements of119882119894 and for119882119894 and119882119896119882119894 cap119882119896 = 0

43 Maximum Disjoint Coverage Problem (MDC) Given aset119882 of subsets of a given finite target set 119879 construct twodisjoint set covers1198821 and1198822 for119879 such that each element oftarget 119879 is covered by at least one element of set1198821 and anelement of1198822 covers the maximum elements of 119879 and forthe set covers1198821 and11988221198821 cap1198822 = 0

The decision variation of theMDC called Disjoint Cover-age (DC) is defined as follows

Disjoint Coverage (DC) Given a finite set of targets 119879 for acollection 119882 of subsets of 119879 determine if 119878 can be dividedinto two set covers with no common element and these setcovers can completely cover all the elements of set 119879

44 Energy Efficient Disjoint Target Coverage Problem(EMDC) Given a collection of 119882 of subsets with 119864relayenergy of a given set 119879 EMDC problem seeks two disjointcover set 1198631 and 1198632 for 119879 such that the following objectivesare achieved

(i) Each element of 119879 is being covered by at least oneelement of1198631

(ii) 1198632 covers maximum elements of 119879(iii) Set covers1198631 and11986321198631 cap 1198632 = 0(iv) 119864relay energy of1198631 is less than or equal to119864relay energy

of1198632

5 Energy Efficient MaximumDisjoint Coverage (EMDC)

EMDC is an approach to the fault tolerant energy efficientproblem and is performed by each sensor EMDC selects twoenergy efficient disjoint sets1198631 and1198632 based on the followingprinciples (i) select a sensor node as a candidate for1198631 or1198632if it can cover maximum possible targets (ii) favour sensornodes that consumes minimum energy to report an event tothe sink node (iii) make sure both the set covers 1198631 and 1198632cover the target nodes 119879 and are completely disjoint with nocommon nodes

It is worth mentioning that EMDC favours a sensor nodeto be added in the set cover1198631 or1198632 depending on the 119864relayenergy which is calculated according to (1) For a subset119872119894representing neighbours of node 119894 119864Relay119894(119872119894) is calculatedaccording to

119864relay119894 (119872119894) =11003816100381610038161003816119872119894

1003816100381610038161003816+sum119895isin119872119894 119864relay119895

10038161003816100381610038161198721198941003816100381610038161003816

(1)

In (1) the first term denotes the expected waiting time anode from a set of sensor nodes119882 takes to report an event toa fixed sink node and is inversely proportional the number ofits 1-hop neighboursThe second terms represents the average


expected time a node has to wait to report the event to aparticular sink node 119861 119864relay119894(119872119894) therefore represents thetotal expected waiting time a node will take to report theevent to the sink node 119861 119864relay119894(119872119894) is a better choice to selectthe nodes with less energy consumption to report an event toa particular sink node

EMDCdetermines two energy efficient disjoint set covers1198631 and1198632 with minimum 119864relay energy Algorithm first con-structs 1198632 by including sensor nodes which have minimum119864relay energy and can cover the maximum elements of set 119879On the other hand1198631 includes sensor nodes with minimum119864relay energy and are able to cover all the given targets fromthe set 119879 In order to compute two disjoint sets 1198631 and1198632 algorithm takes subsets 119879 = 1199051 1199052 119905119898 and 119882 =1199081 1199082 119908119899 EMDC assumes that each subset from thecollection 119882 knows its 119864relay energy Each subset from thecollection119882 is mapped to a certain number of subsets fromthe collection119879 EMDC selects a set119908119894 from the collection119882by using a greedy approach EMDC selects 119908119894 from119882 to beadded into the set 1198632 if 119908119894 covers the maximum number ofelements from the set 119879 and has minimum 119864relay energy andthere exists a set 119908119895 which covers the same or more numberof targets as 119908119894 Further EMDC evaluates if 119908119895 has less orequal 119864relay energy as 119908119894 if it is true EMDC adds the set119908119894 in 1198632 The algorithm EMDC repeats until all the possiblesubsets from the collection 119882 have been added in the setcover 1198632 Subsets in 119882 that is 119882 1198632 are passed to the119863119894119904119895119900119894119899119905119878119890119905(119882) algorithm 119863119894119904119895119900119894119899119905119878119890119905(119882) adds a subset 119908119894in set 1198631 if it covers maximum targets from the set 119879 andhas minimum 119864relay energy among all the subsets coveringthe same number of targets 119863119894s119895119900119894119899119905119878119890119905(119882) repeats until allthe targets are covered from 119879 At the end 119863119894119904119895119900119894119899119905119878119890119905(119882)returns a disjoint set cover 1198631 with minimum 119864relay energywhich covers all the targets from the set 119879 Finally EMDCreturns 1198631 and 1198632 set covers with minimum 119864relay energywhere1198631 covers all the targets from the set 119879 and1198632 coversmaximum of them Algorithm EMDC and its counterpart119863119894119904119895119900119894119899119905119878119890119905(119882) are shown in Algorithms 1 and 2

