Information Sciences 223 (2013) 153–163

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Information Sciences

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Minimum connected cover of a query region in heterogeneouswireless sensor networks

Ahmed M. Khedr a,b,⇑, Walid Osamy c

a Computer Science Department, Faculty of Sciences, University of Sharjah, Sharjah, United Arab Emiratesb Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egyptc Computer Science Department, Faculty of Computers and Informatics, Banha University, Banha, Egypt

a r t i c l e i n f o

Article history:Received 17 April 2011Received in revised form 27 August 2012Accepted 26 September 2012Available online 16 October 2012

Keywords:Arbitrary sensing and communication radiiDistributed algorithmMinimum connected coverQuery regionWireless sensor network

0020-0255/$ - see front matter � 2012 Elsevier Inchttp://dx.doi.org/10.1016/j.ins.2012.09.046

⇑ Corresponding author.E-mail addresses: akhedr@sharjah.ac.ae, amkhed

a b s t r a c t

Wireless sensor networks are composed of a large number of tiny sensors that have limitedresources and yet must form a connected network. The main challenge in the design of sen-sor networks is the limited battery power of the sensors and the difficulty of replacing and/or recharging these batteries due to the nature of the monitored field. Thus, it is necessarythat the sensors be densely deployed and energy-efficient protocols be designed to maxi-mize the network lifetime while meeting the specific application requirements in terms ofcoverage and connectivity. Given a query over a sensor network the minimum connectedsensor cover problem is to select a minimum, or nearly minimum, set of sensors such thatthe selected sensors cover the query region and form a connected network. In this paper,we propose a new distributed algorithm to find the minimum connected cover of the que-ried region for heterogeneous sensors, each with arbitrary sensing and transmission radiiand different energy levels. Each sensor node in the network determines whether to sensethe queried region according to its minimum-weight coverage cost. We provide perfor-mance metrics to analyze the performance of our approach and the simulation resultsshow that our approach clearly improves the network lifetime over existing algorithms.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Wireless sensor networks (WSNs) consist of a large number of tiny sensing devices with very limited resources that mustcoordinate amongst themselves to achieve a larger sensing task. Networks formed by such sensor nodes (SNs), combine sim-ple wireless communication, minimal computation facilities, and some sort of sensing of the physical environment into thenew form of network, which have received significant attention due to their potential applications from civil to military do-mains including environment monitoring, biological detection, vehicle tracking, and battlefield surveillance [1]. WSNs areused to collect sensed data, aggregate them if needed, and transmit them to the base station. The SNs in such networksare deployed in a region of interest and their locations are unknown a priori. Each SN serves not only as a host to sense dataaround its vicinity but also as a router to relay messages for other SNs toward the base station. One critical characteristic of aWSN is that each SN in it is equipped with energy limited battery, and energy-efficiency in network operations is of para-mount importance. Because SNs are often densely deployed, in a WSN there may be some failing SNs or SNs that have merelyexhausted their energy supply. However, it may be impossible or infeasible to recharge SNs once they have been deployed,especially if they have been deployed in an inhospitable or physically unreachable terrain. Therefore, to let all SNs in theregion of interest answer an incoming query is very energy-inefficient and unnecessary. In fact, only subset of the SNs is

. All rights reserved.

r@zu.edu.eg (A.M. Khedr), w.osamy@gmail.com (W. Osamy).

154 A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163

sufficient for sensing a region during the query execution, while other SNs need not be concerned with the incoming query,so it is possible to identify multiple sets of SNs so that they can be activated one after the other in each round to furtherextend the network lifetime [11], i.e., we need to control the density of working SNs to a certain level [45]. Specifically, den-sity control ensures only a subset of SNs operates in active mode. Also, not only should the SNs in the chosen set be able tocover the monitored region with a given coverage guarantee but the communication graph induced by the SNs should beconnected. Thus, in WSN sensing coverage and sensor connectivity are two fundamental issues.

