Research ArticleDesperate Coverage Problem in Mission-Driven CameraSensor Networks

Yi Hong1 Junghyun Kim2 Donghyun Kim2 Deying Li1 and Alade O Tokuta2

1 Key Laboratory of Data Engineering and Knowledge Engineering Renmin University of ChinaMOE and School of Information Renmin University of China Beijing 100872 China

2Department of Mathematics and Physics North Carolina Central University Durham NC 27707 USA

Correspondence should be addressed to Deying Li deyingliruceducn

Received 16 January 2014 Revised 25 March 2014 Accepted 31 March 2014 Published 24 April 2014

Academic Editor KingShan Lui

Copyright copy 2014 Yi Hong et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Recently camera sensor network is attracting huge amount of attention due to the growing popularity of multimedia applicationsThis paper investigates a new scheduling problem in camera sensor network whose goal is to cover a set of targets as efficiently aspossible during a given mission period In particular we consider a desperate situation in which we may not have enough camerasensors to cover all of the targets of interest during the mission The goal of our problem of interest is to schedule the sensors suchthat (a) the number of the most important targets which are fully covered during the mission period is maximized and (b) theoverall target-temporal coverage which is defined as the gross sum of the weight of each target multiplied by the time period whenthe target is covered is maximized We formally introduce the desperate coverage problem in mission-driven camera sensor networks(DCP-MCSN) and propose a new heuristic algorithm for this NP-hard problem To evaluate the performance of the proposedalgorithm we compare it with a theoretical upper bound Our simulation result shows that our algorithm performs very close tothe upper bound and outperforms the existing alternative

1 Introduction

Thanks to the growing popularity of multimedia applicationsof wireless sensor networks camera sensor networks whichare wireless networks of camera sensors are getting moreattention very recently A camera sensor node is a kind ofdirectional sensor node whose sensing range resembles asector of a disk In Figure 1 the sector with a solid lineis the area covered by a directional sensor 119904

119894 Therefore 119904

119894

is covering a target 119906 The beamwidth 120579 is dependent onthe sensorrsquos physical characteristics d

(119894119895)is a vector from

119904119894to the center of the surface of the 119895th sector However

the design and implementation of camera sensor networksinvolve additional challenges on the top of the complexityof directional sensor network due to several key featuresof camera sensor networks For instance a picture of theocciput of a person is hardly useful to verify the identity ofthe person which implies that a camera sensor node may notbe able to cover an object within its sensing sector dependingon the facing direction of the object As shown in Figure 2

a target 119906 is covered by two camera sensors 1199041and 119904

2

The inner angle between the viewing orientation of 1199041and

119906rsquos facing orientation 1205791 is smaller than that between the

viewing orientation of 1199042and 119906rsquos facing orientation 120579

2 As a

result 1199041can capture a more recognizable image of 119906 than 119904

2

Most wireless sensor nodes are battery-operated and it isvery difficult or expensive to replace or recharge the batteryAs a result energy efficiency has been amajor issue ofwirelesssensor networksOne popular approach to extend the lifetimeof wireless sensor network is to exploit the redundancyof coverage in wireless sensor network That is in manyapplication scenarios sensor nodes are randomly deployedand thus it is highly likely that a target of interest can bemonitored by more than one node at the same time Thenwe can make a sleep-wakeup schedule of the nodes whichcan cover the same target and activate them one by one whilethe rest of them fall asleep In the literature the problem ofcomputing a sleep-wakeup schedule of sensor nodes suchthat the total time period satisfies a certain coverage qualityrequirement is referred as a ldquocoverage problemrdquo One popular

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 109785 10 pageshttpdxdoiorg1011552014109785

2 International Journal of Distributed Sensor Networks

Si

120579

urarrd(ij)

Figure 1 The sensing model of the directional sensor

ursquos facing direction (rarrfu)

S2

S

u

1

12057921205791

s1 rsquos viewing direction

s2 rsquos viewing direction

Figure 2 The sensing model of the camera sensor

coverage problem is the full-coverage problem whose goal istomaximize the lifetime of a sensor networkwhile seamlesslycovering an area or targets of interest [1 2]

Most coverage problems in wireless sensor networkshave focused on the lifetime maximization issue In thoseproblems the lifetime of the networks is an optimizationgoal not a constraint However this is not always the casein reality For instance consider an application of wirelesssensor networks in which we have to cover an area of interestor a set of targets during ldquoa given mission periodrdquo (whichis a constraint) but we do not have enough sensors tofully cover the whole area or the targets regardless of thescheduling algorithm we use Certainly the existing coveragealgorithms that we discussed so far cannot deal with thissituation Recently Liu and Cao introduced one way tohandle this challenging issue Given a required surveillancemission period they suggested to maximize the spatial-temporal coverage of the area or targets of interest which isdefined as the gross sum of the total time that each distinctarea is covered multiplied by the size of the area (in case ofarea coverage) [3] or the gross sumof theweight of each targetcoveredmultiplied by the total time duration that the target iscovered (in case of target coverage) [4] Very recently Honget al extended this idea and investigated a spatial-temporalcoverage problem in camera sensor networks [5]

In this paper we introduce another way to deal with thequestion of how to provide the best quality coverage over

Desperate coverage algorithm formission-driven camera sensor

networks (DCA-MCSN)

Network

Sensorscheduler

scheduler (k)

Sector decider

Binary search tomaximize k

Figure 3 DCA-MCSN is a binary search algorithm to identifythe maximum number of the most important targets which can beseamlessly covered by the camera sensors during themission periodand corresponding scheduling

a set of targets of interest during a given mission periodwith insufficient number of camera sensor nodes This studyis motivated by our observation that when we solely aimto maximize the coverage quality (the total target-temporalcoverage) like [4 5] it is possible that some targets withthe highest priority could be deprioritized by a number ofinsignificant targets and as a result relatively ignored inthe course of the schedule building process The problem ofmonitoring a warehouse with two entrances during a certaintime period is a good example Clearly the entrances arethe most important targets since the face of any trespassercan be easily detected by a camera observing the entranceMeanwhile a shelf inside the warehouse without any item isclearly a less-important target To deal with this situation wesuggest providing full coverage to as many higher prioritytargets as possible during the mission period while thespatial-temporal coverage over the rest of targets can bemaximized We would like to emphasize that we are nottrying to refute the significance of the target-temporal-maximization-only approach used in [4 5] but we attemptto propose a new complement for those approaches to dealwith this desperate situation The main contributions of thispaper can be summarized as follows

(a) We introduce a new scheduling problem in camerasensor networks namely desperate coverage prob-lem in mission-driven camera sensor networks (DCP-MCSN) More formal description of the problem isgiven in Section 4

(b) We propose a new heuristic algorithm for our newNP-hard problem called desperate coverage algorithmin mission-driven camera sensor networks (DCA-MCSN) In detail given a set of camera sensors aset of targets and a mission period DCA-MCSNperforms a binary search (see Figure 3) to find a

International Journal of Distributed Sensor Networks 3

constant 119896 such that the most 119896 important tar-gets are fully covered during the mission periodDuring the search process 119896 is assumed to be asome constant (eg initially 119896 larr lceil1198982rceil) andNetwork-Scheduler (Algorithm 3) is executedNetwork-Scheduler internally calls two subproce-dures Sector-Decider (Algorithm 1) and Sensor-Scheduler (Algorithm 2) to determine the sensingsector of each camera sensor and the activation sched-ule of each camera sensor Dependent on Network-Scheduler the 119896 value is increased or decreased andthe whole process is repeated until we finalize 119896 andobtain a schedule which allows the camera sensorsto fully cover the most 119896 important targets and thetarget-temporal coverage is maximized

(c) We compare the average performance ofDCA-MCSNwith the theoretical upper bound in simulation aswellas with the only existing competitor in [5] Our sim-ulation result shows that our algorithm outperformsthe target-temporal-maximization-only algorithm incamera sensor network in [5] in terms of the numberof the most important targets which are fully coveredduring the whole mission period

The rest of this paper is organized as follows Section 2presents related work Some preliminaries are introducedin Section 3 We introduce the formal definition of DCP-MCSN and our algorithm for this problem in Section 4Our simulation result is presented in Section 5 Finally weconclude this paper in Section 6

2 Related Work

Frequently the problem of constructing a sleep-wakeupschedule of a wireless sensor network with the goal ofmaximizing the continuous monitoring time to meet agiven coverage quality requirement is referred as a coverageproblem [2ndash4 6] Most types of wireless sensor networksthoroughly investigated in the literature consider sensornodes with omnidirectional sensing range Consequentlythe area covered by those sensor nodes resembles a diskwith the node in the center of it In contrast the sensingarea covered by a directional sensor node looks more like asector of a disk [7] In [8] Cai et al have investigated themultiple directional cover set problem in directional sensornetworks whose objective is to compute a sleep-wakeupschedule of a given set of sensor nodes such that the timefor the sensor network to fully cover a given set of targets ismaximized In the meantime Ai and Abouzeid [9] studied anew coverage problem in directional sensor networks whosegoal is given a set of sensor nodes with adjustable cameraorientations to determine the direction (orientation) of eachsensor so that the number of covered targets is maximized(primary objective) while the number of sensor nodes usedis minimized (secondary objective) In addition the otheraspects of directional sensor networks are also investigatedlike vulnerability [10] fault-tolerance [11] and so on [12 13]

Briefly speaking camera sensor network is a kind ofdirectional sensor network and thus they share several

properties However due to several unique features of camerasensors especially the effective-sensing surveillance modelin Definition 1 the scheduling algorithms for directionalsensor networks are not directly applicable to camera sensornetworks Most importantly a camera sensor node can covera target only if the face of the target can be seen by thesensor In [14] Liu et al introduced the directional 119896-coverage problem in camera sensor networkswhose objectiveis minimizing the number of camera sensors to cover an areaof interest such that any spot in the area can be monitored byat least 119896 different cameras In [13] Wang and Cao assumed acamera sensor network version of the full coverage problemcalled the full-view coverage problem In this problem atarget is full-view covered by a camera sensor network if wecan capture the face of a target which is within the sensingrange of the camera sensor network independent of the facedirection of the target Previously Ma et al extended theresult in [13] and investigated the full-view barrier coverageproblem in camera sensor networks

So far most coverage problems in wireless sensor net-works have concerned about the lifetimemaximization issueTherefore they are not applicable to a desperate situation inwhich we are required to cover an area or a set of targets ofinterest during a given mission period One possible solutionof this challenging issue is introduced by Liu and Cao [3 4]who suggested to maximize the spatial-temporal coverageof the area or targets of interest In our previous work weextended this idea and investigated a spatial-temporal cover-age problem in camera sensor networks [5] However Liu andCaorsquos approach comes with a nonneglectable shortcomingmdasha target with the highest priority could be deprioritized by anumber of insignificant targets and as a result is ignored by ascheduling algorithm In this paper we address this issue andattempt to propose an alternative solution of the problem asa complement of Liu and Caorsquos approach