We can explain the operation of Algorithm 1 with anexample given in Figure 2 Figure 2 shows a bipartite graphwith two sets119882 and 119879119882 is a covering set which can coverthe elements in set 119879 The coverage relationship between theelements of set119882 and119879 is illustrated with the help of an edgeFrom the bipartite graph given in Figure 2 Algorithms 1 and2 compute two disjoint set covers1198631 and1198632

Algorithm 1 computes 1198632 to cover the set of targets 119879 asfollows

(1) EMDC chooses 1199082 greedily to cover maximum tar-gets that is 1199051 1199052 1199053 1199054 such that still it is possible tocover these targets by 1199083 and 1199085 which has less 119864relaythan 1199082 and adds 1199082 to1198632

1198632 = 1199082 (2)

(2) EMDC chooses 1199086 greedily to cover maximum tar-gets that is 1199054 1199055 1199056 such that still it is possible to

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Figure 2 A bipartite graph with two energy efficient disjoint setcovers

cover these targets by 1199081 and 1199085 having less 119864relayenergy compared to 1199086 and adds 1199086 to1198632

1198632 = 1199082 1199086 (3)

(3) EMDC chooses 1199084 greedily to cover maximum tar-gets that is 1199052 1199055 1199057 such that still it is possible tocover these targets by 1199081 and 1199085 which has less 119864relayenergy compared to 1199084 and adds 1199084 to 1198632 EMDCdoes not select 1199083 or 1199081 because then 1199053 or 1199054 cannotbe covered by1198631

1198632 = 1199082 1199086 1199084 (4)

Targets covered by set cover1198632 are

119879 = 1199051 1199052 1199053 1199054 cup 1199054 1199055 1199056 cup 1199052 1199055 1199057

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 (5)

From the remaining sets that is 1199081 1199082 1199083 Algorithm 2computes1198631 greedily to cover the set of targets 119879 as follows

1198631 = 1199081 1199085 1199083 (6)

Targets covered by set cover1198631119879 = 1199052 1199054 1199057 1199058 cup 1199051 1199055 1199056 cup 1199053 1199057 1199058

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 1199058 (7)

In this example1198631 and1198632 are selected disjoint set covers Byusing Algorithms 1 and 2 1198631 achieves complete coverage ofset 119879 and1198632 covers maximum elements of set 119879


Data Subsets119882 = 1199081 1199082 119908119898 with 119864relay119894Result Disjoint Set Covers1198631 and1198632 with minimum 119864relay119895119863 lArr 1198821198632 lArr 0while119863 = 0 doLet 119908119894 isin 119863 be a set with minimum 119864relay119894 which covers the maximum number of targets from 119879if all targets covered by 119908119894 can still be covered by some other set 119908119895 in119863 which has less or equal 119864relay119895 compared to 119864relay119894of 119908119894 then1198632 lArr 1198632 cup 119908119894119882 lArr 119882 119908119894

end119863 lArr 119863 119908119894

end1198631 lArr 119863119894119904119895119900119894119899119905119878119890119905(119882)Output Disjoint Set Covers1198631 and1198632 with minimum 119864relay

Algorithm 1 Energy Efficient Maximum Disjoint Coverageradic119898-approximation Algorithm (EMDC)

Data Subsets119882 = 1199081 1199082 119908119898Result Set Cover1198631 with minimum 119864relay1198631 lArr 0while1198631 does not cover all targets doLet 119908119894 isin 119882 be a set that increases the coverage of1198631 byas much as possibleLet 119908119894 has less 119864Relay119894 compared to 119864Relay119895 of someother nodes 119908119895 isin 119882Let 119908119895 covers the same or less number of targets as 1199081198941198631 lArr 1198631 cup 119908119894119882 lArr 119882 119908119894

endReturn1198631

Algorithm 2 119863119894119904119895119900119894119899119905119878119890119905(119882) to compute set cover 1198631 withminimum 119864relay

6 Approximation Analysis

Theorem 1 Approximation ratio of EMDC is not worse thanradic119898 where119898 denotes the number of elements in the set 119879

Proof Given a finite set of targets 119879 with 119898 elements let ushave a collection of subsets in 119878which cover all119898 elements of119879 Let EMDC selects 119908119894 which has minimum 119864relay119894 and addsit in set 1198632 which can cover 119896119894 elements from the target set119879 Let us say EMDC adds119872 number of sets with minimum119864relay to set 1198632 Let us say in each iteration 119894 number oftargets covered by particular set 119904119894 with minimum 119864relay isrepresented by 119898119894 Then the total number of targets coveredby EMDC using 1198632 with minimum 119864relay in 119862 iterations isgiven as follows

100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)

Let us say in order to cover 119879 targets with 1198632 withminimum 119864relay we have an OPT solution Given thatOPT solution we can prove that in the worst case EMDC

is a radic119898 approximation compared to OPT Let us say thatEMDC computes |1198632| which covers the number of targetswhich are greater than or equal to radic119898 In this case optimalalgorithm OPT is able to cover maximum 119898 elements Wecan compare the maximum number of targets covered byboth EMDC and OPT as follows

