Localized movement assisted sensor deployment algorithm for hole detection and healing

Localized Movement-Assisted SensorDeployment Algorithm for Hole

Detection and HealingMustapha Reda Senouci, Abdelhamid Mellouk, Senior Member, IEEE, and Khalid Assnoune

Abstract—One of the fundamental services provided by a wireless sensor network (WSN) is the monitoring of a specified region of

interest (RoI). Considering the fact that emergence of holes in the RoI is unavoidable due to the inner nature of WSNs, random

deployment, environmental factors, and external attacks, assuring that the RoI is completely and continuously covered is very

important. This paper seeks to address the problem of hole detection and healing in mobile WSNs. We discuss the main drawbacks of

existing solutions and we identify four key elements that are critical for ensuring effective coverage in mobile WSNs: 1) determining the

boundary of the RoI, 2) detecting coverage holes and estimating their characteristics, 3) determining the best target locations to

relocate mobile nodes to repair holes, and 4) dispatching mobile nodes to the target locations while minimizing the moving and

messaging cost. We propose a lightweight and comprehensive solution, called holes detection and healing (HEAL), that addresses all

of the aforementioned aspects. The computation complexity of HEAL is Oðv2Þ, where v is the average number of 1-hop neighbors.

HEAL is a distributed and localized algorithm that operates in two distinct phases. The first identifies the boundary nodes and discovers

holes using a lightweight localized protocol over the Gabriel graph of the network. The second treats the hole healing, with novel

concept, hole healing area. We propose a distributed virtual forces-based local healing approach where only the nodes located at an

appropriate distance from the hole will be involved in the healing process. Through extensive simulations we show that HEAL deals

with holes of various forms and sizes, and provides a cost-effective and an accurate solution for hole detection and healing.

Index Terms—Hole detection, coverage, deployment, hole healing, mobile WSN, movement-assisted algorithms

Ç

1 INTRODUCTION

A wireless sensor network (WSN) comprises small sen-sors with limited computational and communication

power. By design, sensors are quite fragile and vulnerableto various forms of failure, such as sudden shock caused bytheir deployment (air dropping) or depletion of their lim-ited energy resources. This intrinsic fragility must beregarded as a normal property of the network.

Several anomalies can occur in WSNs that impair theirdesired functionalities resulting in the formation of dif-ferent kinds of holes, namely: coverage holes, routingholes, jamming holes, and worm holes [1]. In this workwe are interested in large bounded holes, i.e., large holesthat are circumscribed by sensor nodes. In this case, cov-erage holes, i.e., areas not covered by any node, andcommunication holes, i.e., areas devoid of any nodes,become equivalent and will be referred to as holes in theremainder of this paper.

One of the fundamental services provided by a WSN isthe monitoring of a specified region of interest (RoI), wherethe main duty is sensing the environment and communicat-ing the information to the sink. Assuring that the RoI iscompletely covered at all time is very important [2]. How-ever, the emergence of holes in the RoI is unavoidable dueto the inner nature of WSNs, random deployment, environ-mental factors, and external attacks. Thus, an event occur-ring within these holes is neither detected nor reported and,therefore, the main task of the network will not be com-pleted. Thus, it is primordial to provide a self-organizingmechanism to detect and recover holes.

This paper seeks to address the problem of hole detectionand healing. Most of the existing solutions use global opera-tions to calculate the size of a big hole and then relocate agroup of mobile sensors to heal the hole. While some exist-ing localized solutions requires strong assumptions or evenunrealistic ones. The incompleteness of previous worksmotivates our research presented here.

We propose a comprehensive solution, called holesdetection and healing (HEAL) that has a very low complex-ity and avoid some drawbacks noticed in previous works.HEAL is a distributed and localized algorithm that operatesin two distinct phases. The first phase consists of three sub-tasks; hole identification, hole discovery (HD) and borderdetection. Unlike prior efforts, we propose a distributedand localized hole detection algorithm (DHD) that operatesover the Gabriel graph (GG) of the network. DHD has avery low complexity and deals with holes of various formsand sizes despite the nodes distribution and density.

� M.R. Senouci is with the A.I. Laboratory, Ecole Militaire Polytechnique,Algiers, Algeria, and with the LiSSi Laboratory, University of Paris-EstCreteil (UPEC), France. E-mail: [email protected].

� A. Mellouk is with the LiSSi Laboratory, University of Paris-Est Creteil(UPEC), France. E-mail: [email protected].

� K. Assnoune is with the A.I. Laboratory, Ecole Militaire Polytechnique,Algiers, Algeria. E-mail: [email protected].