WSNs are typically used to monitor a region of interest. The SNs can cover the entire region, depending on applicationdomains. The ratio between the covered area by SNs and the entire monitored region is an important metric in terms ofthe quality of service of sensing coverage, i.e. how accurate the WSN monitors the region of interest, how far away a pointin an uncovered area is from its nearest active SN. The full coverage problem, in which each point in the entire monitoredregion is covered by at least one SN, has been extensively studied in literature [5,6,47]. However, in some applications, fullcoverage may not be necessary and minimum coverage is sufficient. Since the number of SNs used for minimum coverage issignificantly less than that for full coverage, the network lifetime by minimum coverage is further prolonged through keep-ing a small number of SNs in active mode. One such an example is the environment monitoring. We define the minimumcoverage problem as follows: Given a monitored region with densely deployed SNs, the problem is to find a subset of SNsand keep them in active mode while the other SNs are kept in sleep mode so as to preserve their precious energy, in orderto prolong the network lifetime and to meet the full coverage guarantee simultaneously. On the other hand, the sensed databy active SNs must be transmitted to the base station for further processing. To do so, it requires that the selected SNs be ableto communicate with each other, directly or through relay SNs. Therefore, our objective is to not only find a subset of SNs forminimum coverage with a given coverage guarantee but also ensure that the communication between them induced by thechosen SNs is connected, we refer to this as the connected, minimum coverage problem. One of its special cases is the con-nected, full coverage problem that has been explored in many research works for example [6,16,30,34,42,46,47].

Most applications and research work focus on homogeneous WSNs, where all SNs are identical in terms of energy re-source, computation and wireless communication capabilities. However, homogeneous sensor network lacks good supportfor network scalability, data aggregation, and is usually not energy efficient with the many-to-one communication pattern.To overcome these problems, heterogeneous sensor networks consisting of two or more different types of SNs with differentsensing and communication radii and energy levels. A mixed deployment of these SNs can achieve a balance of performanceand cost of WSN. A number of real life examples of large scale WSNs can use heterogeneous SNs. An already deployed HighPerformance Wireless Research and Education Network (HPWREN) in Southern California [13] is a great example of theneeds of such a heterogeneous WSN. The data is transmitted when needed to the HPWREN wireless backbone, which routesit out to the internet. Such organization is appropriate for large scale heterogeneous WSNs as the sensor data is often col-lected in remote and possibly hazardous locations, and thus needs to be both accessed at the location and also forwardedto the internet backbone for further analysis and storage [26].

The main contributions of this paper are as follows: formulates the minimum connected sensor cover problem in heter-ogeneous sensor networks, proposes a rule to select a minimum sensor cover based on local neighborhood information, anddesigns a distributed algorithm to construct an approximate optimal minimum connected sensor cover by selecting the min-imum number of SNs which can entirely cover a particular query region, while remaining strongly connected, by consideringthe case, where every SN has a different sensing and communication radii and different energy level.

The rest of the paper is organized as follows: In Section 2, we briefly discuss the related research of our proposed problem.The problem statement and the terms used in our problem formulation are covered in Section 3. In Section 4, we introduceour approach in carrying out our proposed algorithm. The simulation of our approach is presented in Section 5. We concludeour work in Section 6.

2. Related research

Given a set of SNs, tremendous effort in WSNs has been taken on covering the monitored region, preserving network con-nectivity, and maximizing energy efficiency and network lifetime [6,10,12,16,20–23,25,29,30,32,34,37,40–44,46,47]. In [7],the authors surveyed the recent progress of the coverage and connectivity problem. The problem of computing connectedsensor cover of a query region, was first introduced in [16], where the authors proposed two self-organizing solutions. How-ever, both solutions follow a greedy strategy and none of the them is localized. In the first solution, centralized approxima-tion algorithm, an arbitrary SN in the centralized algorithm within a queried region is selected at the start of the algorithm.Then, a path of SNs that connects an already selected SN to another SN (candidate SN), which is partially covered by alreadyselected SNs, is selected as a candidate path. Among the selected candidate paths in each step, the one that covers the mostuncovered area in the queried region (most beneficial candidate path) is added to the already selected SNs. Such a processoperates continuously until the selected set of SNs cover the queried region completely. In the second solution, decentralizesapproximation algorithm (DAA), a particular SN (which is not always the same SN) behaves as the coordinator or the leader.This special SN collects global information in order to select the SNs to be included in the final cover set. However, such solu-tion does not consider the total energy consumption and require large number of messages overhead. [30] considered thecoverage as the measure of quality of service of a WSN. In [35], an efficient distributed protocol is proposed to find a subsetof connected SNs to cover the queried region. Each SN determines whether to be a sensing node according to its priority,

A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163 155

which is determined by the residual power or sensing area within the queried region. In [36], the protocol in [35] is extendedto solve the k-coverage request.