100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr

radic119898-Approximation

(9)

On the contrary let the number of targets covered by1198632 using EMDC be less than or equal to radic119898 Let for eachiteration 119894 EMDC selects a set 119908119894 for 1198632 and 119908119894 is the lastavailable set in 119882 Let us say 119908119894 covers 119898119894minus1 targets in eachiteration In worst case for all iterations and for each set 119904119894EMDC loses at most119898119894(119898119894minus1) elements where 1 lt 119894 lt 119872 Itmeans EMDC loses atmost1198981(1198981minus1)+1198982(1198982minus1)+1198983(1198983minus1) + sdot sdot sdot + 119898119860(119898119860 minus 1) denoted by |Loss1198632 | that is

10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)

On the other hand |OPT| is able to cover all the targetseither part of |1198632| or |Loss1198632 | For all the iterations 119860 themaximum number of targets covered by |OPT| can berepresented as follows

|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)


Table 2 Simulation setting for EMDC

Parameter ValueSimulation area 1000 times 1000Node sensing range 100mTransmission range 200mNumber of sensors 50ndash150Number of targets 10ndash80

Table 3 Energy consumption model for EMDC

State EnergyListening 109mATransmit 116mAReceive 70mA

We compare the number of targets covered by EMDC to themaximum number of targets covered by OPT algorithm asfollows

100381610038161003816100381611986321003816100381610038161003816 le 1198981 + 1198982 + 1198983 + sdot sdot sdot + 119898119860 le radic119898

|OPT| le 11989821 + 11989822 + 11989823 + sdot sdot sdot + 119898

2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2

le (1198981 + 1198982 + 1198983 + sdot sdot sdot + 119898119860) sdot radic119898 997904rArr

|OPT|1198981 + 1198982 + 1198983 + sdot sdot sdot + 119898119860

le radic119898 997904rArr


(12)

From the above analysis it is proved that EMDC is aradic119898-approximation

7 Performance Evaluations

In our simulation scenarios we use a sensor network withstatic sensor and target nodes randomly deployed in a 1000mtimes 1000m area We specify the number of sensors and targetsin each simulation scenario In the sensing region deployedtargets and sensors are fixed during whole simulation time Ifnot stated otherwise all deployed sensor nodes use uniformsensing range of 100m Sensing range of each node isassumed to be twice of its transmission range All resultsare averaged over 10 runs The simulation parameters for theevaluation of EMDC are summarized in Table 2

For the average network lifetime energymodel ofMICA2is considered Each sensor is assumed to has an initial energyof 200 J We assume that energy consumed by each sensor isJminute Each simulation run lasts for 100 minutes Table 3summarizes the energy model for our simulations

In the first scenario sensors are varied from 50 to 150to cover 50 targets deployed in an area of 1000 times 1000 Allsensor nodes have uniform sensing range of 100m Figure 3shows the average disjoint set covers generated under varyingnumber of sensor nodes for EMDC and DSC-MDC [60]We can see that disjoint set covers tend to increase with an

EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

60 70 80 90 100 110 120 130 140 15050Number of sensors

Figure 3 Number of disjoint set covers versus Number of Sensors

EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

20 30 40 50 60 70 8010Number of targets

Figure 4 Number of disjoint set covers versus Number of Targets

increase in sensor nodes for both EMDC and DSC-MDCDisjoint set covers increase with an increase in the numberof sensors since more sensor nodes are available to qualify asset covers

In the second scenario 100 nodes with sensing range of100m are deployed in a fixed simulation area of 1000m times1000m to cover targets varying from 10 to 80 Figure 4shows disjoint set covers generated for varying number oftargets We observe that average disjoint set covers decreasesas targets increase for both The reason is that when targetsincrease while keeping the number of sensor nodes fixeddisjoint set covers decrease as likelihood of disjoint targetcoverage decreases We can observe that EMDC has lessdisjoint set covers for all the targets due to the constraint ofenergy during the selection of set covers

In third scenario 100 sensors are deployed in a fixedsimulation area of 1000m times 1000 to cover 50 targets Sensingrange of each node is varied from 100m to 500m In Figure 5


EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)

Figure 5 Number of disjoint set covers versus Sensing Range (m)

we observe the effect of sensing range on disjoint set coversWe can observe that for both theEMDCandDSC-MDCwithan increase in the sensing range number of disjoint set coversincreases Disjoint set covers tend to increase consistently forall sensing ranges since each sensor node is able to covermore targets This coverage increase results in an increasein disjoint set covers However we can observe that EMDCconsistently has less disjoint set covers compared to the DSC-MDCdue to theminimum energy constraint on the selectionof disjoint set covers