3 Preliminaries

In this section we review two important preliminaries of ourpaper the effective-sensingmodel in camera sensor networks[14] and the Identifiability Test [5] which is a procedure tocheck given a set of targets and a set of camera sensors ifthe target is effectively covered by the camera sensors Aswe mentioned earlier this paper assumes that a target isrecognized or effectively sensed (covered) by a camera sensorif the facial view of the target is observed by a camera sensorThe face direction of each target can be estimated by anexisting head pose estimating strategy such as the one in [15]A more formal definition of the effective-sensing model incamera sensor networks is as follows

Definition 1 (effective-sensing model) Consider a target 119905119896

located at (119909119896 119910119896) and a sensor 119904

119894located at (119909

119894 119910119894) 119905119896is

effectively sensed (covered) by 119904119894if 119905119896is within the sensing

area of 119904119894and the internal angle between two vectors f

119896and

k(119896119894)

is not greater than 120601 that is 120572(f119896 k(119896119894)) le 120601 (see

Figure 4) where vector f119896is the facing orientation of 119905

119896

k(119896119894)= (119909119894minus 119909119896 119910119894minus 119910119896) and 120601 isin [0 1205872) is a predefined

parameter called the max viewing angle

4 International Journal of Distributed Sensor Networks

Si

tkrarr (ki)

rarrfk

120579

2

rarrd(ij)

le120593

Figure 4 In this figure a target 119905119896is effectively sensed by a camera

119904119894

In this paper we consider a camera sensor network of 119899camera sensors and119898 targets of interest Each camera sensoris with uniformbeamwidth 120579 andwith 119902 ge 1 available sectorsthat is 119902 = lceil2120587120579rceil We denote the face direction of a target 119905

119896

by a vector f119896 By the effective-sensing model in Definition 1

we can define the conditions to be satisfied for a target 119905119896to

be effectively covered by a camera sensor 119904119894with its 119895th sector

as below

Definition 2 (identifiability test) A target 119905119896is effectively-

covered by the 119895th sensing sector of a camera sensor 119904119894only if

it passes all of the following three subtests

Subtest 1 Checkwhether 119905119896is in the sensing range of 119904

119894 that is

check if k(119896119894) le 119877 is true where 119877 is the maximum sensing

range of 119904119894

Subtest 2 Check whether 119905119896is within the 119895th sensing sector of

119904119894 that is check if d119879

(119894119895)sdotk(119894119896)ge k(119896119894) sdotcos(1205792) is true where

d(119894119895)

is a vector from 119904119894to the center of the surface of the 119895th

sector

Subtest 3 Check whether 119905119896is effectively covered by the 119895th

sensing sector of 119904119894 that is check if f119879

119896sdot k(119896119894)ge k(119896119894) sdot cos120601

is true

From now on 119878(119894119895)

will be used to represent (a) the setof targets effectively covered by the 119895th sensing sector of 119904

119894

and (b) the 119895th sensing sector of 119904119894 depending on the context

Note that in the first case all 119878(119894119895)

s can be determined withina polynomial time

4 Desperate Coverage Problem inMission-Driven Camera Sensor Networks(DCP-MCSN) and Its Solution

Now we introduce the formal definition of DCP-MCSNin Section 41 and our solution for this problem namelydesperate coverage algorithm in mission-driven camera sensornetworks (DCA-MCSN) in Section 42 Table 1 summarizesthe terms notations and their semantics used in this paper

41 Formal Definition of DCP-MCSN

Definition 3 (DCP-MCSN) DCP-MCSN is to find a subcol-lection (schedule) Z sub F such that (a) for each sensornode 119904

119894 at most one sector 119878

(119894119895)is used to form the subsets

in Z (b) the number of the first 119896 pivotal targets whichare fully covered during 119861 is maximized (primary objective)and (c) the overall target-temporal coverage is maximized(secondary objective)

Theorem 4 DCP-MCSN is NP-hard

Proof A simpler form of DCP-MCSN without the secondrequirement regarding maximizing the number of the first119896 pivotal targets is already proven to be NP-hard in [5]Therefore this problem is NP-hard

42 Desperate Coverage Algorithm in Mission-Driven CameraSensor Networks (DCA-MCSN) In this section we introduceour algorithm for DCP-MCSN namely DCA-MCSN Givena set of camera sensors a set of targets and a missionperiod DCA-MCSN performs a binary search (see Figure 3)In detail initially the number of the most important targetswhich can be seamlessly covered by the camera sensors isset to 119896 larr lceil1198982rceil and executes Network-Scheduler(Algorithm 3) which internally invokes two subproceduresSector-Decider (Algorithm 1) and Sensor-Scheduler(Algorithm 2) At the end if Network-Scheduler returnsa schedule of camera sensors such that the most 119896 importanttargets are fully covered during the mission period we set119896 larr lceil(119898 + (1198982))2rceil and execute Network-SchedulerOtherwise we set 119896 larr lceil((1198982) minus 1)2rceil and executeNetwork-Scheduler At the end the search will be termi-nated and we will find the maximum 119896 that can be achievedby our algorithm as well as its corresponding scheduleWe would like to emphasize that similar to our schedulingstrategy in [5] the mission period 119861 is divided into multiplecycles with a uniform length 119903 and Network-Scheduler isinvoked to construct a schedule for a short term with 119903 unittime length As a result Network-Scheduler is invoked for119861119903 times during the total mission period 119861 In the followingwe introduce the description of Sector-Decider Sensor-Scheduler and Network-Scheduler

421 Sector-Decider Algorithm 1 is the formal description ofSector-Decider The input of this algorithm is the set ofcamera sensors 119878 the set of targets 119879 and the set of the mostimportant 119896 targets (thosewith the heaviest weights) in119879Thegoal of this greedy algorithm is to determine one active sectorfrom all available ones for each camera sensor In Lines 1ndash3for each sector of each camera sensor the set 119878

(119894119895)of targets

which can be effectively covered by a sensor 119904119894with its 119895 sector

is computedIn detail in the preliminary phase (Lines 5ndash7) for each

target 1198861198961015840 among the first 119896 pivotal targets the accumulated

time recorder 1198621198961015840 that this target is effectively covered by

some camera sensor is set to 0 Then the loop spanning overLines 8ndash24 is repeated to determine the set of sectorsZ suchthat one sector (represented by those targets eg 119878

(119894119895) which

are covered by the sector) is selected from each sensor nodeThis loop largely consists of two parts

(a) The first part (Lines 9ndash15) is for the case that thereexists at least one target among the most important

International Journal of Distributed Sensor Networks 5

Table 1

Terms symbols Semantics119878 A set of homogenous camera sensor nodes 119904

1 119904

119899

119879 A set of targets 1199051 119905

119898

119882 The set of the weights of the targets in 119879 1199081 119908

119898

120579 The uniform field-of-vision of the camera sensors119877119904= 1 The normalized sensing range of the camera sensors

119877119905= 1 The transmission range of the camera sensors with omnidirectional transmission radios

119871119894

The battery lifetime of 119904119894

f119905119896

The face direction vector of 119905119896

119861 119903 The length of a given mission and the length of each cycle (we assume 119861119903 is an integer for simplicity)119902 2120587120579 the number of available orientations for each sensord(119894119895)

119878(119894119895)

The vector of 119904119894rsquos 119895th available orientation and the set of targets covered by 119904

119894using its 119895th sector

F A collection of the subsets of 119878(119894119895)| 1 le 119894 le 119899 1 le 119895 le 119902

(1) for each (119894 119895) pair 1 le 119894 le 119899 1 le 119895 le 119902 do(2) Run Identifiability Test and compute 119878

(119894119895) the set of targets effectively covered by 119904

119894with its 119895th sector

(3) end for(4) SetZlarr 0119880119862

119896larr 1198861198981 119886

119898119896

1198801198621015840larr 119879 119880119862

119896 and 119880119882 larr 119878

(5) for each target 1198861198961015840 isin 119880119862

119896do

(6) 1198621198961015840 larr 0

(7) end for(8) loop(9) (119894 119895) larr arg max

119904119894isin1198801198821le119895le119902

10038161003816100381610038161003816119878(119894119895)⋂119880119862

119896

10038161003816100381610038161003816

(10) if 119878(119894119895)⋂119880119862

119896= 0 then

(11) ZlarrZ⋃119878(119894119895) 119880119882 larr 119880119882 119904

119894 1198801198621015840 larr 1198801198621015840 119878

(119894119895)

(12) for each 1198861198961015840 isin 119878(119894119895)⋂119880119862

119896do

(13) 1198621198961015840 larr 119862

1198961015840 + 119897119894= 1198621198961015840 + 119871119894(119861119903)

(14) end for(15) 119880119862

119896larr 119880119862

119896 1198861198961015840 | 1198621198961015840 ge 119903 where 1198961015840 isin 119898

1 119898

119896

(16) else(17) (119894

1015840 1198951015840) larr arg max

119904 1015840isin1198801198821le1198951015840le119902

10038161003816100381610038161003816119878(11989410158401198951015840)⋂119880119862

101584010038161003816100381610038161003816

(18) if 119878(11989410158401198951015840)⋂119880119862

1015840= 0 then

(19) break lowast quit the loop lowast(20) else(21) ZlarrZ⋃119878

(11989410158401198951015840) 119880119882 larr 119880119882 119904

1198941015840 1198801198621015840 larr 1198801198621015840 119878

(11989410158401198951015840)

(22) end if(23) end if(24) end loop(25) ReturnZ

Algorithm 1 sector-decider (119878 119879 1198861198981 119886

119898119896

)

119896 ones which may not be fully covered during thewhole period 119903 And this part is used to determinean active sector for an undecided sensor node suchthat there aremore uncovered targets among themostimportant 119896 targets which will be covered Once wefind such a sector for example 119878

(119894119895) in Line 11 we add

it toZ Line 13 is used to update the total time that themost important 119896 targets can be covered by the sectorsinZ so far

(b) The second part (Lines 17ndash22) is for the case that allthe most important 119896 targets could be fully coveredduring the whole period 119903 This part is used to add

more sectors toZ such that the total target-temporalcoverage can be maximized

422 Sensor-Scheduler Algorithm 2 is the formal descrip-tion of Sensor-Scheduler The inputs of this algorithm areas follows

(a) a single sector 119888119894= 119878(119894119895)

of a sensor node 119904119894for some 119895

selected by Sector-Decider

(b) 119873119894which is the set of sectors for example 119878

(119894119895)s

selected by Sector-Decider such that there exist

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

Si

120579

urarrd(ij)

Figure 1 The sensing model of the directional sensor

ursquos facing direction (rarrfu)

S2

S

u

1

12057921205791

s1 rsquos viewing direction

s2 rsquos viewing direction

Figure 2 The sensing model of the camera sensor

coverage problem is the full-coverage problem whose goal istomaximize the lifetime of a sensor networkwhile seamlesslycovering an area or targets of interest [1 2]