For the full coverage problem, the work in [37] initially studied this problem by partitioning the SNs in the network intomutually exclusive subsets such that the SNs in each subset can fully cover the monitored region, and their goal is to max-imize the number of the subsets. Thus, it suffices to have the SNs in one subset to be active at any time. A heuristic solution isthen proposed for SN partitioning due to the NP-hardness of the concerned problem. However, they focused only on full cov-erage without taking into account the connectivity of SNs in each subset. In [40], the authors considered the full coverageproblem as well by exploring an energy-efficient coverage-preserving node-scheduling scheme to prolong the networklifetime.

The authors of [47] generalized the connected, full coverage problem into the connected k-coverage problem, which aimsat finding a set of SNs such that each point in the monitored region is covered by at least k SNs in the set of selected SNs. In[46], the authors addressed the problem of maintaining sensing coverage and connectivity, with an objective to minimize thenumber of active SNs. With an assumption that the transmission range of each SN is at least twice its sensing range, theyproved that if a set of SNs fully covers the entire region, then the communication graph induced by the SNs is connected.Thus, they only consider the coverage problem under the assumption by proposing a distributed algorithm for the con-nected, full coverage problem. They also considered the case of the transmission range is less than twice its sensing rangeby giving a heuristic algorithm as well. [42] extended the approach in [46] to solve the k-coverage problem by showing thatk-coverage implies k-connectivity under the same assumption, where a graph is k-connected if it is still connected after theremoval of any ðk� 1Þ SNs from it. It must be mentioned that although [46] showed with an assumption of transmissionrange is greater than or equal twice sensing range that if a set of SNs fully covers a given monitored region, then the com-munication graph induced by the SNs is connected, this property, however, is no longer held if it is minimum rather than fullcoverage. In [46], initially it is expected to obtain full coverage. After a certain number of rounds, it is impossible to obtain afull coverage using active SNs, due to the expiration of energy of some SNs, instead, a minimum coverage with a giventhreshold is acceptable. In [18], the authors proposed algorithm to construct minimum relay connected sensor cover in het-erogeneous WSN with only two types of SNs (sensors and relay sensors) based on triangular lattice.

In [2], the authors proposed optimal deployment patterns to achieve full coverage and three-connectivity, and full cov-erage and five-connectivity under different ratios of sensor communication range over sensing range for WSNs, where Voro-noi polygons generated by sensor nodes are congruent. They also proposed a new deployment-polygon based methodology,and proved their optimality among regular patterns for all values of rc=rs P 1, where rc is the communication radius and rs isthe sensing radius. The optimality objective concerns minimization of the number of SNs required to construct a connectedcoverage. They assumed disc-based sensing and communication, homogeneous sensing and communication ranges, andbounded value of rs=rc . Some WSN applications like border guard require accuracy in sensed data as well as robustness ofthe system. Some studies introduced the constraint called k-coverage of the target sensing field for all values of rc=rs, [3].In [19], the authors addressed the problem of optimal node placement for ensuring connected coverage in sensor networks.They considered two different practical scenarios. In the first scenario, a certain region or a set of regions are to be providedconnected coverage, while in the second case, a given set of n points are to be covered and connected. For the first case, theyprovided solutions that are within a small factor of the optimum. For the second case, they presented an algorithm that runsin polynomial time, and guarantees a constant factor approximation ratio. In [27], the authors developed a robust and scal-able algorithm to cope with the sensor placement problem for target location under constraints of the cost limitation and thecomplete coverage for grid based WSNs. The sensor placement problem formulated as a combinatorial optimization problemfor minimizing the maximum distance error in a sensor field under the constraints.

The connected minimum coverage problem proposed in this paper is essentially different from the above related papersin the following aspects: (1) We select the minimum number of sensors to be activated from a set of randomly pre-deployedsensors such that all interested discrete locations are k-covered, this problem is known to be NP-hard. This is not the case in[2,3,19,27]. (2) We aim to find the minimum number of SNs as active SNs in the beginning of the network operation and thisis not the case in [36,42,46]. (3) We aim to cover the monitored region evenly, whereas in [36,42,46,47], they consider nei-ther the distribution of covered areas nor the bound on the above distance, and thus minimum coverage obtained by theirapproach may be unfair, i.e. some areas are covered while other reasonably large areas may not be covered. (4) In our ap-proach, the communication graph induced by the selected SNs is guaranteed to be connected, whereas the graph induced bythe selected SNs in [46] may be disconnected. (5) We generalize the solution by relaxing the conditions on the sensing andtransmission radii and energy level of SNs, whereas all above work is proposed for homogenous WSNs[2,3,18,19,27,36,42,46,47].