Simulation parameters used in this experiment are sameas used in scenario 1 All the nodes consume energy byusing the energy model shown in Table 3 In Figure 6 weobserve the effect of varying number of sensors on the averagenetwork lifetime In case of DSC-MDC more number ofdisjoint set covers is computed compared to EMDC sincethere is no constraint on the sensor nodes to qualify as amember of the set covers Average network lifetime for bothEMDC and DSC-MDC is directly proportional to disjointsets produced We already observed that EMDC has lessdisjoint set covers compared to the DSC-MDC as shownin Figure 4 However we can observe that EMDC is stillcompetitive to DSC-MDC for the average network lifetimebecause EMDC always selects disjoint set covers by takinginto account the minimum energy

Simulation parameters used in this experiment are thesame as those used in scenario 2 All the nodes use theenergy model as listed in Table 3 Figure 7 shows the networklifetime while increasing sensor nodes It is clear from theFigure that network lifetime of EMDC is better than DSC-MDC when number of nodes increases In case of DSC-MDC assuming constant energy consumption for each nodeto forward the event we can observe that average networklifetime consistently drops with an increase in targets Inorder to monitor more targets more energy is consumed tonotify the event to the sink node EMDC has better networklifetime compared to DSC-MDC because EMDC considersthe nodes with minimum energy in order to qualify for the

EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime

Figure 6 Network Lifetime versus Number of Sensors

EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime


Figure 7 Network Lifetime versus Number of Targets

set covers for both the disjoint sets Results show that networklifetime is significantly improved when set covers are selectedaccording to minimum energy This observation is still validwhen the number of targets tends to increase For examplewith 60 targets average lifetime of EMDC is more than 80better compared to DSC-MDC

8 Conclusion

The proposed algorithm EMDC maximizes network lifetimeby using two energy efficient disjoint set covers in a single hopWSN with a single sink EMDC achieves energy efficiencyand fault tolerance by selecting two disjoint set covers withminimum relay energy On one hand two disjoint set coversachieve fault tolerance by providing double coverage and onthe other hand they maximize network lifetime by consider-ing the relay nodes with minimum energy required to reportthe event to the sink node The experimental results reveal


that EMDC achieves reasonable number of disjoint set coversto achieve fault tolerance under varying number of nodesand sensing ranges Further EMDC achieves better networklifetime compared to DSC-MDC for different number ofnodes and sensing ranges

Conflicts of Interest

The author declares no conflicts of interest

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E CayircildquoWireless sensor networks a surveyrdquo Computer Networks vol38 no 4 pp 393ndash422 2002

[2] PGuo JWangXHGengC S Kim and J-UKim ldquoAvariablethreshold-value authentication architecture for wireless meshnetworksrdquo Journal of Internet Technology vol 15 no 6 pp 929ndash935 2014

[3] J Shen H Tan J Wang J Wang and S Lee ldquoA novel routingprotocol providing good transmission reliability in underwatersensor networksrdquo Journal of Internet Technology vol 16 no 1pp 171ndash178 2015

[4] Y Liu N Xiong Y Zhao A V Vasilakos J Gao and Y JialdquoMulti-layer clustering routing algorithm for wireless vehicularsensor networksrdquo IET Communications vol 4 no 7 pp 810ndash816 2010

[5] H Sajedi and Z Saadati ldquoA hybrid structure for data aggre-gation in wireless sensor networkrdquo Journal of ComputationalEngineering vol 2014 Article ID 395868 7 pages 2014

[6] P Li S Guo S Yu and A V Vasilakos ldquoReliable multicastwith pipelined network coding using opportunistic feeding androutingrdquo IEEE Transactions on Parallel and Distributed Systemsvol 25 no 12 pp 3264ndash3273 2014

[7] A Sangwan and R P Singh ldquoSurvey on coverage problems inwireless sensor networksrdquo Wireless Personal Communicationsvol 80 no 4 pp 1475ndash1500 2015

[8] B Wang ldquoCoverage problems in sensor networks a surveyrdquoACM Computing Surveys vol 43 no 4 article no 32 2011

[9] Y Yao Q Cao and A V Vasilakos ldquoEDAL an energy-efficientdelay-aware and lifetime-balancing data collection protocol forheterogeneous wireless sensor networksrdquo IEEEACM Transac-tions on Networking vol 23 no 3 pp 810ndash823 2015

[10] M Ashouri Z Zali S R Mousavi and M R HashemildquoNew optimal solution to disjoint set K-coverage for lifetimeextension in wireless sensor networksrdquo IET Wireless SensorSystems vol 2 no 1 pp 31ndash39 2012

[11] Y Lin J Zhang H S-H Chung W H Ip Y Li and Y-H Shi ldquoAn ant colony optimization approach for maximizingthe lifetime of heterogeneous wireless sensor networksrdquo IEEETransactions on Systems Man and Cybernetics Part C Applica-tions and Reviews vol 42 no 3 pp 408ndash420 2012

[12] K Islam and S G Akl ldquoTarget monitoring in wireless sensornetworks a localized approachrdquo Ad-Hoc and Sensor WirelessNetworks vol 9 no 3-4 pp 223ndash237 2010