Most coverage problems in wireless sensor networkshave focused on the lifetime maximization issue In thoseproblems the lifetime of the networks is an optimizationgoal not a constraint However this is not always the casein reality For instance consider an application of wirelesssensor networks in which we have to cover an area of interestor a set of targets during ldquoa given mission periodrdquo (whichis a constraint) but we do not have enough sensors tofully cover the whole area or the targets regardless of thescheduling algorithm we use Certainly the existing coveragealgorithms that we discussed so far cannot deal with thissituation Recently Liu and Cao introduced one way tohandle this challenging issue Given a required surveillancemission period they suggested to maximize the spatial-temporal coverage of the area or targets of interest which isdefined as the gross sum of the total time that each distinctarea is covered multiplied by the size of the area (in case ofarea coverage) [3] or the gross sumof theweight of each targetcoveredmultiplied by the total time duration that the target iscovered (in case of target coverage) [4] Very recently Honget al extended this idea and investigated a spatial-temporalcoverage problem in camera sensor networks [5]

In this paper we introduce another way to deal with thequestion of how to provide the best quality coverage over

Desperate coverage algorithm formission-driven camera sensor

networks (DCA-MCSN)

Network

Sensorscheduler

scheduler (k)

Sector decider

Binary search tomaximize k

Figure 3 DCA-MCSN is a binary search algorithm to identifythe maximum number of the most important targets which can beseamlessly covered by the camera sensors during themission periodand corresponding scheduling

a set of targets of interest during a given mission periodwith insufficient number of camera sensor nodes This studyis motivated by our observation that when we solely aimto maximize the coverage quality (the total target-temporalcoverage) like [4 5] it is possible that some targets withthe highest priority could be deprioritized by a number ofinsignificant targets and as a result relatively ignored inthe course of the schedule building process The problem ofmonitoring a warehouse with two entrances during a certaintime period is a good example Clearly the entrances arethe most important targets since the face of any trespassercan be easily detected by a camera observing the entranceMeanwhile a shelf inside the warehouse without any item isclearly a less-important target To deal with this situation wesuggest providing full coverage to as many higher prioritytargets as possible during the mission period while thespatial-temporal coverage over the rest of targets can bemaximized We would like to emphasize that we are nottrying to refute the significance of the target-temporal-maximization-only approach used in [4 5] but we attemptto propose a new complement for those approaches to dealwith this desperate situation The main contributions of thispaper can be summarized as follows

(a) We introduce a new scheduling problem in camerasensor networks namely desperate coverage prob-lem in mission-driven camera sensor networks (DCP-MCSN) More formal description of the problem isgiven in Section 4

(b) We propose a new heuristic algorithm for our newNP-hard problem called desperate coverage algorithmin mission-driven camera sensor networks (DCA-MCSN) In detail given a set of camera sensors aset of targets and a mission period DCA-MCSNperforms a binary search (see Figure 3) to find a

International Journal of Distributed Sensor Networks 3

constant 119896 such that the most 119896 important tar-gets are fully covered during the mission periodDuring the search process 119896 is assumed to be asome constant (eg initially 119896 larr lceil1198982rceil) andNetwork-Scheduler (Algorithm 3) is executedNetwork-Scheduler internally calls two subproce-dures Sector-Decider (Algorithm 1) and Sensor-Scheduler (Algorithm 2) to determine the sensingsector of each camera sensor and the activation sched-ule of each camera sensor Dependent on Network-Scheduler the 119896 value is increased or decreased andthe whole process is repeated until we finalize 119896 andobtain a schedule which allows the camera sensorsto fully cover the most 119896 important targets and thetarget-temporal coverage is maximized

(c) We compare the average performance ofDCA-MCSNwith the theoretical upper bound in simulation aswellas with the only existing competitor in [5] Our sim-ulation result shows that our algorithm outperformsthe target-temporal-maximization-only algorithm incamera sensor network in [5] in terms of the numberof the most important targets which are fully coveredduring the whole mission period

The rest of this paper is organized as follows Section 2presents related work Some preliminaries are introducedin Section 3 We introduce the formal definition of DCP-MCSN and our algorithm for this problem in Section 4Our simulation result is presented in Section 5 Finally weconclude this paper in Section 6

2 Related Work

Frequently the problem of constructing a sleep-wakeupschedule of a wireless sensor network with the goal ofmaximizing the continuous monitoring time to meet agiven coverage quality requirement is referred as a coverageproblem [2ndash4 6] Most types of wireless sensor networksthoroughly investigated in the literature consider sensornodes with omnidirectional sensing range Consequentlythe area covered by those sensor nodes resembles a diskwith the node in the center of it In contrast the sensingarea covered by a directional sensor node looks more like asector of a disk [7] In [8] Cai et al have investigated themultiple directional cover set problem in directional sensornetworks whose objective is to compute a sleep-wakeupschedule of a given set of sensor nodes such that the timefor the sensor network to fully cover a given set of targets ismaximized In the meantime Ai and Abouzeid [9] studied anew coverage problem in directional sensor networks whosegoal is given a set of sensor nodes with adjustable cameraorientations to determine the direction (orientation) of eachsensor so that the number of covered targets is maximized(primary objective) while the number of sensor nodes usedis minimized (secondary objective) In addition the otheraspects of directional sensor networks are also investigatedlike vulnerability [10] fault-tolerance [11] and so on [12 13]

Briefly speaking camera sensor network is a kind ofdirectional sensor network and thus they share several

properties However due to several unique features of camerasensors especially the effective-sensing surveillance modelin Definition 1 the scheduling algorithms for directionalsensor networks are not directly applicable to camera sensornetworks Most importantly a camera sensor node can covera target only if the face of the target can be seen by thesensor In [14] Liu et al introduced the directional 119896-coverage problem in camera sensor networkswhose objectiveis minimizing the number of camera sensors to cover an areaof interest such that any spot in the area can be monitored byat least 119896 different cameras In [13] Wang and Cao assumed acamera sensor network version of the full coverage problemcalled the full-view coverage problem In this problem atarget is full-view covered by a camera sensor network if wecan capture the face of a target which is within the sensingrange of the camera sensor network independent of the facedirection of the target Previously Ma et al extended theresult in [13] and investigated the full-view barrier coverageproblem in camera sensor networks

So far most coverage problems in wireless sensor net-works have concerned about the lifetimemaximization issueTherefore they are not applicable to a desperate situation inwhich we are required to cover an area or a set of targets ofinterest during a given mission period One possible solutionof this challenging issue is introduced by Liu and Cao [3 4]who suggested to maximize the spatial-temporal coverageof the area or targets of interest In our previous work weextended this idea and investigated a spatial-temporal cover-age problem in camera sensor networks [5] However Liu andCaorsquos approach comes with a nonneglectable shortcomingmdasha target with the highest priority could be deprioritized by anumber of insignificant targets and as a result is ignored by ascheduling algorithm In this paper we address this issue andattempt to propose an alternative solution of the problem asa complement of Liu and Caorsquos approach

3 Preliminaries

In this section we review two important preliminaries of ourpaper the effective-sensingmodel in camera sensor networks[14] and the Identifiability Test [5] which is a procedure tocheck given a set of targets and a set of camera sensors ifthe target is effectively covered by the camera sensors Aswe mentioned earlier this paper assumes that a target isrecognized or effectively sensed (covered) by a camera sensorif the facial view of the target is observed by a camera sensorThe face direction of each target can be estimated by anexisting head pose estimating strategy such as the one in [15]A more formal definition of the effective-sensing model incamera sensor networks is as follows

Definition 1 (effective-sensing model) Consider a target 119905119896

located at (119909119896 119910119896) and a sensor 119904

119894located at (119909

119894 119910119894) 119905119896is

effectively sensed (covered) by 119904119894if 119905119896is within the sensing

area of 119904119894and the internal angle between two vectors f

119896and

k(119896119894)

is not greater than 120601 that is 120572(f119896 k(119896119894)) le 120601 (see

Figure 4) where vector f119896is the facing orientation of 119905

119896

k(119896119894)= (119909119894minus 119909119896 119910119894minus 119910119896) and 120601 isin [0 1205872) is a predefined

parameter called the max viewing angle

4 International Journal of Distributed Sensor Networks

Si

tkrarr (ki)

rarrfk

120579

2

rarrd(ij)

le120593

Figure 4 In this figure a target 119905119896is effectively sensed by a camera

119904119894

In this paper we consider a camera sensor network of 119899camera sensors and119898 targets of interest Each camera sensoris with uniformbeamwidth 120579 andwith 119902 ge 1 available sectorsthat is 119902 = lceil2120587120579rceil We denote the face direction of a target 119905

119896

by a vector f119896 By the effective-sensing model in Definition 1

we can define the conditions to be satisfied for a target 119905119896to

be effectively covered by a camera sensor 119904119894with its 119895th sector

as below

Definition 2 (identifiability test) A target 119905119896is effectively-

covered by the 119895th sensing sector of a camera sensor 119904119894only if

it passes all of the following three subtests

Subtest 1 Checkwhether 119905119896is in the sensing range of 119904

119894 that is

check if k(119896119894) le 119877 is true where 119877 is the maximum sensing

range of 119904119894

Subtest 2 Check whether 119905119896is within the 119895th sensing sector of

119904119894 that is check if d119879

(119894119895)sdotk(119894119896)ge k(119896119894) sdotcos(1205792) is true where

d(119894119895)

is a vector from 119904119894to the center of the surface of the 119895th

sector

Subtest 3 Check whether 119905119896is effectively covered by the 119895th

sensing sector of 119904119894 that is check if f119879

119896sdot k(119896119894)ge k(119896119894) sdot cos120601

is true

From now on 119878(119894119895)

will be used to represent (a) the setof targets effectively covered by the 119895th sensing sector of 119904

119894

and (b) the 119895th sensing sector of 119904119894 depending on the context

Note that in the first case all 119878(119894119895)

s can be determined withina polynomial time

4 Desperate Coverage Problem inMission-Driven Camera Sensor Networks(DCP-MCSN) and Its Solution

Now we introduce the formal definition of DCP-MCSNin Section 41 and our solution for this problem namelydesperate coverage algorithm in mission-driven camera sensornetworks (DCA-MCSN) in Section 42 Table 1 summarizesthe terms notations and their semantics used in this paper

41 Formal Definition of DCP-MCSN

Definition 3 (DCP-MCSN) DCP-MCSN is to find a subcol-lection (schedule) Z sub F such that (a) for each sensornode 119904

119894 at most one sector 119878

(119894119895)is used to form the subsets

in Z (b) the number of the first 119896 pivotal targets whichare fully covered during 119861 is maximized (primary objective)and (c) the overall target-temporal coverage is maximized(secondary objective)

Theorem 4 DCP-MCSN is NP-hard

Proof A simpler form of DCP-MCSN without the secondrequirement regarding maximizing the number of the first119896 pivotal targets is already proven to be NP-hard in [5]Therefore this problem is NP-hard