A dominating set is a set of vertices such that every vertex in the graph that represents WSN is either in the dominatingset, or adjacent to a vertex in the dominating set. A connected dominating set is a dominating set which is also a connectedsubgraph. The main difference between a connected dominating set and a query region connected cover stems from theselection of dominators. In the former case, a SN is a dominator of another SN if the dominated SN is in the transmissionrange of the dominator. In the latter case, a dominated SN is the SN that communicates with at least one dominator in itsneighborhood, and whose sensing region is completely covered by dominators. The strategy we use in our proposed algo-rithm is similar to pruning used in the computation of connected dominating sets [8,24,28], however, the notion of domi-nating set is significantly different than that of sensor connected cover [16]. In [14,15], decentralized, self-stabilizing, andfault-tolerant algorithms for the minimum connected dominating sets covering of a query region in WSNs were proposed.

156 A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163

The first solution in [15] uses a greedy strategy. It requires the knowledge of the distance to the center of the query region.That is, the region is covered in successive waves from outside to inside. The coverage stops once the wave reaches the centerof the monitored area. The second solution proposed in the same paper uses a pruning strategy. Redundant SNs are removedfrom the final cover if their removal does not disconnect their respective neighborhoods, and if their sensing regions arecompletely covered by their chosen neighbors. In [14], the authors proposed a pruning-based algorithm, where SNs are con-sidered redundant if their sensing regions are covered by other neighbors, and their neighbors are connected through a con-nection path. This solution assumes that the SNs are homogenous. The work in [14,15] is close to ours, however, ourproposed approach is based on local neighborhood information and uses different assumptions.

3. Problem statement and definitions

Most existing work on sensing coverage in the literature has focused on the (connected) full coverage problem. However,in some scenarios, full coverage is either impossible or unnecessary. Here, we are considering a WSN in which the minimumnumber of SNs which can entirely cover a particular query region, while remaining strongly connected, considering the case,where every SN has a different sensing and communication radii and different energy level, i.e., given a query QR over a re-gion R in WSN, we find a set of SNs M that covers QR and satisfies the following:

1. The sensing region of the selected set of SNs covers the entire geographical region of the query,2. The selected set of SNs can communicate with each other, and3. The selected set should form a minimum connected sensor cover size.

In this section, we give some definitions and notations that will be used in developing our proposed algorithm. We as-sume that there are randomly scattered n SNs over a monitored area and form the set S, where S ¼ fsi : i ¼ 1; . . . ;ng. Also,we assume that the application requires every part of the area to be covered by the SNs throughout the network lifetime.

Definition 1. The sensing area of a SN siðAðsiÞ) is the area in which si can sense a physical phenomenon.

Definition 2. The communication area of a SN siðCðsiÞ) is the area in which si can communicate directly with other SNs.

Definition 3. The communication neighbors of a SN si (NðsiÞ) is the set of all SNs that located inside CðsiÞ. As shown in Fig. 1,the communication neighbors of S1 is fS2; S3; S4; S5g.

Definition 4. The coverage neighbors of a SN siðCNðsiÞ) is the set of all SNs sjs that satisfy the condition AðsiÞT

AðsjÞ – /. Asshown in Fig. 1, the coverage neighbors of S1 is fS2; S3; S5g.

Fig. 1. Heterogenous WSN Example.

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Definition 5. The ReachabilityTable (RTBLðsiÞ) of a SN si is the table that maintains the reachability information for each SNsj 2 CNðsiÞ. The RTBL structure is formed from the attributes ID, Path, where ID is the SN identification number, and Path is asequence/path of SNs that form the shortest communication path connecting si with sj.

Definition 6. The available total energy Etotalðx; yÞ for monitoring a location is defined as follows:

Etotalðx; yÞ ¼X

sj :ðx;yÞ2AðsjÞEðsjÞ; ð1Þ

for each point ðx; yÞ of the monitored area, where EðsjÞ is the remaining energy of a SN sj.