[13] J SWilson Sensor TechnologyHandbook Newnes OxfordUK2004

[14] D G Costa and L A Guedes ldquoThe coverage problem in video-based wireless sensor networks a surveyrdquo Sensors vol 10 no 9pp 8215ndash8247 2010

[15] X Wang G Xing Y Zhang C Lu R Pless and C GillldquoIntegrated coverage and connectivity configuration in wirelesssensor networksrdquo in Proceedings of the First InternationalConference onEmbeddedNetworked Sensor Systems (SenSys rsquo03)pp 28ndash39 Los Angeles Calif USA November 2003

[16] D Tian and N D Georganas ldquoA coverage-preserving nodescheduling scheme for large wireless sensor networksrdquo inProceedings of the 1st ACM International Workshop on WirelessSensor Networks and Applications pp 32ndash41 September 2002

[17] J Carle and D Simplot-Ryl ldquoEnergy-efficient area monitoringfor sensor networksrdquo Computer vol 37 no 2 pp 40ndash46 2004

[18] S Slijepcevic and M Potkonjak ldquoPower efficient organizationof wireless sensor networksrdquo in Proceedings of the InternationalConference of Communications (ICC rsquo01) pp 472ndash476 HelsinkiFinland June 2001

[19] K Kar and S Banerjee ldquoNode placement for connected cov-erage in sensor networksrdquo in Proceedings of the Conferenceon Modeling and Optimization in Mobile AdHoc and WirelessNetworks 2003

[20] J Luo and S Zou ldquoStrong k-barrier coverage for one-wayintruders detection in wireless sensor networksrdquo InternationalJournal of Distributed Sensor Networks vol 2016 Article ID3807824 16 pages 2016

[21] M Cardei D MacCallum M X Cheng et al ldquoWirelesssensor networks with energy efficient organizationrdquo Journal ofInterconnection Networks vol 3 no 4 pp 213ndash229 2002

[22] J Wu and H Li ldquoOn calculating connected dominating set forefficient routing in ad hoc wireless networksrdquo in Proceedingsof the ACM Workshop on Discrete Algorithms and Methods forMobile Computing and Communications pp 7ndash14 August 1999

[23] M Cardei and D-Z Du ldquoImproving wireless sensor networklifetime through power aware organizationrdquoWireless Networksvol 11 no 3 pp 333ndash340 2005

[24] F Ye G Zhong S Lu and L Zhang ldquoEnergy efficient robustsensing coverage in large sensor networksrdquo Tech Rep UCLA2002

[25] H Zhang and J C Hou ldquoMaintaining sensing coverage andconnectivity in large sensor networksrdquo Tech Rep UIUCDCS-R-2003-2351 Department of Computer Science University ofIllinois at Urbana Champaign Ill USA 2003

[26] J Chen J Li andTH Lai ldquoEnergy-efficient intrusion detectionwith a barrier of probabilistic sensors global and localrdquo IEEETransactions on Wireless Communications vol 12 no 9 pp4742ndash4755 2013

[27] T-W Sung and C-S Yang ldquoVoronoi-based coverage improve-ment approach for wireless directional sensor networksrdquo Jour-nal of Network and Computer Applications vol 39 no 1 pp202ndash213 2014

[28] M R Senouci A Mellouk and K Assnoune ldquoLocalizedmovement-assisted sensordeployment algorithm for holedetec-tion and healingrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 5 pp 1267ndash1277 2014

[29] E Yildiz K Akkaya E Sisikoglu and M Y Sir ldquoOptimalcamera placement for providing angular coverage in wirelessvideo sensor networksrdquo IEEE Transanctions on Computing vol63 no 7 pp 1812ndash1825 2014

[30] L Kong M Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[31] Y-G Fu J Zhou and L Deng ldquoSurveillance of a 2D plane areawith 3D deployed camerasrdquo Sensors (Switzerland) vol 14 no 2pp 1988ndash2011 2014


[32] C Qiu and H Shen ldquoA delaunay-based coordinate-free mech-anism for full coverage in wireless sensor networksrdquo IEEETransanctions on Parallel Distributed System vol 25 pp 500ndash509 2012

[33] Y Wang and G Cao ldquoAchieving full-view coverage in camerasensor networksrdquo ACM Transactions on Sensor Networks vol10 no 1 article 3 2013

[34] D Zorbas and T Razafindralambo ldquoProlonging network life-time under probabilistic target coverage in wireless mobilesensor networksrdquo Computer Communications vol 36 no 9 pp1039ndash1053 2013

[35] D Tao S Tang H Zhang X Mao and H Ma ldquoStrongbarrier coverage in directional sensor networksrdquo ComputerCommunications vol 35 no 8 pp 895ndash905 2012

[36] Z Wang J Liao Q Cao H Qi and Z Wang ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[37] T H Cormen C Stein R L Rivest and C E LeisersonIntroduction to Algorithms McGraw-Hill Higher Education2001