42 Desperate Coverage Algorithm in Mission-Driven CameraSensor Networks (DCA-MCSN) In this section we introduceour algorithm for DCP-MCSN namely DCA-MCSN Givena set of camera sensors a set of targets and a missionperiod DCA-MCSN performs a binary search (see Figure 3)In detail initially the number of the most important targetswhich can be seamlessly covered by the camera sensors isset to 119896 larr lceil1198982rceil and executes Network-Scheduler(Algorithm 3) which internally invokes two subproceduresSector-Decider (Algorithm 1) and Sensor-Scheduler(Algorithm 2) At the end if Network-Scheduler returnsa schedule of camera sensors such that the most 119896 importanttargets are fully covered during the mission period we set119896 larr lceil(119898 + (1198982))2rceil and execute Network-SchedulerOtherwise we set 119896 larr lceil((1198982) minus 1)2rceil and executeNetwork-Scheduler At the end the search will be termi-nated and we will find the maximum 119896 that can be achievedby our algorithm as well as its corresponding scheduleWe would like to emphasize that similar to our schedulingstrategy in [5] the mission period 119861 is divided into multiplecycles with a uniform length 119903 and Network-Scheduler isinvoked to construct a schedule for a short term with 119903 unittime length As a result Network-Scheduler is invoked for119861119903 times during the total mission period 119861 In the followingwe introduce the description of Sector-Decider Sensor-Scheduler and Network-Scheduler

421 Sector-Decider Algorithm 1 is the formal description ofSector-Decider The input of this algorithm is the set ofcamera sensors 119878 the set of targets 119879 and the set of the mostimportant 119896 targets (thosewith the heaviest weights) in119879Thegoal of this greedy algorithm is to determine one active sectorfrom all available ones for each camera sensor In Lines 1ndash3for each sector of each camera sensor the set 119878

(119894119895)of targets

which can be effectively covered by a sensor 119904119894with its 119895 sector

is computedIn detail in the preliminary phase (Lines 5ndash7) for each

target 1198861198961015840 among the first 119896 pivotal targets the accumulated

time recorder 1198621198961015840 that this target is effectively covered by

some camera sensor is set to 0 Then the loop spanning overLines 8ndash24 is repeated to determine the set of sectorsZ suchthat one sector (represented by those targets eg 119878

(119894119895) which

are covered by the sector) is selected from each sensor nodeThis loop largely consists of two parts

(a) The first part (Lines 9ndash15) is for the case that thereexists at least one target among the most important

International Journal of Distributed Sensor Networks 5

Table 1

Terms symbols Semantics119878 A set of homogenous camera sensor nodes 119904

1 119904

119899

119879 A set of targets 1199051 119905

119898

119882 The set of the weights of the targets in 119879 1199081 119908

119898

120579 The uniform field-of-vision of the camera sensors119877119904= 1 The normalized sensing range of the camera sensors

119877119905= 1 The transmission range of the camera sensors with omnidirectional transmission radios

119871119894

The battery lifetime of 119904119894

f119905119896

The face direction vector of 119905119896

119861 119903 The length of a given mission and the length of each cycle (we assume 119861119903 is an integer for simplicity)119902 2120587120579 the number of available orientations for each sensord(119894119895)

119878(119894119895)

The vector of 119904119894rsquos 119895th available orientation and the set of targets covered by 119904

119894using its 119895th sector

F A collection of the subsets of 119878(119894119895)| 1 le 119894 le 119899 1 le 119895 le 119902

(1) for each (119894 119895) pair 1 le 119894 le 119899 1 le 119895 le 119902 do(2) Run Identifiability Test and compute 119878

(119894119895) the set of targets effectively covered by 119904

119894with its 119895th sector

(3) end for(4) SetZlarr 0119880119862

119896larr 1198861198981 119886

119898119896

1198801198621015840larr 119879 119880119862

119896 and 119880119882 larr 119878

(5) for each target 1198861198961015840 isin 119880119862

119896do

(6) 1198621198961015840 larr 0

(7) end for(8) loop(9) (119894 119895) larr arg max

119904119894isin1198801198821le119895le119902

10038161003816100381610038161003816119878(119894119895)⋂119880119862

119896

10038161003816100381610038161003816

(10) if 119878(119894119895)⋂119880119862

119896= 0 then

(11) ZlarrZ⋃119878(119894119895) 119880119882 larr 119880119882 119904

119894 1198801198621015840 larr 1198801198621015840 119878

(119894119895)

(12) for each 1198861198961015840 isin 119878(119894119895)⋂119880119862

119896do

(13) 1198621198961015840 larr 119862

1198961015840 + 119897119894= 1198621198961015840 + 119871119894(119861119903)

(14) end for(15) 119880119862

119896larr 119880119862

119896 1198861198961015840 | 1198621198961015840 ge 119903 where 1198961015840 isin 119898

1 119898

119896

(16) else(17) (119894

1015840 1198951015840) larr arg max

119904 1015840isin1198801198821le1198951015840le119902

10038161003816100381610038161003816119878(11989410158401198951015840)⋂119880119862

101584010038161003816100381610038161003816

(18) if 119878(11989410158401198951015840)⋂119880119862

1015840= 0 then

(19) break lowast quit the loop lowast(20) else(21) ZlarrZ⋃119878

(11989410158401198951015840) 119880119882 larr 119880119882 119904

1198941015840 1198801198621015840 larr 1198801198621015840 119878

(11989410158401198951015840)

(22) end if(23) end if(24) end loop(25) ReturnZ

Algorithm 1 sector-decider (119878 119879 1198861198981 119886

119898119896

)

119896 ones which may not be fully covered during thewhole period 119903 And this part is used to determinean active sector for an undecided sensor node suchthat there aremore uncovered targets among themostimportant 119896 targets which will be covered Once wefind such a sector for example 119878

(119894119895) in Line 11 we add

it toZ Line 13 is used to update the total time that themost important 119896 targets can be covered by the sectorsinZ so far

(b) The second part (Lines 17ndash22) is for the case that allthe most important 119896 targets could be fully coveredduring the whole period 119903 This part is used to add

more sectors toZ such that the total target-temporalcoverage can be maximized

422 Sensor-Scheduler Algorithm 2 is the formal descrip-tion of Sensor-Scheduler The inputs of this algorithm areas follows

(a) a single sector 119888119894= 119878(119894119895)

of a sensor node 119904119894for some 119895

selected by Sector-Decider

(b) 119873119894which is the set of sectors for example 119878

(119894119895)s

selected by Sector-Decider such that there exist

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

constant 119896 such that the most 119896 important tar-gets are fully covered during the mission periodDuring the search process 119896 is assumed to be asome constant (eg initially 119896 larr lceil1198982rceil) andNetwork-Scheduler (Algorithm 3) is executedNetwork-Scheduler internally calls two subproce-dures Sector-Decider (Algorithm 1) and Sensor-Scheduler (Algorithm 2) to determine the sensingsector of each camera sensor and the activation sched-ule of each camera sensor Dependent on Network-Scheduler the 119896 value is increased or decreased andthe whole process is repeated until we finalize 119896 andobtain a schedule which allows the camera sensorsto fully cover the most 119896 important targets and thetarget-temporal coverage is maximized

(c) We compare the average performance ofDCA-MCSNwith the theoretical upper bound in simulation aswellas with the only existing competitor in [5] Our sim-ulation result shows that our algorithm outperformsthe target-temporal-maximization-only algorithm incamera sensor network in [5] in terms of the numberof the most important targets which are fully coveredduring the whole mission period

The rest of this paper is organized as follows Section 2presents related work Some preliminaries are introducedin Section 3 We introduce the formal definition of DCP-MCSN and our algorithm for this problem in Section 4Our simulation result is presented in Section 5 Finally weconclude this paper in Section 6

2 Related Work

Frequently the problem of constructing a sleep-wakeupschedule of a wireless sensor network with the goal ofmaximizing the continuous monitoring time to meet agiven coverage quality requirement is referred as a coverageproblem [2ndash4 6] Most types of wireless sensor networksthoroughly investigated in the literature consider sensornodes with omnidirectional sensing range Consequentlythe area covered by those sensor nodes resembles a diskwith the node in the center of it In contrast the sensingarea covered by a directional sensor node looks more like asector of a disk [7] In [8] Cai et al have investigated themultiple directional cover set problem in directional sensornetworks whose objective is to compute a sleep-wakeupschedule of a given set of sensor nodes such that the timefor the sensor network to fully cover a given set of targets ismaximized In the meantime Ai and Abouzeid [9] studied anew coverage problem in directional sensor networks whosegoal is given a set of sensor nodes with adjustable cameraorientations to determine the direction (orientation) of eachsensor so that the number of covered targets is maximized(primary objective) while the number of sensor nodes usedis minimized (secondary objective) In addition the otheraspects of directional sensor networks are also investigatedlike vulnerability [10] fault-tolerance [11] and so on [12 13]

Briefly speaking camera sensor network is a kind ofdirectional sensor network and thus they share several

properties However due to several unique features of camerasensors especially the effective-sensing surveillance modelin Definition 1 the scheduling algorithms for directionalsensor networks are not directly applicable to camera sensornetworks Most importantly a camera sensor node can covera target only if the face of the target can be seen by thesensor In [14] Liu et al introduced the directional 119896-coverage problem in camera sensor networkswhose objectiveis minimizing the number of camera sensors to cover an areaof interest such that any spot in the area can be monitored byat least 119896 different cameras In [13] Wang and Cao assumed acamera sensor network version of the full coverage problemcalled the full-view coverage problem In this problem atarget is full-view covered by a camera sensor network if wecan capture the face of a target which is within the sensingrange of the camera sensor network independent of the facedirection of the target Previously Ma et al extended theresult in [13] and investigated the full-view barrier coverageproblem in camera sensor networks

So far most coverage problems in wireless sensor net-works have concerned about the lifetimemaximization issueTherefore they are not applicable to a desperate situation inwhich we are required to cover an area or a set of targets ofinterest during a given mission period One possible solutionof this challenging issue is introduced by Liu and Cao [3 4]who suggested to maximize the spatial-temporal coverageof the area or targets of interest In our previous work weextended this idea and investigated a spatial-temporal cover-age problem in camera sensor networks [5] However Liu andCaorsquos approach comes with a nonneglectable shortcomingmdasha target with the highest priority could be deprioritized by anumber of insignificant targets and as a result is ignored by ascheduling algorithm In this paper we address this issue andattempt to propose an alternative solution of the problem asa complement of Liu and Caorsquos approach

3 Preliminaries

In this section we review two important preliminaries of ourpaper the effective-sensingmodel in camera sensor networks[14] and the Identifiability Test [5] which is a procedure tocheck given a set of targets and a set of camera sensors ifthe target is effectively covered by the camera sensors Aswe mentioned earlier this paper assumes that a target isrecognized or effectively sensed (covered) by a camera sensorif the facial view of the target is observed by a camera sensorThe face direction of each target can be estimated by anexisting head pose estimating strategy such as the one in [15]A more formal definition of the effective-sensing model incamera sensor networks is as follows