Manuscript received 11 June 2012; revised 19 Nov. 2012; accepted 19 Apr.2013; date of publication 22 May 2013; date of current version 21 Mar. 2014.Recommended for acceptance by D. Wang.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TPDS.2013.137

IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 25, NO. 5, MAY 2014 1267

1045-9219 � 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

The second phase treats the hole healing with novel con-cept, hole healing area (HHA). It consists of two sub-tasks;hole healing area determination and node relocation. Wepropose a distributed virtual forces-based local healingapproach based on the hole healing area, in which the forceswill be effective. This allows a local healing where only thenodes located at an appropriate distance from the hole willbe involved in the healing process.

The main contribution of this work is the design andevaluation of HEAL, a distributed, localized and compre-hensive two-phase protocol, that can effectively estimateand enhance the area coverage in a mobile WSN. Thispaper makes the following specific contributions. First, acollaborative mechanism, called distributed hole detec-tion (DHD), is proposed to identify the boundary nodesand discover holes. We have conducted extensive simu-lations to validate DHD. Second, we present a virtualforces-based hole healing algorithm. Unlike existingalgorithms, our algorithm relocates only the adequatenodes within the shortest times with the lowest cost.Experimental results show that HEAL provides a cost-effective and an accurate solution for hole detection andhealing in mobile WSNs.

The remainder of the paper is organized as follows. Sec-tion 2 looks at the related work. Section 3 defines the prob-lem statement while Section 4 details our proposedmechanisms. Section 5 presents our experiments. Section 6concludes the paper and discusses some future directions.

2 RELATED WORK

2.1 Hole and Border Detection

There has been much related research on the hole andborder detection problem [3], [4], [5], [6], [7], [8], [9],[10], [11], [12], [13]. Authors in [3] studied the problemof detecting topological holes in WSN with no localiza-tion information. They presented a distributed schemethat is based on the communication topology graph. Anode decides whether it is on the boundary of a holeby comparing its degree with the average degree of its2-hop neighbors. Not all boundary nodes can be identi-fied correctly by this algorithm. Indeed, for a large WSNwith few holes this method is not efficient [3].

An algebraic topological method using homology the-ory detects single overlay coverage holes without coordi-nates [4], [5]. Ghrist and Muhammad [4] employed acentral control algorithm that requires connectivity infor-mation for all nodes in the RoI. For N nodes, the timecomplexity is OðN5Þ. For [5], it is OðHD2Þ, where D is themaximum number of other active nodes that overlap anode’s sensing area, and H is the worst-case number ofredundant nodes in a large hole, with H � D. In [5], thecomplexity does not depend on the overall size of thenetwork, whereas the homology algorithm encounterssevere difficulties with dense networks. Additionally, themessage forwarding overhead can be impractically large,since the algorithm is centralized.

Funke in [6] presented a heuristic for detecting holesbased on the topology of the communication graph. Theheuristic computation is not localized as it requires thecomputation of distance fields over the whole network.

In a more recent paper [7], Funke and Klein described alinear-time algorithm for hole detection. They requirethat the communication graph follows the unit diskgraph model. Compared to the heuristic approach pre-sented in [6], the algorithm does slightly worse. Further-more, when decreasing the node density, the algorithmbreaks down more and more.

Fekete et al. [8] presented a coordinate-free method toidentify boundaries in WSNs. They assume a uniformnode distribution in non-hole areas. In a more recentpaper [9], the same authors presented a deterministicapproach for boundary recognition that does not rely ona uniform node distribution but requires a high nodedensity. Wang et al. [10] described a distributed algo-rithm to find the boundary nodes by using only connec-tivity information. They exploit a special structure of theshortest path tree to detect the existence of holes. Theauthors did not provide a complexity analysis but theproposed algorithm relies heavily on a repetitive net-work flooding.

Fang et al. [11] proposed the BoundHole algorithm usingthe right-hand rule to identify nodes on the boundary ofgeometric holes. Kr€oller et al. [12] proposed an overallframework for self-organization based on topological con-siderations and geometric packing arguments to determinethe boundary nodes and the topology of the whole network.Although, authors make few assumptions, they deal withrelatively complex combinatorial structures, such as flow-ers. Shirsat and Bhargava [13] presented a hole boundarydetection algorithm assuming the relative geographic infor-mation of 2-hop neighbors. The proposed algorithm takes alocal best-effort approach and requires synchronizationamong nodes.

Table 1 summarizes the main drawbacks of hole and bor-der detection algorithms found in the literature.