Definition 7. The minimum-weight coverage cost of a SN si is defined as [38]:

CmwðsiÞ ¼ max1

Etotalðx; yÞ; ðx; yÞ 2 AðsiÞ: ð2Þ

Lemma 1. The sensing area of a SN si (AðsiÞ) is said to be fully covered by CNðsiÞ if the following condition is satisfied:

CmwðsiÞ <1

EðsiÞ: ð3Þ

Proof. From Definition 7, if there exists a region in AðsiÞ that is covered only by SN si, then CmwðsiÞ will be 1EðsiÞ. If AðsiÞ is fully

covered then any region in AðsiÞ will be covered by at least one SN other than si therefore, Etotal of each subregion of AðsiÞ isgreater than EðsiÞ, hence CmwðsiÞ will be less than 1

EðsiÞ.

For more clarification, in Fig. 1, if Eðs1Þ ¼ 2, Eðs2Þ ¼ 3; Eðs3Þ ¼ 4; Eðs4Þ ¼ 1, and Eðs5Þ ¼ 3 then.

Etotalðx; yÞ ¼

3; ðx; yÞ 2 A24; ðx; yÞ 2 A33; ðx; yÞ 2 A55; ðx; yÞ 2 A126; ðx; yÞ 2 A135; ðx; yÞ 2 A157; ðx; yÞ 2 A234; ðx; yÞ 2 A246; ðx; yÞ 2 A259; ðx; yÞ 2 A1238; ðx; yÞ 2 A1259; ðx; yÞ 2 A135

8>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>:

) ð4Þ

Cmwðs1Þ ¼1

minðA12;A13;A15;A123;A125Þ ¼15

Cmwðs2Þ ¼1

minðA2;A12;A23;A24;A25;A123;A125Þ ¼13

)Cmwðs3Þ ¼1

minðA3;A13;A23;A123;A135Þ ¼14

Cmwðs4Þ ¼1

minðA24Þ ¼14

Cmwðs5Þ ¼1

minðA5;A15;A25;A135;A125Þ ¼13

ð5Þ

According to Lemma 1, we can say that SNs s1 and s4 are full covered. h

4. Minimum connected cover determination

In this section, we outline our proposed algorithm to select the minimum connected SNs that cover the requested region.First, we state the assumptions and then we provide a step by step description.

158 A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163

4.1. Algorithm assumptions

Our approach relies on the following key assumptions regarding the field and the SNs:

1. Hardware capability: We assume that each SN is equipped with a sensing device (to sense the phenomenon), a broad-cast communication device (to communicate with neighboring SNs), and a processing unit to process the data locally.

2. All the SNs are randomly deployed in the monitored region. Moreover, the SNs are deployed densely enough such thatthere exists no isolated SN.

3. Localization: Each SN is static and aware of its own location. SNs can use location services such as [4,31,33] to estimatetheir locations, and no GPS receiver is required at each SN. For simplicity, we assume that every SN knows its locationin space in terms of an ðx; yÞ coordinate.

4. The sensing range of a SN may be different from its transmission range and the sensing ranges are different betweenSNs.

It is also assumed that each SN knows its communicating neighbors, including their identifications and coordinates. Thisinformation can be collected statically via one time beacon or hello message, or periodically if frequent changes in the topol-ogy is anticipated. Note that this neighbor discovery cost is not specific to our technique. Any technique that needs to for-ward a message exclusively to only one communication neighbor (i.e., a link-layer unicast) has to inure this neighbordiscovery cost one way or the other.

4.2. Algorithm description

Here, we give a discussion on how the algorithm finds the minimum connected sensors cover in WSN. The algorithm in-cludes two phases: initial phase, and identification phase. In the initial phase, each SN discovers its coverage neighbors andcollects their information. In the identification phase, each SN determines whether to be a sensing node in the set that is usedto cover the queried area or not.

4.2.1. Initial phase: constructing coverage neighbors setThe difference of the sensing range of SNs in heterogeneous WSNs augments difficulty on determining coverage neigh-

bors, where, a SN may take more than one hope to communicate with its coverage neighbors. Therefore, we cannot considerthe information provided by only the neighbors in its transmission range to find the coverage neighbors of a SN. In order toconstruct coverage neighbors set while maintaining the connectivity of the coverage neighbor nodes; every SN x executesthe following steps:

1. Initialize CNðxÞ to empty.2. 8sj 2 NðxÞ, add sj to CNðxÞ, if its sensing disk intersects with the current sensing disk of x.3. Broadcast coverage neighbor discovery request CovReqðxÞ to representative nodes (Representative nodes provide x

with the information about the coverage neighbors).Nodes in NðxÞ can be chosen as representative nodes if there exists s in NðxÞ such that its sensing disk intersects withyour sensing disk.