Definition 1 (effective-sensing model) Consider a target 119905119896

located at (119909119896 119910119896) and a sensor 119904

119894located at (119909

119894 119910119894) 119905119896is

effectively sensed (covered) by 119904119894if 119905119896is within the sensing

area of 119904119894and the internal angle between two vectors f

119896and

k(119896119894)

is not greater than 120601 that is 120572(f119896 k(119896119894)) le 120601 (see

Figure 4) where vector f119896is the facing orientation of 119905

119896

k(119896119894)= (119909119894minus 119909119896 119910119894minus 119910119896) and 120601 isin [0 1205872) is a predefined

parameter called the max viewing angle

4 International Journal of Distributed Sensor Networks

Si

tkrarr (ki)

rarrfk

120579

2

rarrd(ij)

le120593

Figure 4 In this figure a target 119905119896is effectively sensed by a camera

119904119894

In this paper we consider a camera sensor network of 119899camera sensors and119898 targets of interest Each camera sensoris with uniformbeamwidth 120579 andwith 119902 ge 1 available sectorsthat is 119902 = lceil2120587120579rceil We denote the face direction of a target 119905

119896

by a vector f119896 By the effective-sensing model in Definition 1

we can define the conditions to be satisfied for a target 119905119896to

be effectively covered by a camera sensor 119904119894with its 119895th sector

as below

Definition 2 (identifiability test) A target 119905119896is effectively-

covered by the 119895th sensing sector of a camera sensor 119904119894only if

it passes all of the following three subtests

Subtest 1 Checkwhether 119905119896is in the sensing range of 119904

119894 that is

check if k(119896119894) le 119877 is true where 119877 is the maximum sensing

range of 119904119894

Subtest 2 Check whether 119905119896is within the 119895th sensing sector of

119904119894 that is check if d119879

(119894119895)sdotk(119894119896)ge k(119896119894) sdotcos(1205792) is true where

d(119894119895)

is a vector from 119904119894to the center of the surface of the 119895th

sector

Subtest 3 Check whether 119905119896is effectively covered by the 119895th

sensing sector of 119904119894 that is check if f119879

119896sdot k(119896119894)ge k(119896119894) sdot cos120601

is true

From now on 119878(119894119895)

will be used to represent (a) the setof targets effectively covered by the 119895th sensing sector of 119904

119894

and (b) the 119895th sensing sector of 119904119894 depending on the context

Note that in the first case all 119878(119894119895)

s can be determined withina polynomial time

4 Desperate Coverage Problem inMission-Driven Camera Sensor Networks(DCP-MCSN) and Its Solution

Now we introduce the formal definition of DCP-MCSNin Section 41 and our solution for this problem namelydesperate coverage algorithm in mission-driven camera sensornetworks (DCA-MCSN) in Section 42 Table 1 summarizesthe terms notations and their semantics used in this paper

41 Formal Definition of DCP-MCSN

Definition 3 (DCP-MCSN) DCP-MCSN is to find a subcol-lection (schedule) Z sub F such that (a) for each sensornode 119904

119894 at most one sector 119878

(119894119895)is used to form the subsets

in Z (b) the number of the first 119896 pivotal targets whichare fully covered during 119861 is maximized (primary objective)and (c) the overall target-temporal coverage is maximized(secondary objective)

Theorem 4 DCP-MCSN is NP-hard

Proof A simpler form of DCP-MCSN without the secondrequirement regarding maximizing the number of the first119896 pivotal targets is already proven to be NP-hard in [5]Therefore this problem is NP-hard

42 Desperate Coverage Algorithm in Mission-Driven CameraSensor Networks (DCA-MCSN) In this section we introduceour algorithm for DCP-MCSN namely DCA-MCSN Givena set of camera sensors a set of targets and a missionperiod DCA-MCSN performs a binary search (see Figure 3)In detail initially the number of the most important targetswhich can be seamlessly covered by the camera sensors isset to 119896 larr lceil1198982rceil and executes Network-Scheduler(Algorithm 3) which internally invokes two subproceduresSector-Decider (Algorithm 1) and Sensor-Scheduler(Algorithm 2) At the end if Network-Scheduler returnsa schedule of camera sensors such that the most 119896 importanttargets are fully covered during the mission period we set119896 larr lceil(119898 + (1198982))2rceil and execute Network-SchedulerOtherwise we set 119896 larr lceil((1198982) minus 1)2rceil and executeNetwork-Scheduler At the end the search will be termi-nated and we will find the maximum 119896 that can be achievedby our algorithm as well as its corresponding scheduleWe would like to emphasize that similar to our schedulingstrategy in [5] the mission period 119861 is divided into multiplecycles with a uniform length 119903 and Network-Scheduler isinvoked to construct a schedule for a short term with 119903 unittime length As a result Network-Scheduler is invoked for119861119903 times during the total mission period 119861 In the followingwe introduce the description of Sector-Decider Sensor-Scheduler and Network-Scheduler

421 Sector-Decider Algorithm 1 is the formal description ofSector-Decider The input of this algorithm is the set ofcamera sensors 119878 the set of targets 119879 and the set of the mostimportant 119896 targets (thosewith the heaviest weights) in119879Thegoal of this greedy algorithm is to determine one active sectorfrom all available ones for each camera sensor In Lines 1ndash3for each sector of each camera sensor the set 119878

(119894119895)of targets

which can be effectively covered by a sensor 119904119894with its 119895 sector

is computedIn detail in the preliminary phase (Lines 5ndash7) for each

target 1198861198961015840 among the first 119896 pivotal targets the accumulated

time recorder 1198621198961015840 that this target is effectively covered by

some camera sensor is set to 0 Then the loop spanning overLines 8ndash24 is repeated to determine the set of sectorsZ suchthat one sector (represented by those targets eg 119878

(119894119895) which

are covered by the sector) is selected from each sensor nodeThis loop largely consists of two parts

(a) The first part (Lines 9ndash15) is for the case that thereexists at least one target among the most important

International Journal of Distributed Sensor Networks 5

Table 1

Terms symbols Semantics119878 A set of homogenous camera sensor nodes 119904

1 119904

119899

119879 A set of targets 1199051 119905

119898

119882 The set of the weights of the targets in 119879 1199081 119908

119898

120579 The uniform field-of-vision of the camera sensors119877119904= 1 The normalized sensing range of the camera sensors

119877119905= 1 The transmission range of the camera sensors with omnidirectional transmission radios

119871119894

The battery lifetime of 119904119894

f119905119896

The face direction vector of 119905119896

119861 119903 The length of a given mission and the length of each cycle (we assume 119861119903 is an integer for simplicity)119902 2120587120579 the number of available orientations for each sensord(119894119895)

119878(119894119895)

The vector of 119904119894rsquos 119895th available orientation and the set of targets covered by 119904

119894using its 119895th sector

F A collection of the subsets of 119878(119894119895)| 1 le 119894 le 119899 1 le 119895 le 119902

(1) for each (119894 119895) pair 1 le 119894 le 119899 1 le 119895 le 119902 do(2) Run Identifiability Test and compute 119878

(119894119895) the set of targets effectively covered by 119904

119894with its 119895th sector

(3) end for(4) SetZlarr 0119880119862

119896larr 1198861198981 119886

119898119896

1198801198621015840larr 119879 119880119862

119896 and 119880119882 larr 119878

(5) for each target 1198861198961015840 isin 119880119862

119896do

(6) 1198621198961015840 larr 0

(7) end for(8) loop(9) (119894 119895) larr arg max

119904119894isin1198801198821le119895le119902

10038161003816100381610038161003816119878(119894119895)⋂119880119862

119896

10038161003816100381610038161003816

(10) if 119878(119894119895)⋂119880119862

119896= 0 then

(11) ZlarrZ⋃119878(119894119895) 119880119882 larr 119880119882 119904

119894 1198801198621015840 larr 1198801198621015840 119878

(119894119895)

(12) for each 1198861198961015840 isin 119878(119894119895)⋂119880119862

119896do

(13) 1198621198961015840 larr 119862

1198961015840 + 119897119894= 1198621198961015840 + 119871119894(119861119903)

(14) end for(15) 119880119862

119896larr 119880119862

119896 1198861198961015840 | 1198621198961015840 ge 119903 where 1198961015840 isin 119898

1 119898

119896

(16) else(17) (119894

1015840 1198951015840) larr arg max

119904 1015840isin1198801198821le1198951015840le119902

10038161003816100381610038161003816119878(11989410158401198951015840)⋂119880119862

101584010038161003816100381610038161003816

(18) if 119878(11989410158401198951015840)⋂119880119862

1015840= 0 then

(19) break lowast quit the loop lowast(20) else(21) ZlarrZ⋃119878

(11989410158401198951015840) 119880119882 larr 119880119882 119904

1198941015840 1198801198621015840 larr 1198801198621015840 119878

(11989410158401198951015840)

(22) end if(23) end if(24) end loop(25) ReturnZ

Algorithm 1 sector-decider (119878 119879 1198861198981 119886

119898119896

)

119896 ones which may not be fully covered during thewhole period 119903 And this part is used to determinean active sector for an undecided sensor node suchthat there aremore uncovered targets among themostimportant 119896 targets which will be covered Once wefind such a sector for example 119878

(119894119895) in Line 11 we add

it toZ Line 13 is used to update the total time that themost important 119896 targets can be covered by the sectorsinZ so far

(b) The second part (Lines 17ndash22) is for the case that allthe most important 119896 targets could be fully coveredduring the whole period 119903 This part is used to add

more sectors toZ such that the total target-temporalcoverage can be maximized

422 Sensor-Scheduler Algorithm 2 is the formal descrip-tion of Sensor-Scheduler The inputs of this algorithm areas follows

(a) a single sector 119888119894= 119878(119894119895)

of a sensor node 119904119894for some 119895

selected by Sector-Decider

(b) 119873119894which is the set of sectors for example 119878

(119894119895)s

selected by Sector-Decider such that there exist

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

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Active and Passive Electronic Components

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

Si

tkrarr (ki)

rarrfk

120579

2

rarrd(ij)

le120593

Figure 4 In this figure a target 119905119896is effectively sensed by a camera

119904119894

In this paper we consider a camera sensor network of 119899camera sensors and119898 targets of interest Each camera sensoris with uniformbeamwidth 120579 andwith 119902 ge 1 available sectorsthat is 119902 = lceil2120587120579rceil We denote the face direction of a target 119905