[38] S S Dhillon and K Chakrabarty ldquoSensor placement foreffective coverage and surveillance in distributed sensor net-worksrdquo in Proceedings of the IEEEWireless Communications andNetworking Conference The Dawn of Pervasive Communication(WCNC rsquo03) vol 3 pp 1609ndash1614 March 2003

[39] S S Dhillon K Chakrabarty and S S Iyengar ldquoSensorplacement for grid coverage under imprecise detectionsrdquo inProceedings of the 5th International Conference on InformationFusion (FUSION rsquo02) pp 1581ndash1587 July 2002

[40] Y Zou and K Chakrabarty ldquoUncertainty-aware and coverage-oriented deployment for sensor networksrdquo Journal of Paralleland Distributed Computing vol 64 no 7 pp 788ndash798 2004

[41] Z Fang and J Wang ldquoSensor placement for grid coverageunder imprecise detectionsrdquo in Proceedings of the 3rd Interna-tional ConferenceWireless Algorithms Systems and Applications(WASA rsquo08) pp 188ndash199 Dallas Tex USA 2008

[42] F Y S Lin and P L Chiu ldquoA near-optimal sensor placementalgorithm to achieve complete coverage-discrimination in sen-sor networksrdquo IEEE Communications Letters vol 9 no 1 pp43ndash45 2005

[43] F Y S Lin and P L Chiu ldquoEnergy-efficient sensor networkdesign subject to complete coverage and discrimination con-straintsrdquo in Proceedings of the IEEE International Conference onSensor and Ad hoc Communication and Networks pp 586ndash5932005

[44] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of theIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[45] M X Cheng L Ruan and W Wu ldquoCoverage breach problemsin bandwidth-constrained sensor networksrdquoACMTransactionson Sensor Networks vol 3 no 2 article 12 2007

[46] Z Abrams A Goel and S Plotkin ldquoSet k-cover algorithmsfor energy efficient monitoring in wireless sensor networksrdquoin Proceedings of the Symposium on Information Processing inSensor Networks pp 26ndash27 Berkeley Calif USA April 2004

[47] A Deshpande S Khuller A Malekian and M Toossi ldquoEnergyefficient monitoring in sensor networksrdquo in Proceedings of theInternational Conference on Theoretical Informatics pp 7ndash112008

[48] I Cardei and M Cardei ldquoEnergy-efficient connected-coveragein wireless sensor networksrdquo International Journal of SensorNetworks vol 3 no 3 pp 201ndash210 2008

[49] P Ostovari M Dehghan and JWu ldquoConnected point coveragein wireless sensor networks using robust spanning treesrdquo inProceedings of the 31st International Conference on DistributedComputing Systems Workshops (ICDCSW rsquo11) pp 287ndash293Minneapolis Minn USA June 2011

[50] M Saravanan and M Madheswaran ldquoA hybrid optimizedweighted minimum spanning tree for the shortest intrapathselection in wireless sensor networkrdquoMathematical Problems inEngineering vol 2014 Article ID 713427 8 pages 2014

[51] R Lachowski M E Pellenz M C Penna E Jamhour and RD Souza ldquoAn efficient distributed algorithm for constructingspanning trees in wireless sensor networksrdquo Sensors (Switzer-land) vol 15 no 1 pp 1518ndash1536 2015

[52] Q Zhao and M Gurusamy ldquoLifetime maximization for con-nected target coverage in wireless sensor networksrdquo IEEEACMTransactions on Networking vol 16 no 6 pp 1378ndash1391 2008

[53] D Zorbas D Glynos P Kotzanikolaou and C DouligerisldquoSolving coverage problems in wireless sensor networks usingcover setsrdquo Ad Hoc Networks vol 8 no 4 pp 400ndash415 2010

[54] J Yu XDengD YuGWang andXGu ldquoCWSC connected k-coverageworking sets construction algorithm inwireless sensornetworksrdquo International Journal of Electronics and Communica-tions vol 67 no 11 pp 937ndash946 2013

[55] K-P Shih D-J Deng R-S Chang and H-C Chen ldquoOnconnected target coverage for wireless heterogeneous sensornetworks with multiple sensing unitsrdquo Sensors vol 9 no 7 pp5173ndash5200 2009

[56] J Yu Y Chen L Ma B Huang and X Cheng ldquoOn connectedtarget k-coverage in heterogeneous wireless sensor networksrdquoSensors vol 16 no 1 article 104 pp 262ndash265 2016

[57] S Yang F Dai M Cardei and J Wu ldquoOn multiple pointcoverage in wireless sensor networksrdquo in Proceedings of the 2ndIEEE International Conference on Mobile Ad-hoc and SensorSystems (MASS rsquo05) pp 757ndash764 November 2005

[58] I Cardei ldquoEnergy-efficient target coverage in heterogeneouswireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference onMobile Ad Hoc and Sensor Sysetems (MASSrsquo06) pp 397ndash406 Vancouver Canada October 2006

[59] M A Khan H Hasbullah and B Nazir ldquoMulti-node reposi-tioning technique for mobile sensor networkrdquo AASRI Procediavol 5 pp 85ndash91 2013