4. If CovReqðsÞ received, execute ProcessCovReq procedure (node x considers itself as currentNode; s as CovReq owner, andi as the targetNode where, i is the node that forward the request and it will be the node s if node s is the forwarder orrequest sender node).

5. If update message received (U and the associated path), update CNðxÞ by adding every sk in U, and update RTBL byadding associated path.

Note that the information about a particular coverage neighbor of x will be sent once by exactly one representative node,since the sent neighbor information by different nodes in RepresentativeNodes dos not overlap with each other. Thus, there isno redundant neighbor information, and so, less traffic is generated. The calculation to determine which node information tobe sent by a particular representative node is based on the representative node information. Since the WSN is static, the ter-mination will be reached after a finite number of exchanged messages.

ProcessCovReq Procedure (currentNode; targetNode, CovReq owner)Every node s that receives CovReq will execute the ProcessCovReq procedure. Here, x will be the currentNode; s is the Cov-

Req owner, and i is the targetNode. The procedure steps will be as follows:

1. Initialize the Update set U (coverage neighbors of x) to empty.2. Add to U, every neighbor j that has sensing disk intersects with your sensing disk, and satisfies one of the following

two conditions:(a) j 2 NðkÞ and the distance between j and the currentNode is less than the distance between j and k;(b) j R NðkÞ; for all k 2 NðcurrentNodeÞ

TNðtargetNodeÞ.

3. Add j into RepresentativeNodes.

A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163 159

4. Check if U is empty, it ceases itself to be further involved in the neighbor discovery process. Hence, you do not need totransmit any information to targetNode. Otherwise, forward the CovReq(s) message to RepresentativeNodes and waittill receive the response back. For each received response, update U and paths.

5. After the expiration of the time, send response message piggybacked with the set U and the path Pi to the node thatoriginates the CovReqðsÞ message.

4.2.2. Identification phaseIn the Identification Phase, each SN x broadcasts an update packet with information about its remaining energy to its cov-

erage neighbors. In order to reduce packet collisions, the SNs use random back-offs before sending the update packets.Throughout the entire execution of the algorithm, each SN executes the following steps: (Algorithm 1).

Step 1: Upon receiving the update information from all neighbors, in order to decide to be a sensing node or not, each SN xcalculates CmwðxÞ using Definition 7 and decides to be sensing node if its coverage neighbors are not sufficient to cover itssensing area i.e., CmwðxÞ ¼ 1

EðxÞ (Algorithm 1 Lines 2–6).Note that the located SNs near the boundary of QR may have no choices other than to be sensing nodes since they are theonly SNs that able to monitor the boundary of QR, so this will cause redundant SNs on the boundary of QR. To overcomethis problem, a solution would consist in not considering the portions of disks outside the area on which SNs are deployed[9], i.e., SNs find the intersection of their sensing area with QR, and consider it as their revised sensing area.Step 2: SN x assigns back-off timer that is proportional to its CmwðxÞ value then wait for back-off timer expiration beforedeciding whether it will be sensing node or not (Algorithm 1 Lines 7–8).Step 3: While waiting for its back-off timer to be expired, SN x may receive an announcement message from its coverageneighbors that have smaller back-off timer, SN x recalculates its CmwðxÞ based on its coverage neighbors that declarethemselves as sensing nodes and decides to be a non-sensing node (i.e., not included in cover set M) if it has CmwðxÞ valueless than the invert value of its residual energy (Lemma 1) (Algorithm 1 Lines 9–15).Step 4: After the expiration of its back-off timer, if the sensing area of x is not completely covered by its coverage neigh-bors, it declares itself as sensing node otherwise, x decides to be non-sensing node (Algorithm 1 Lines 17–25).