119896

by a vector f119896 By the effective-sensing model in Definition 1

we can define the conditions to be satisfied for a target 119905119896to

be effectively covered by a camera sensor 119904119894with its 119895th sector

as below

Definition 2 (identifiability test) A target 119905119896is effectively-

covered by the 119895th sensing sector of a camera sensor 119904119894only if

it passes all of the following three subtests

Subtest 1 Checkwhether 119905119896is in the sensing range of 119904

119894 that is

check if k(119896119894) le 119877 is true where 119877 is the maximum sensing

range of 119904119894

Subtest 2 Check whether 119905119896is within the 119895th sensing sector of

119904119894 that is check if d119879

(119894119895)sdotk(119894119896)ge k(119896119894) sdotcos(1205792) is true where

d(119894119895)

is a vector from 119904119894to the center of the surface of the 119895th

sector

Subtest 3 Check whether 119905119896is effectively covered by the 119895th

sensing sector of 119904119894 that is check if f119879

119896sdot k(119896119894)ge k(119896119894) sdot cos120601

is true

From now on 119878(119894119895)

will be used to represent (a) the setof targets effectively covered by the 119895th sensing sector of 119904

119894

and (b) the 119895th sensing sector of 119904119894 depending on the context

Note that in the first case all 119878(119894119895)

s can be determined withina polynomial time

4 Desperate Coverage Problem inMission-Driven Camera Sensor Networks(DCP-MCSN) and Its Solution

Now we introduce the formal definition of DCP-MCSNin Section 41 and our solution for this problem namelydesperate coverage algorithm in mission-driven camera sensornetworks (DCA-MCSN) in Section 42 Table 1 summarizesthe terms notations and their semantics used in this paper

41 Formal Definition of DCP-MCSN

Definition 3 (DCP-MCSN) DCP-MCSN is to find a subcol-lection (schedule) Z sub F such that (a) for each sensornode 119904

119894 at most one sector 119878

(119894119895)is used to form the subsets

in Z (b) the number of the first 119896 pivotal targets whichare fully covered during 119861 is maximized (primary objective)and (c) the overall target-temporal coverage is maximized(secondary objective)

Theorem 4 DCP-MCSN is NP-hard

Proof A simpler form of DCP-MCSN without the secondrequirement regarding maximizing the number of the first119896 pivotal targets is already proven to be NP-hard in [5]Therefore this problem is NP-hard

42 Desperate Coverage Algorithm in Mission-Driven CameraSensor Networks (DCA-MCSN) In this section we introduceour algorithm for DCP-MCSN namely DCA-MCSN Givena set of camera sensors a set of targets and a missionperiod DCA-MCSN performs a binary search (see Figure 3)In detail initially the number of the most important targetswhich can be seamlessly covered by the camera sensors isset to 119896 larr lceil1198982rceil and executes Network-Scheduler(Algorithm 3) which internally invokes two subproceduresSector-Decider (Algorithm 1) and Sensor-Scheduler(Algorithm 2) At the end if Network-Scheduler returnsa schedule of camera sensors such that the most 119896 importanttargets are fully covered during the mission period we set119896 larr lceil(119898 + (1198982))2rceil and execute Network-SchedulerOtherwise we set 119896 larr lceil((1198982) minus 1)2rceil and executeNetwork-Scheduler At the end the search will be termi-nated and we will find the maximum 119896 that can be achievedby our algorithm as well as its corresponding scheduleWe would like to emphasize that similar to our schedulingstrategy in [5] the mission period 119861 is divided into multiplecycles with a uniform length 119903 and Network-Scheduler isinvoked to construct a schedule for a short term with 119903 unittime length As a result Network-Scheduler is invoked for119861119903 times during the total mission period 119861 In the followingwe introduce the description of Sector-Decider Sensor-Scheduler and Network-Scheduler

421 Sector-Decider Algorithm 1 is the formal description ofSector-Decider The input of this algorithm is the set ofcamera sensors 119878 the set of targets 119879 and the set of the mostimportant 119896 targets (thosewith the heaviest weights) in119879Thegoal of this greedy algorithm is to determine one active sectorfrom all available ones for each camera sensor In Lines 1ndash3for each sector of each camera sensor the set 119878

(119894119895)of targets

which can be effectively covered by a sensor 119904119894with its 119895 sector

is computedIn detail in the preliminary phase (Lines 5ndash7) for each

target 1198861198961015840 among the first 119896 pivotal targets the accumulated

time recorder 1198621198961015840 that this target is effectively covered by

some camera sensor is set to 0 Then the loop spanning overLines 8ndash24 is repeated to determine the set of sectorsZ suchthat one sector (represented by those targets eg 119878

(119894119895) which

are covered by the sector) is selected from each sensor nodeThis loop largely consists of two parts

(a) The first part (Lines 9ndash15) is for the case that thereexists at least one target among the most important

International Journal of Distributed Sensor Networks 5

Table 1

Terms symbols Semantics119878 A set of homogenous camera sensor nodes 119904

1 119904

119899

119879 A set of targets 1199051 119905

119898

119882 The set of the weights of the targets in 119879 1199081 119908

119898

120579 The uniform field-of-vision of the camera sensors119877119904= 1 The normalized sensing range of the camera sensors

119877119905= 1 The transmission range of the camera sensors with omnidirectional transmission radios

119871119894

The battery lifetime of 119904119894

f119905119896

The face direction vector of 119905119896

119861 119903 The length of a given mission and the length of each cycle (we assume 119861119903 is an integer for simplicity)119902 2120587120579 the number of available orientations for each sensord(119894119895)

119878(119894119895)

The vector of 119904119894rsquos 119895th available orientation and the set of targets covered by 119904

119894using its 119895th sector

F A collection of the subsets of 119878(119894119895)| 1 le 119894 le 119899 1 le 119895 le 119902

(1) for each (119894 119895) pair 1 le 119894 le 119899 1 le 119895 le 119902 do(2) Run Identifiability Test and compute 119878

(119894119895) the set of targets effectively covered by 119904

119894with its 119895th sector

(3) end for(4) SetZlarr 0119880119862

119896larr 1198861198981 119886

119898119896

1198801198621015840larr 119879 119880119862

119896 and 119880119882 larr 119878

(5) for each target 1198861198961015840 isin 119880119862

119896do

(6) 1198621198961015840 larr 0

(7) end for(8) loop(9) (119894 119895) larr arg max

119904119894isin1198801198821le119895le119902

10038161003816100381610038161003816119878(119894119895)⋂119880119862

119896

10038161003816100381610038161003816

(10) if 119878(119894119895)⋂119880119862

119896= 0 then

(11) ZlarrZ⋃119878(119894119895) 119880119882 larr 119880119882 119904

119894 1198801198621015840 larr 1198801198621015840 119878

(119894119895)

(12) for each 1198861198961015840 isin 119878(119894119895)⋂119880119862

119896do

(13) 1198621198961015840 larr 119862

1198961015840 + 119897119894= 1198621198961015840 + 119871119894(119861119903)

(14) end for(15) 119880119862

119896larr 119880119862

119896 1198861198961015840 | 1198621198961015840 ge 119903 where 1198961015840 isin 119898

1 119898

119896

(16) else(17) (119894

1015840 1198951015840) larr arg max

119904 1015840isin1198801198821le1198951015840le119902

10038161003816100381610038161003816119878(11989410158401198951015840)⋂119880119862

101584010038161003816100381610038161003816

(18) if 119878(11989410158401198951015840)⋂119880119862

1015840= 0 then

(19) break lowast quit the loop lowast(20) else(21) ZlarrZ⋃119878

(11989410158401198951015840) 119880119882 larr 119880119882 119904

1198941015840 1198801198621015840 larr 1198801198621015840 119878

(11989410158401198951015840)

(22) end if(23) end if(24) end loop(25) ReturnZ

Algorithm 1 sector-decider (119878 119879 1198861198981 119886

119898119896

)

119896 ones which may not be fully covered during thewhole period 119903 And this part is used to determinean active sector for an undecided sensor node suchthat there aremore uncovered targets among themostimportant 119896 targets which will be covered Once wefind such a sector for example 119878

(119894119895) in Line 11 we add

it toZ Line 13 is used to update the total time that themost important 119896 targets can be covered by the sectorsinZ so far

(b) The second part (Lines 17ndash22) is for the case that allthe most important 119896 targets could be fully coveredduring the whole period 119903 This part is used to add

more sectors toZ such that the total target-temporalcoverage can be maximized

422 Sensor-Scheduler Algorithm 2 is the formal descrip-tion of Sensor-Scheduler The inputs of this algorithm areas follows

(a) a single sector 119888119894= 119878(119894119895)

of a sensor node 119904119894for some 119895

selected by Sector-Decider

(b) 119873119894which is the set of sectors for example 119878

(119894119895)s

selected by Sector-Decider such that there exist

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

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RotatingMachinery

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

Table 1

Terms symbols Semantics119878 A set of homogenous camera sensor nodes 119904

1 119904

119899

119879 A set of targets 1199051 119905

119898

119882 The set of the weights of the targets in 119879 1199081 119908

119898

120579 The uniform field-of-vision of the camera sensors119877119904= 1 The normalized sensing range of the camera sensors

119877119905= 1 The transmission range of the camera sensors with omnidirectional transmission radios

119871119894

The battery lifetime of 119904119894

f119905119896

The face direction vector of 119905119896

119861 119903 The length of a given mission and the length of each cycle (we assume 119861119903 is an integer for simplicity)119902 2120587120579 the number of available orientations for each sensord(119894119895)

119878(119894119895)

The vector of 119904119894rsquos 119895th available orientation and the set of targets covered by 119904

119894using its 119895th sector

F A collection of the subsets of 119878(119894119895)| 1 le 119894 le 119899 1 le 119895 le 119902

(1) for each (119894 119895) pair 1 le 119894 le 119899 1 le 119895 le 119902 do(2) Run Identifiability Test and compute 119878

(119894119895) the set of targets effectively covered by 119904

119894with its 119895th sector

(3) end for(4) SetZlarr 0119880119862

119896larr 1198861198981 119886

119898119896

1198801198621015840larr 119879 119880119862

119896 and 119880119882 larr 119878

(5) for each target 1198861198961015840 isin 119880119862

119896do

(6) 1198621198961015840 larr 0

(7) end for(8) loop(9) (119894 119895) larr arg max

119904119894isin1198801198821le119895le119902

10038161003816100381610038161003816119878(119894119895)⋂119880119862

119896

10038161003816100381610038161003816

(10) if 119878(119894119895)⋂119880119862

119896= 0 then

(11) ZlarrZ⋃119878(119894119895) 119880119882 larr 119880119882 119904

119894 1198801198621015840 larr 1198801198621015840 119878

(119894119895)

(12) for each 1198861198961015840 isin 119878(119894119895)⋂119880119862

119896do

(13) 1198621198961015840 larr 119862

1198961015840 + 119897119894= 1198621198961015840 + 119871119894(119861119903)

(14) end for(15) 119880119862

119896larr 119880119862

119896 1198861198961015840 | 1198621198961015840 ge 119903 where 1198961015840 isin 119898

1 119898

119896

(16) else(17) (119894

1015840 1198951015840) larr arg max

119904 1015840isin1198801198821le1198951015840le119902

10038161003816100381610038161003816119878(11989410158401198951015840)⋂119880119862