The incompleteness of previous work motivates ourresearch presented here. Our proposed hole and borderdetection algorithm is distributed and lightweight, and thusmore suited to the energy constrained WSNs. It does notrequire flooding for gathering the topology information, asis the case in [10] or synchronization among nodes as in

TABLE 1Comparison of Proposed Solutions to the Hole

and Border Detection Problem

1268 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 25, NO. 5, MAY 2014

[13]. In addition, we do not assume a particular nodes distri-bution as done in [8].

2.2 Coverage Enhancement and Hole Healing

Mobile sensor nodes (for example, Robomote [14] andiMouse [15]) are equipped with mobile platforms and canmove around after initial deployment. In a mobile WSN,one of the objectives of the movement is to maximize areacoverage. Several movement strategies for improving net-work coverage exist in the literature. Algorithms that belongto this category include [2], [7], [16], [17], [18], [19], [20], [21],[22], [23], [24], [25], [26], [27], [28], [29], to name a few. Incoverage pattern-based movement [16], [17], the target loca-tions for mobile nodes are computed based on a predefinedcoverage pattern, while mobile nodes are likened as electro-magnetic particles in virtual forces-based movement [16],[17], [18], [19]. In grid-quorum based movement, the mobil-ity-assisted network redeployment problem is viewed as aload-balancing problem in traditional parallel processingsystems [16], [17], [20]. The RoI is partitioned into manysmall grid cells, and the number of nodes in each cell is con-sidered as the load of the cell [20]. In [21], authors considerthe point coverage problem with novel evaluation metric,coverage radius.

Wang et al. [22] proposed three different deploymentprotocols that relocate mobile sensors once coverageholes are detected using Voronoi diagrams. In [23], theauthors proposed a scheme called Co-Fi that relocatesmobile nodes to replace low energy nodes. Authors in[24] developed three hole-movement strategies for mov-ing an existing big hole in a way that either the totalenergy consumption is minimized or the power con-sumption of sensors is balanced.

In a hybrid network consisting of both stationary andmobile sensor nodes, one objective for using mobile sen-sor nodes is to minimize coverage holes created by thosestationary nodes [25], [26], [27], [28]. Authors in [25]solve the coverage problem by using a moving robot.They describe a tracking mechanism and a robot repair-ing algorithm. The tracking mechanism leaves the robot’sfootmark on sensors so that they can learn better routesfor sending repairing requests to the robot while therepairing algorithm constructs an efficient path thatpasses through all failure regions. Li et al. [29] propose afamily of localized robot-assisted sensor relocation algo-rithms, by which mobile robots pickup passive sensorsand deliver them to encountered sensing holes. Nadeemet al. [27] proposed MAPC, a mobility-assisted probabi-listic coverage for enhancing and maintaining the areacoverage by moving mobile sensor nodes to strategicpositions in the uncovered area.

Table 2 summarizes the main drawbacks of proposedsolutions to coverage enhancement and hole healing prob-lem. The incompleteness of previous work motivates ourresearch presented here. In this work we propose HEAL, alocalized and distributed hole healing algorithm as opposedto the centralized approach employed in [19]. The Co-Fiprotocol [23] fails if the coverage loss is due to physicaldamage of the nodes. Our work addresses the problem ofcoverage loss due to both energy depletion and physicaldamage of the nodes. In addition, we do not assume that

the WSN boundary is known a priori as done in [29]. InHEAL the hole detection and healing process can be trig-gered by any node in the network or even by several nodesas opposed to MAPC [27], where the sink is used for start-ing the hole detection and healing process.

HEAL is based on a localized healing process that: 1)minimizes the WSNs’ resources consumption; 2) acceleratesthe healing process; and 3) preserves as much as possiblethe initial WSN topology. The number of nodes solicited inthe healing process depends on the holes’ characteristics. Inaddition, only the nodes located at an appropriate distancefrom the hole will be involved in the healing process.

3 PROBLEM STATEMENT

The basic scenario can be described as follows: during nor-mal operation of the network, a great loss of nodes occurs,due to an external attack for example, causing the creationof one or several large holes within the network making itineffective. Our problem is to design a mechanism fordetecting and recovering holes by exploiting only the nodesmobility. It should be noted that only the holes within thenetwork are considered. The holes on the border that arethe result of the initial deployment are not addressed.

Most hole healing algorithms require coordinate infor-mation about the sensor nodes in the RoI and use computa-tional geometry with tools, such as Voronoi diagrams todetect holes [2], [16], [17], [22], [26], [28]. With these algo-rithms, each node, independently of other nodes in the RoI,tries to detect and repair holes in its Voronoi polygon.

Fig. 1 illustrates the principle of hole detection andhealing of a well-known approach proposed by Wanget al. [22]. A node needs only to check its own Voronoipolygon. If it detects the existence of a hole, it will movetoward its farthest Voronoi vertex and stops when thisvertex can be covered.