[60] S Henna and T Erlebach ldquoApproximating maximum disjointcoverage in wireless sensor networksrdquo in Proceedings of the12th International Conference on Ad-Hoc Mobile and WirelessNetworks (ADHOC-NOW rsquo13) Lecture Notes in ComputerScience pp 148ndash159 Springer July 2013

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



tolerance because all the cover sets have exclusive sensornodes among their sets Each cover set can alternatively workto maximize the network lifetime

A number of studies have addressed the issue of targetcoverage however only fewer of them considered the disjointtarget coverage based on minimum relay energy In thisarticle our key focus is on the fault tolerant target coverageproblem with minimum relay energy We formulate thedisjoint target coverage problem based on 119864relay energy Thisproblem differs from the target coverage which is based ondisjoint covering sets since coverage ensures that the 119864relayenergy of each sensor from each of the disjoint sets is kept atminimum We aim to select two disjoint covering sets withminimum 119864relay to cover the targets that is each sensor hasminimum 119864relay energy It is crucial to select sensor nodeswhich consume minimum energy to report an event to thesink node Therefore our primary objective is to maximizethe network lifetime by selecting two disjoint covering setswith minimum overall 119864relay energy In order to fulfil boththe fault tolerance and energy efficiency requirements wepropose an efficient approximation algorithm Energy Effi-cient Maximum Disjoint Coverage (EMDC) with provableapproximation bound Our key contributions in this paperare summarized as follows

(i) We present a comprehensive comparison of wellknown target coverage area coverage and barriercoverage schemes

(ii) We formulate disjoint coverage problem with mini-mum 119864relay energy

(iii) Wepropose an efficient bounded approximation algo-rithm the EMDC to the minimum 119864relay energy cov-erage problem and present an appropriate theoreticalanalysis of the EMDC approximation ratio

(iv) We perform simulations under different scenarios toestablish the effectiveness of EMDC

The remaining article is organized as follows Section 2gives a comprehensive background of the coverage andpresents a comparison of different coverage schemes inWSNs Section 3 summarizes the relatedwork followed by theformulation of minimum energy disjoint coverage problemin Section 4 Section 5 presents EMDC algorithm designSection 6presents the theoretical analysis of EMDC Section 7presents the EMDC simulation results and finally Section 8concludes the paper

2 Coverage in WSNs

Asensor is a devicewith the capability of responding to differ-ent physical stimuli including sound heat smoke pressureand any other event and transforming it into correspondingelectrical or mechanical signal [13]These signals are mappedto sensor information A sensor node consists of one or moresensing units batterymemory data processing unit and datatransmission unit AWSN consists of different sensing nodesplaced in an area to detect or monitor certain activity Oneof the most recent trends in WSNs research is the coverage

question which reflects how well a particular area target orbarrier is monitored Coverage problems in WSNs can ariseduring the network design deployment or operation [14]During the design of the network coverage questions canbe addressed by deciding the number of sensors to cover aparticular area In WSN deployment sensors are deployedto achieve the coverage of desired targets barriers or areasin a geographical region During the operational phase of asensor network a schedule is decided to conserve energy andincrease network life time Sensor coverage problems can bedivided into three categories

(i) Area coverage [15ndash18] where the primary objective isto continuously observe or cover some particular areaor whole sensor field

(ii) Target coverage [19] where the key objective is tomonitor some particular points also termed as targets

(iii) Barrier coverage [20] a barrier coverage is a circulararea where the presence of any intruder can bedetected by a set of sensor deployed in this area

Table 1 summarizes different coverage approaches with typeof coverage and objectives in WSNs Our work in this paperfocuses on targeting coverage only

21 Target Coverage Problems In target coverage the pri-mary objective is to cover some particular set of pointsor targets deployed in a sensor field for example missilelaunchers in a battlefield These targets can be covered byusing a random or deterministic placement of sensors

Optimal Placement of Sensors In the deterministic approachto node placement nodes are placed at predetermined loca-tions to cover targets The deterministic approach to nodeplacement is convenient to use for reachable and friendlysensor fields The main objective of this approach is tocover optimal locations by using a minimum number ofcovering nodes In this technique it is assumed that thelocations of targets to be monitored are fixed known andare limited In some cases coverage of all the targets is notnecessary when the number of covering sensors is limited orit is expensive to cover them Most of the problems relatedto sensor placement are optimization problems and it ispossible to formulate them as mathematical programmingproblems However greedy solutions may not produce thebest possible placementThe problem to construct minimumnumber of disjoint sensors to cover targets is a well-knownset cover problem [37] Covering sensors can be representedas set covers used to cover particular deployed targets or areaTo place a covering sensor it must be placed on a locationto cover at least one target and it is possible to cover allthe targets if the covering sensors are deployed on all theavailable locations Different variants of the greedy approachfor set cover arewell documented in literature to solve variousproblems related to optimal node placement [38ndash41] Apart






















T4

T3T2T1

s5

s3

s1

s2s4

s6

(a)