101584010038161003816100381610038161003816

(18) if 119878(11989410158401198951015840)⋂119880119862

1015840= 0 then

(19) break lowast quit the loop lowast(20) else(21) ZlarrZ⋃119878

(11989410158401198951015840) 119880119882 larr 119880119882 119904

1198941015840 1198801198621015840 larr 1198801198621015840 119878

(11989410158401198951015840)

(22) end if(23) end if(24) end loop(25) ReturnZ

Algorithm 1 sector-decider (119878 119879 1198861198981 119886

119898119896

)

119896 ones which may not be fully covered during thewhole period 119903 And this part is used to determinean active sector for an undecided sensor node suchthat there aremore uncovered targets among themostimportant 119896 targets which will be covered Once wefind such a sector for example 119878

(119894119895) in Line 11 we add

it toZ Line 13 is used to update the total time that themost important 119896 targets can be covered by the sectorsinZ so far

(b) The second part (Lines 17ndash22) is for the case that allthe most important 119896 targets could be fully coveredduring the whole period 119903 This part is used to add

more sectors toZ such that the total target-temporalcoverage can be maximized

422 Sensor-Scheduler Algorithm 2 is the formal descrip-tion of Sensor-Scheduler The inputs of this algorithm areas follows

(a) a single sector 119888119894= 119878(119894119895)

of a sensor node 119904119894for some 119895

selected by Sector-Decider

(b) 119873119894which is the set of sectors for example 119878

(119894119895)s

selected by Sector-Decider such that there exist

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Propagation

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DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

(1) Sch119894larr 0

(2) if exist1198861198961015840 isin 119888119894⋂119879119896such that (119905

1198961015840 minus red

1198961015840 ) lt 119903 where

(21) 1199051198961015840 = sum

119888119895isin119860(1198961015840)Z1015840 119897119895

(22) 1199031198901198891198961015840 = sum

119888119909 119888119910isin119860(1198961015840)Z1015840and119909 = 119910maxmin(119888119909 sdot 119891 119888119910 sdot 119891) minusmax(119888119909 sdot 119887 119888119910 sdot 119887) 0 and

(23) 119860(1198961015840) is the set of selected sectors by SECTOR-DECIDER effectively covering 1198861198961015840 isin 119879

then(3) Sch

119894larr Sch

119894⋃max

1198881198941015840isin119873119894 ⋂119860(119896

1015840)Z1015840 1198881198941015840 sdot 119891 | forall1198861198961015840 isin 119888119894⋂119879119896

(4) else(5) Sch

119894larr Sch

119894⋃1198881198941015840 sdot 119887 119888

1198941015840 sdot 119891 119888

1198941015840 sdot 119887 minus 119897

119894 1198881198941015840 sdot 119891 minus 119897

119894| forall1198881198941015840 isin 119873

119894Z1015840⋃0 119903

(6) end if(7) Find the 119888

119894sdot 1198870satisfying Δ119879119862

119894= min

119888119894 sdot119887isinSch119894 red119894 wherered119894= sum119888119895isin119873119894Z

1015840 (maxmin(119888119894 sdot 119891 119888119895 sdot 119891) minusmax(119888119894 sdot 119887 119888119895 sdot 119887) 0 sdot sum119886119896isin119888119894cap119888119895

119908119896)

Note that if 119888119894sdot 119891 is larger than the length of the round 119903 we should rewrite the original working

period [119888119894sdot 119887 119888119894sdot 119891] as [119888

119894sdot 119887 119903] and [0 119888

119894sdot 119891 minus 119903]

(8) Return ⟨119888119894sdot 1198870 119888119894sdot 1198910larr 119888119894sdot 1198870+ 119871119894 (119861119903)⟩

Algorithm 2 sensor-scheduler (119888119894 119873119894Z1015840Z 119879

119896 Sch)

(1)Zlarrsector-decider (119878 119879 119879119896) 119879119862 larr 0

(2) for each 119909 isin 119894 | 119878(119894119895)isinZ do

(3) 119888119909larr 0Z1015840 larr 0 119879

119896larr 1198861198981 119886

119898119896

and119873119894larr 0

(4) end for(5) for each 119878

(119894119895)isinZ do

(6) 119888119894larr 119878(119894119895)

Z1015840 larrZ1015840⋃119888119894 and119873

119894larr 119888119909| 119888119909isinZ 119888

119894and 119888119894⋂119888119909= 0

(7) end for(8) for each 119904

119894isin 119878 do

(9) Schlarr 0 and 119879119862119894larr 0

(10) end for(11) while Z1015840 = 0 do(12) Construct a maximal independent set119872(Z1015840) ofZ1015840(13) for each 119888

119894isin 119872(Z1015840) do

(14) ⟨119888119894sdot 119887 119888119894sdot 119891⟩ larr sensor-scheduler (119888

119894119873119894Z1015840Z 119879

119896 Sch)

(15) end for(16) Z1015840 larrZ1015840 119872(Z1015840) Schlarr Sch⋃⟨119888

119894sdot 119887 119888119894sdot 119891⟩ | forall119888

119894isin 119872(Z1015840)

(17) end while(18) for each 119909 isin 119898

1 119898

119896 do

(19) if 119886119909is not fully covered during 119903 time slots based on Sch then

(20) Return ⟨false 0 0 minus1⟩(21) end if(22) end for(23) 119879119862 larr sum

119896isin11198981198981 119898119896119908119896sdot (119905119896minus red119896) + 119903 sdot sum

119896isin1198981 119898119896119908119896 where

(231) 119905119896= sum119888119894isin119860(119896)

119897119894 and

(232) red119896= sum119888119894 119888119895isin119860(119896)and119894 = 119895

maxmin(119888119894sdot 119891 119888119895sdot 119891) minusmax(119888

119894sdot 119887 119888119895sdot 119887) 0

(24) Return ⟨trueZ Sch 119879119862⟩

Algorithm 3 network-scheduler (119861 119878 119879119882 119879119896= 1198861198981 119886

119898119896

)

some targets which can be covered by both theselected sector of 119904

119894and another sector in119873

119894

(c) a subcollectionZ1015840 ofZ

(d) Z itself

(e) the set 119879119896of the most important 119896 targets

(f) Sch which is the schedule of cameras which aredetermined so far

The goal of this algorithm is to determine the schedule ofsector 119888

119894within each short term with 119903 unit time The most

important part is to make sure that the most important 119896targets are getting coverage during the whole period 119903 Forthis purpose Line 2 checks if there exists a target in 119879

119896which

has not received sufficient coverage based on the schedule Sch(which is still under consideration) but still can be covered by119888119894 If so we add the latest finish time of sensors in Sch which

covers such a target to Sch119894as the beginning time of 119888

119894(Line 3)

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

International Journal of

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Journal ofEngineeringVolume 2014

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VLSI Design

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

If no such target exists we just try to find a point to start to use119888119894so that the target-temporal coverage is maximized At the

end the activation period of 119888119894 which is represented by two

moments c119894sdot1198870and 119888119894sdot1198910 is returnedNote thatwe utilize a new

metric namely the target-temporal coverage redundancy ofa camera sensor node red

119894in Line 7 of Algorithm 2 This

metric is used to evaluate how much the node 119888119894is wasted by

monitoring targets which are already monitored by the othernodes By rescheduling the current node such that the overalltarget-temporal coverage redundancy can be decreased wecan improve the quality of the current schedule

423 Network-Scheduler Based on the above twosubprocedures Sector-Decider and Sensor-SchedulerNetwork-Schedulerrsquos formal description is shown inAlgorithm 3 The inputs of this algorithm are the missionperiod 119861 the set of camera sensors 119878 the set of targets 119879 theweight of the targets 119882 and the set of the most important119896 targets 119886

1198981

119886119898119896

The outcome of this algorithmconsists of four tuplesThe first one is either true or false It istrue if the schedule generated by this algorithm is providingfull coverage of the most important 119896 targets during themission period 119861 Otherwise it returns false The seconditem returned is Z which includes one sector for eachcamera sensor to achieve the target-temporal coverage 119879119862which is the fourth item of the output of this algorithm Thethird one is Sch which is the schedule of each camera sensor

This algorithm is based on the assumption that all camerasensor nodes are already scheduled that is the activationperiod of each camera sensor node is already determinedrandomly and we try to refine the schedule of each node(one by one) based on the current schedule of the othernodes such that the overall target-temporal coverage can bemaximized Note that the preassignment of the schedule ofall nodes can be done via assigning each nodersquos beginningtime with 0 Based on the preassignment of the schedule wecan improve the quality of it by iteratively identifying a nodewhich canmake the overall target-temporal coverage increaseand rescheduling this node

In detail in Line 1 Sector-Decider is called to deter-mine the active sector for each sensor node Lines 2ndash10are used to initialize the variables Lines 11ndash17 are used todetermine the schedule of camera sensors In particular Line12 utilizes maximal independent set ofZ1015840 so that the camerasensorswhose activation period is determined donot overlapIn this way we can further maximize the target-temporalcoverage Finally Lines 18ndash24 are checking if the determinedschedule is satisfiable

424 A Big Picture Now we give a simple example toillustrate how the overall algorithmworksThe camera sensornetwork is composed of 5 camera sensors each of which has8 available orientations and 5 targets each of which has itsown facing direction (as shown by the shorter arrow of eachtarget in Figure 5) Among these 5 targets there are 2 pivotaltargets 119886

1and 119886

2 that is 119879

119896= 1198861 1198862 and 119908

1= 4 119908

2= 3

1199083= 2 119908

4= 1 119908

5= 1 In the scheduling of each sensor

S1

S2

S3

S4

a3

a2a5

S5

a1

a4

Figure 5 An instance of the overall algorithm

the length of each round 119903 = 10 and the sensorsrsquo batterylifetime per round 119897

1 1198972 1198973 1198974 1198975are 5 6 4 4 6 respectively

In Figure 5 each sensor has been assigned the workingdirection that is Lines 1ndash7 of Algorithm 3 have been accom-plished for this network andweobtain each sensorrsquos neighborset 119873

1= 1198782 1198784 1198732= 1198781 1198783 1198733= 1198782 1198734= 1198781

1198735= 0Then we begin to generate a sleep-wakeup schedule

for each sensor (Lines 8ndash17 of Algorithm 3) We first go intothe while loop (Lines 11ndash17 of Algorithm 3)