Algorithm 1. IsSensingNode? Each SN x executes this algorithm in order to decide to be a sensing node or not

1: Output: True if it is a sensing node; False otherwise.{EðxÞ > 0 : EðxÞ is the residual energy of x}{A set of minimum connected sensors M. Initially M ¼ fg} {the sensing area of x intersects with QR}

2: Calculate CmwðxÞ using CNðxÞ3: if CmwðxÞ ¼ 1

EðxÞ then

4: {x declares itself as a sensing node, M ¼ MS

x}5: Return True6: end if7: Set back-off time T proportional to CmwðxÞ8: while T is not expired do9: {x may receive declaration messages from its neighbors and in this case x reset its timer T if it is located inside the

sensing area of the declaration message sender}10: CSN ¼ CNðxÞ

TM, {CSN maintains sensing node coverage neighbors}

11: Calculate CmwðsiÞ12: if CmwðxÞ < 1

EðxÞ then

13: {x declares itself as non-sensing node}14: Return False15: end if16: end while

T expired:17: CSN ¼ CNðxÞ

TM, {CSN maintain sensing node coverage neighbors}.

18: Calculate CmwðxÞ19: if CmwðxÞ ¼ 1

EðxÞ then

20: {x declares itself as a sensing node, M ¼ MS

x}21: Return True22: else23: {x declares itself as non-sensing node}24: Return False25: end if

160 A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163

5. Simulation results

The program has been simulated in ns-2, with statistical data gathered to analyze performance runtime and scalability ofour proposed algorithm. The SNs are assumed to be randomly deployed on a two dimensional plane of size 100 m � 100 m.We compare the simulation results of our algorithm with the distributed greedy algorithm by Gupta et al. [16], the minimumsensor cover (MSC) algorithm by Jiang et al. [18], and TTS algorithm by Tezcan and Georganas [39]. We use the followingperformance metrics to investigate the performance of our approach:

� The number of sensing nodes: The number of selected sensing nodes to sense the monitored region.� The communication overhead: The communication overhead is measured by the total number of exchanged messages.� The energy dissipation: The energy dissipation is measured by the total amount of energy dissipation to find the min-

imum connected sensor cover of a query region.

In order to measure the energy dissipation of SNs, we use the same energy parameters and radio model as discussed in[17], wherein energy consumption is mainly divided into two parts: receiving and transmitting messages. The transmissionenergy consumption needs additional energy to amplify the signal depending on the distance to the destination. Thus, totransmit a k-bit message a distance d, the radio power consumption will be,

Fig. 2.interpr

ETxðk; dÞ ¼kEelec þ k�fsd

2 d < ðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�fs=�mp

pÞ

kEelec þ k�mpd4 d P ðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�fs=�mp

pÞ

(ð6Þ

and to receive this message, the radio expends will be

ERxðkÞ ¼ k � Eelec ð7Þ

Simulated model parameters are set as: Eelec ¼ 50nJ=bit; �fs ¼ 10pJ=bit=m2; �mp ¼ 1310000 pJ=bit=m4.

We evaluate the performance of our algorithm by simulating networks of varying density and topology. We vary thenumber of deployed SNs from 200 to 600 SNs in the increments of 100 SNs to represent sparse to significantly dense net-work. Each SN chooses its communication range as well as its sensing range from 30 m to 60 m. Since the proposed algo-rithm and the algorithms in [16,18,39] take the same overhead for a query request sent from the sink to the queryregion, we treat the whole WSN as a query region and evaluate the performance of the query execution over the WSN.

Fig. 2a and b illustrate an example of a generated WSN of sizes 200. The figures show the network before and after querycover selection.

Fig. 3 shows that the communication overhead of our proposed algorithm is less than the communication overhead of thedistributed greedy, MSC, and TTS algorithms. Also, it shows that the communication overhead of the distributed greedymethod dramatically increases as the number of SNs increases this is because in distributed greedy algorithm, the candidateSN will be selected in each round by searching all the paths through local flooding. Among the newly searched paths and thepaths already added before, the candidate SN selects the most beneficial path and makes the SNs in that path as sensingnodes. Then, the candidate SN has to uni-cast a packet to notify the tail SN in the path to become a new selected candidateSN which executes similar operation. This operation will be repeated until the query region is fully covered by the selectedsensing nodes. Though the already added sensing nodes need not broadcast in the succeeding local flooding, the unselectedSNs to be sensing nodes still need to broadcast in the local flooding originated from different candidate SN. Hence, the total

(a) Example of a generated WSN of size 200 SNs, (b) the WSN after selecting the SNs in the query cover (marked as red with white sensing area). (Foretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Communication overhead in our proposed, MSC, TTS and distributed greedy algorithms for different network sizes.