T1

T2

T3

T4

s1

s2

s3

s4

s5

s6

(b)





3 Related Works










4 Preliminaries











of1198632




119864relay119894 (119872119894) =11003816100381610038161003816119872119894

1003816100381610038161003816+sum119895isin119872119894 119864relay119895

10038161003816100381610038161198721198941003816100381610038161003816

(1)








1198632 = 1199082 (2)


TW

w1

w2

w3

w4

w5

w6

t1

t2

t3

t4

t5

t6

t7

t8



1198632 = 1199082 1199086 (3)


1198632 = 1199082 1199086 1199084 (4)


119879 = 1199051 1199052 1199053 1199054 cup 1199054 1199055 1199056 cup 1199052 1199055 1199057

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 (5)


1198631 = 1199081 1199085 1199083 (6)


= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 1199058 (7)




end119863 lArr 119863 119908119894




endReturn1198631





100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)



100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr


(9)


10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)


|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)









2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























T4

T3T2T1

s5

s3

s1

s2s4

s6

(a)

T1

T2

T3

T4

s1

s2

s3

s4

s5

s6

(b)





3 Related Works










4 Preliminaries











of1198632




119864relay119894 (119872119894) =11003816100381610038161003816119872119894

1003816100381610038161003816+sum119895isin119872119894 119864relay119895

10038161003816100381610038161198721198941003816100381610038161003816

(1)








1198632 = 1199082 (2)


TW

w1

w2

w3

w4

w5

w6

t1

t2

t3

t4

t5

t6

t7

t8



1198632 = 1199082 1199086 (3)


1198632 = 1199082 1199086 1199084 (4)


119879 = 1199051 1199052 1199053 1199054 cup 1199054 1199055 1199056 cup 1199052 1199055 1199057

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 (5)


1198631 = 1199081 1199085 1199083 (6)


= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 1199058 (7)




end119863 lArr 119863 119908119894




endReturn1198631





100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)



100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr


(9)


10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)


|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)









2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














4 Preliminaries











of1198632




119864relay119894 (119872119894) =11003816100381610038161003816119872119894

1003816100381610038161003816+sum119895isin119872119894 119864relay119895

10038161003816100381610038161198721198941003816100381610038161003816

(1)








1198632 = 1199082 (2)


TW

w1

w2

w3

w4

w5

w6

t1

t2

t3

t4

t5

t6

t7

t8



1198632 = 1199082 1199086 (3)


1198632 = 1199082 1199086 1199084 (4)


119879 = 1199051 1199052 1199053 1199054 cup 1199054 1199055 1199056 cup 1199052 1199055 1199057

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 (5)


1198631 = 1199081 1199085 1199083 (6)


= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 1199058 (7)




end119863 lArr 119863 119908119894




endReturn1198631





100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)



100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr


(9)


10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)


|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)









2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















1198632 = 1199082 (2)


TW

w1

w2

w3

w4

w5

w6

t1

t2

t3

t4

t5

t6

t7

t8



1198632 = 1199082 1199086 (3)


1198632 = 1199082 1199086 1199084 (4)


119879 = 1199051 1199052 1199053 1199054 cup 1199054 1199055 1199056 cup 1199052 1199055 1199057

= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 (5)


1198631 = 1199081 1199085 1199083 (6)


= 1199051 1199052 1199053 1199054 1199055 1199056 1199057 1199058 (7)




end119863 lArr 119863 119908119894




endReturn1198631





100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)



100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr


(9)


10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)


|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)









2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











end119863 lArr 119863 119908119894




endReturn1198631





100381610038161003816100381611986321003816100381610038161003816 = 1198881 + 1198882 + 1198883 + sdot sdot sdot + 119888119862 (8)



100381610038161003816100381611986321003816100381610038161003816 ge radic119898

|OPT| le 119898 997904rArr

|OPT|100381610038161003816100381611986321003816100381610038161003816le radic119898 997904rArr


(9)


10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) (10)


|OPT| le 10038161003816100381610038161003816Loss119863210038161003816100381610038161003816 +100381610038161003816100381611986321003816100381610038161003816 le119860

sum119894=1

119898119894 (119898119894 minus 1) +119860

sum119894=1

119898119894 (11)









2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















2119860

le (1198981 + 1198982 + 1198981198963 + sdot sdot sdot + 119898119860)2





(12)






EMDCDSC-MDC

0

5

10

15

20

25

30

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers



EMDCDSC-MDC

20

25

30

35

40

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers







EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










EMDCDSC-MDC

05

1015202530354045505560

Aver

age n

umbe

r of d

isjoi

nt se

t cov

ers

150 200 250 300 350 400 450 500100Sensing range (m)





EMDCDSC-MDC


0102030405060708090

100110

Aver

age n

etw

ork

lifet

ime


EMDCDSC-MDC

0102030405060708090

100110120130

Aver

age n

etw

ork

lifet

ime




8 Conclusion






References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













References






























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation







































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









energy efficient fault tolerant coverage in wireless...

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