(a) In the first loop Z1015840 = 1198781 1198782 1198783 1198784 1198785 and an MIS

of Z1015840 is 1198781 1198783 1198785 which is obtained based on each

sensorrsquos neighbor set For each sensor in 1198781 1198783 1198785

we run Algorithm 2 to get its starting time point

(i) For 1198781 1198781cap 119879119896= 1198861 and 119905

1minus red1= 0 lt 119903

so Sch1= 1198782sdot 119891 = 0 It is easy to find that

1198781sdot 119887 = 0 satisfying Δ119879119862

1= 0 thus we can

return 1198781sdot 119887 = 0

(ii) Theoutput ofAlgorithm 2on 1198783is similar to that

of 1198781and 1198783sdot 119887 = 0

(iii) For 1198785 since 119878

5cap 119879119896= 0 and 119873

5= 0 Sch

5=

0 10

We can easily get that 1198785sdot 119887 = 0 satisfying Δ119879119862

5= 0

thus we can return 1198785sdot 119887 = 0

(b) In the second loop Z1015840 is updated into 1198782 1198784 and

the MIS of the currentZ1015840 is 1198782 1198784 For each sensor

in 1198782 1198784 we run Algorithm 2 to get its starting time

point

(i) For 1198782 1198782cap 119879119896= 1198861 1198862 and 119905

1minus red1= 5 lt 119903

1199052minusred2= 0 lt 119903 so Sch

2= 1198781sdot119891 1198783sdot119891 = 5 4

It is easy to find that 1198782sdot 119887 = 4 satisfying Δ119879119862

2=

4 (= min7 4) thus we can return 1198782sdot 119887 = 4

(ii) For 1198784 since 119878

4cap 119879119896= 0 Sch

4= 1198781sdot 119887 1198781sdot

119891 0 10 = 0 5 10

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

150 200 250 300 350 4001600

1700

1800

1900

2000

2100

2200

2300

2400

2500

Targ

et-te

mpo

ral c

over

age (

TC)

Upper bound

Number of sensor nodes (n)

bl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 6 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of sensors

We can easily get that 1198784sdot 119887 = 5 satisfying Δ119879119862

4= 0

thus we can return 1198784sdot 119887 = 5

After the second loopZ1015840 is updated into 0 that is the whileloop can be terminated Finally we obtain that the schedulingis 1198781sdot 119887 = 0 119878

2sdot 119887 = 4 119878

3sdot 119887 = 0 119878

4sdot 119887 = 5 119878

5sdot 119887 = 0 and

119879119862 = 94 (= 4lowast(5+6minus1)+3lowast(4+6)+2lowast(5+4)+1lowast6+1lowast0)

5 Simulation Results and Analysis

In this section we present our results and discuss theperformance of our algorithm for DCA-MCSN Specificallywe randomly deploy 119899 camera sensor nodes and 119898 targetswithin a 100 times 100 2-D virtual space where 119899 is set to 150200 400 It is expected that the number 119899 of availablecamera sensor nodes whose battery lifetime is significantlylower than the mission lifetime 119871 is greater than the numberof 119898 of targets and thus we set 119898 as 20 30 70 We setmaximum sensing radius 119877 of each camera sensor to be 50We assume the weight of each target is a random numberwithin the range of (0 10) We assume that the missionlifetime per a unit 119903 is 10 unit time Lastly we randomly assignthe face direction vector of each target and the maximumviewing angle is 1205874 In this problem each camera sensornode has 119902 sensing sectors and we will use one of them thatis the beamwidth 120579 of each sector is 2120587119902

In the simulation we study the average characteristicbehavior of the proposed algorithm and evaluate its averageperformance with regard to the target-temporal coverage 119879119862and the number of the most important targets fully coveredby sensors given Especially we will check how this algorithmworks with two important parameters the uniform batterylifetime 119887119897 of each sensor and the beamwidth 120579 of each

20 25 30 35 40 45 50 55 60 65 70

1000

1500

2000

2500

3000

3500

Number of targets (m)

Targ

et-te

mpo

ral c

over

age (

TC)

Upper boundbl = 4 120579 = 1205876

bl = 4 120579 = 1205874bl = 4 120579 = 1205873

bl = 6 120579 = 1205876

bl = 6 120579 = 1205874

bl = 6 120579 = 1205873

Figure 7 Target-temporal coverage achieved by DCA-MCSN ver-sus the number of targets

camera sensor In particular we will check the following sixcases Case (a) 119887119897 = 4 120579 = 1205876 Case (b) 119887119897 = 4 120579 = 1205874 Case(c) 119887119897 = 4 120579 = 1205873 Case (d) 119887119897 = 6 120579 = 1205876 Case (e) 119887119897 = 6120579 = 1205874 Case (f) 119887119897 = 6 120579 = 1205873 We also use the sum of theweights of all targets sum

1le119896le119898119908119896 multiplied by the mission

time duration per a unit 119903 as the theoretical upper boundwhich is notated by 119880119861 Clearly 119880119861 can be larger than actualachievable optimum

51 Simulation Results for DCA-MCSN In Figure 6 wecompare the performance of DCA-MCSN against 119880119861 underthe 6 parameter settings (Cases (a)ndash(f)) while the number oftargets to be covered is fixed to 50 By comparing the resultswith 119887119897 = 4 (Cases (a) (b) and (c)) against 119887119897 = 6 (Cases(d) (e) and (f)) we can learn that if the beamwidth 120579 ofeach sensorrsquos sector is fixed the performance of the algorithmbecomes close to 119880119861 with larger longer battery lifetime 119887119897This is because with larger 119887119897 value we have more number ofsensor nodes to fully covermore number of targets during themission period Next we study how the total 119879119862 is affectedby the beamwidth 120579 of each sensorrsquos sector while we fix 119887119897to 4 and 6 respectively By comparing Cases (a) (b) and (c)in Figure 6 as well as Cases (d) (e) and (f) in Figure 6 wecan learn that 119879119862 increases as 120579 grows This is because thenumber of targets covered by each sensor increases as 120579 isgetting larger Overall from Figure 6 we can observe that theinitial battery lifetime 119887119897 of each sensor has more significantinfluence than the beamwidth 120579 on the performance of thealgorithm

Next we study Figure 7 in which we fix the number ofsensor nodes deployed to 250 and vary the number of targetsto be covered from 20 to 70This result clearly shows that theperformance of our algorithm is close to the theoretical upperbound independent of the other parameters including 119887119897 120579

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 9

150 200 250 300 350 4004

6

8

10

12

14

16

Number of sensor nodes (n)

The n

umbe

r of t

he fi

rst k

piv

otal

ta

rget

s cov

ered

ACA (bl = 6 120579 = 1205876)ACA (bl = 6 120579 = 1205874)ACA (bl = 6 120579 = 1205873)

DCA (bl = 6 120579 = 1205876)DCA (bl = 6 120579 = 1205874)DCA (bl = 6 120579 = 1205873)

Figure 8 The number of the first 119896 important targets covered bysensors by DCA-MCSN versus ACA

and the number of targets119898 once we obtain enough coverageover the area

52 Simulation Results for DCA-MCSN versus ACA In thissubsection we compare the performance of DCA-MCSNagainst ACA (TEC-NC-Adjuster) in [5] (which showedoutstanding performance for solving the target-temporaleffective-sensing coverage with adjustable cameras problemTEC-AC in the simulations) under the 3 parameter settings(Cases (d)ndash(f)) while the number of targets to be covered isfixed to 50 We study how many important targets are fullycovered by the two strategies (see Figure 8) From this resultwe can observe that for both of the strategies the number 119896 ofthemost important targets which are fully covered during themission period is affected by 120579 that is 119896 is steadily increasingalong with the growth of 120579 Furthermore DCA-MCSNworksbetter than ACA under all parameter settings which impliesthat DCA-MCSN is more efficient than ACA for the mission-driven application considering the coverage quality of thetargets with higher priority

6 Conclusion

In this paper we investigate a new coverage problem incamera sensor networks In this problem we study how toschedule a given set of camera sensor nodes to cover a setof given targets with weight related to their importance andfixed face directions such that the number of the first 119896 impor-tant targets effectively covered during a given mission periodcan be maximized as well as the overall target-temporalcoverage is maximized (as the secondary optimization goal)The main contribution of this paper is the possibility ofusing insufficient number of camera sensors to best support acoverage mission in a way that was never considered beforeSince we do not always have enough number of sensornodes to complete a coverage mission our paper is of greatapplicability in many real application scenarios As a future

work we plan to study the applicability of this model inthe hybrid sensor network of both a number of cheap staticsensor nodes and a few expensivemobile sensor nodes whichwe believe also have awide range of applications inmany real-life scenarios

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was jointly supported by National NaturalScience Foundation of China under Grant 91124001 theFundamental Research Funds for the Central Universitiesand the Research Funds of Renmin University of China10XNJ032

References

[1] M Cardei M TThai Y Li andWWu ldquoEnergy-efficient targetcoverage in wireless sensor networksrdquo in Proceedings of the 24thIEEE International Conference on Computer Communications(INFOCOM rsquo05) pp 1976ndash1984 March 2005

[2] M Cardei and J Wu ldquoEnergy-efficient coverage problems inwireless ad-hoc sensor networksrdquo Computer Communicationsvol 29 no 4 pp 413ndash420 2006

[3] C Liu and G Cao ldquoSpatial-temporal coverage optimizationin wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 10 no 4 pp 465ndash478 2011

[4] C Liu and G H Cao ldquoDistributed critical location coveragein wireless sensor networks with lifetime constraintrdquo in Pro-ceedings of the 31th IEEE International Conference on ComputerCommunications (INFOCOM rsquo13) 2012

[5] Y Hong D Kim D Li W Chen A O Tokuta and ZDing ldquoTarget-temporal effective-sensing coverage in mission-driven camera sensor networksrdquo in Proceedings of the IEEEInternational Conference on Computer Communications andNetworks (ICCCN rsquo13) 2013

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

[7] H Ma and Y Liu ldquoOn coverage problems of directional sensornetworksrdquo in Proceedings of the 1st International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo05) 2005

[8] Y Cai W Lou M Li and X-Y Li ldquoTarget-oriented schedulingin directional sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) pp 1550ndash1558 May 2007

[9] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[10] J Adriaens S Megerian and M Potkonjak ldquoOptimal worst-case coverage of directional field-of-view sensor networksrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)pp 336ndash345 September 2006

[11] G Fusco andHGupta ldquoSelection and orientation of directionalsensors for coverage maximizationrdquo in Proceedings of the 6th

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Distributed Sensor Networks

Annual IEEE Communications Society Conference on SensorMesh and Ad Hoc Communications and Networks (SECON rsquo09)June 2009

[12] W Cheng S Li X Liao S Changxiang andH Chen ldquoMaximalcoverage scheduling in randomly deployed directional sensornetworksrdquo in Proceedings of the International Conference onParallel Processing Workshops (ICPPW rsquo07) September 2007

[13] Y Wang and G Cao ldquoOn full-view coverage in camera sensornetworksrdquo in Proceedings of the 30th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo11) pp 1781ndash1789 April 2011

[14] L Liu H Ma and X Zhang ldquoOn directional K-coverageanalysis of randomly deployed camera sensor networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo08) pp 2707ndash2711 May 2008

[15] B Raytchev I Yoda and K Sakaue ldquoHead pose estimationby nonlinear manifold learningrdquo in Proceedings of the 17thInternational Conference on Pattern Recognition (ICPR rsquo04) pp462ndash466 August 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of