Fig. 4. Total energy dissipation in our proposed, MSC, TTS and distributed greedy algorithms for different network sizes.

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communication overhead and so the energy dissipation (see Fig. 4) of each local flooding and the notification for new can-didate SN increases substantially when the number of SNs increases. In case of MSC algorithm, the communication overheadincreases as the number of SNs increases, this is because in MSC algorithm, every SN needs to establish a communicationpath to the sink and maintain that path, determine if it is sensing node or not based on triangular lattice, and also backbonecommunication network need to be maintained. This will increase the communication overhead and so the energy dissipa-tion (see Fig. 4) as the network size increases. TTS runs in a manner, i.e., the sink collects the coordinates of all SNs in thenetwork which consumes more communication overhead and so more energy (see Fig. 4). while in our proposed algorithm,the communication overhead and so the energy slightly increases as the number of SNs increases this is because the com-munication overhead of initialization protocol is executed only in the network deployment or re-deployment stages and theminimum-weight coverage cost of each SN is a main factor to determine whether a SN becomes a sensing node or not. Also,the difference between our proposed algorithm and the three algorithms grows with the increasing of the network size.

Fig. 4 presents the network energy dissipation of our proposed, distributed greedy, MSC, and TTS algorithms for differentnetwork sizes. It shows that the energy dissipation in our proposed algorithm is less than the energy dissipation of distrib-uted greedy, MSC, and TTS algorithms and the difference between the energy dissipation of our proposed algorithm and thethree algorithms grows with the increasing of the network size.

Fig. 5 shows the number of selected sensing nodes in our proposed, distributed greedy, MSC, and TTS algorithms. It showsthat our proposed algorithm requires fewer number of sensing nodes than the three algorithms. The simulation result of ourproposed algorithm shows that the number of sensing nodes slightly increases as the SNs in the WSN is dramatically increas-ing specially in distributed greedy algorithms. Also, the results show that the three algorithms reduce a large number ofredundancy sensing nodes. In distributed greedy algorithm, the candidate SN will be selected in each round as the SN thathas intersection with the previous selected nodes and then searching all the paths through local flooding. Among the newlysearched paths and the paths already added before, the candidate SN selects the most beneficial path and makes the SNs in

Fig. 5. The number of sensing nodes as a function of WSN size in our proposed, MSC, TTS and distributed greedy algorithms, for different network sizes.

162 A.M. Khedr, W. Osamy / Information Sciences 223 (2013) 153–163

that path as sensing nodes. In MSC algorithm, first it initializes two fixed SNs with distance l between them (where l < rs; rs isthe sensing range) and the desired location of the third SN should keep

ffiffiffi3p

rs from the two given SNs. By considering therandom distribution of the SNs, it is not guaranteed that there always exists a SN located at the desired location [46]. InTTS algorithm, first it decides the essential nodes which belong to the coverage nodes C and then create the connected dom-inating set D as a connected set of essential nodes (D # C), where each essential node in C � D can directly communicate withone of the sensors in D. In our proposed algorithm, the selection of sensing node is based on the coverage neighbors’ infor-mation of each SN which is collected as they are deployed.

In general, according to the simulation results of Figs. 3–5 our proposed algorithm scales very well and fits large scalenetworks and can achieve remarkable communication overhead and energy saving and keep only minimum number of ac-tive SNs.

6. Conclusion

In this paper, we have proposed an efficient two-phases algorithm for selecting the minimum number of SNs to cover thequeried region in a heterogeneous WSN. In the identification phase, each SN determines whether to be a sensing node tocover the queried region or not while in the initial phase, each SN discovers which of its neighbors are the coverage neigh-bors and then makes a connection with them. Each sensing node can communicate with the recognized coverage nodesthrough the relay SNs if they cannot communicate directly with each other. SNs in the proposed algorithm are efficientlydivided into two groups, according to their roles sensing nodes and relay SNs. The minimum-weight coverage cost is usedas metric by which SN determine wether to be sensing node or not. The simulation results demonstrate that the proposedalgorithm has fewer sensing nodes than the distributed greedy, MSC, and TTS algorithms. The four algorithms can effectivelyreduce the number of redundant SNs. Furthermore, the simulation results show that for various network size, the proposedalgorithm has a lower communication overhead than the distributed greedy, MSC, TTS algorithms.

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