TABLE 2Comparison of Proposed Solutions to the Coverage

Enhancement and Hole Healing Problem

SENOUCI ET AL.: LOCALIZED MOVEMENT-ASSISTED SENSOR DEPLOYMENT ALGORITHM FOR HOLE DETECTION AND HEALING 1269

This way of doing is not suitable for large holes becauseeach node, in the hole’s boundary, moves without takinginto account the movement of other nodes, which, gener-ally, will not help to recover the hole. In the example ofFig. 1, the nodes S1 and S6 move in the direction that coverstheir holes, which does not contribute in the healing of thehole bounded by the six vertices.

Before discussing our proposal, we make the followingassumptions:

1. A dense mobile WSN is deployed in an obstacle-freeRoI;

2. The deployment can be either deterministic orrandom;

3. All deployed nodes are homogeneous;4. Location information is available to each sensor node

by using some GPS-less sensor network localizationscheme [30];

5. We consider the isotropic sensing model [2]. Wedenote by Rs, the sensing range and Rc, the commu-nication range. We assume that Rc � 2Rs to ensurethat the TENT rule [11] is applicable.

4 PROPOSED MECHANISMS

In our algorithm we propose collaborative mechanisms todetect and heal holes. Our hole detection mechanism dealswith holes of various forms and sizes. We try to alert a lim-ited number of nodes surrounding the hole, only thosenodes have the task of moving and repairing the hole.

As suggested by Wang [2], when designing a hole heal-ing algorithm, the following issues need to be addressed:1) How to detect a hole and how to estimate its size?2) Where are the best target locations to relocate mobilenodes to repair coverage holes? 3) How to dispatch mobilenodes to the target locations while minimizing the movingand messaging cost? In this section, we address all of theaforementioned issues.

Our DHD algorithm allows us to discover holes, to com-pute their characteristics and to discover the network

boundary. In a second phase, HEAL performs a local heal-ing where only the nodes located at an appropriate distancefrom the hole will be involved in the healing process. Wedefine an attractive force that acts from the hole center andattracts the nodes towards the hole center. At the sametime, a repulsive force is defined among nodes to minimizethe overlapping among them. These forces will be effectivein a limited area, which we call the HHA. The proposedalgorithms consist of hole detection and hole healing steps.We first discuss how to detect and heal a single hole andthen we show how to deal with several holes.

4.1 Hole Detection

Fang et al. [11] defined the stuck nodes where packetscan possibly get stuck in greedy multi-hop forwarding.A node p 2 S is a stuck node if there exists a location qoutside p‘s transmission range in, IR2 so that none of the1-hop neighbors of p is closer to q than p itself. Fang etal. [11] developed a local rule, the TENT rule, for eachnode in the network to test if it is a stuck node. TheTENT rule specifies that a node is not a stuck nodewhen there is no angle spanned by a pair of its angularlyadjacent neighbors greater than 2p=3. We adapt this tech-nique to conceive our distributed hole detection algo-rithm and integrated it in HEAL. To identify holes in thenetwork, we proceed in three steps.

4.1.1 Hole Identification

First, we have to assess the existence of a hole, which isdone by identifying stuck nodes. Each node p in the net-work executes the TENT rule to check if it is a stuck node asfollow. First, it orders all its 1-hop neighbors counterclock-wise. Let u and v be a pair of angularly adjacent nodes. Sec-ond, it draws the perpendicular bisector of up and vp; l1; l2.l1 and l2 intersect at point o and divide the plane into fourquadrants (see Fig. 2).

Only the points in the quadrant containing p are closer top than u and v. Finally, if o is outside the communicationrange of p, the angle dvpu is a stuck angle and p considersitself stuck node.

Fig. 2. p is a strongly stuck node [11].

Fig. 1. Ineffectiveness of VOR in treatment of large holes.


4.1.2 Hole Discovery

All the nodes that are marked as stuck nodes by the TENTrule trigger the discovery of holes. The aim of this step is tofind the boundary of the hole and the computation of theholes’ characteristics (center and radius).

A stuck node bi creates a new hole-discovery packet,marked with its ID (the hole will take the same ID as that ofthe node bi), whose mission is to collect location informationof hole boundary nodes, and forwards it to the next bound-ary node biþ1 by right-hand rule over the GG of the network.Node biþ1 inserts its location information into the receivedHD packet and forwards it to the node biþ2 by right-handrule over the GG and so on. This process is repeated untilthe HD packet has traveled around the hole and eventuallybeen received by the initiator node bi.

Node bi extracts from the received HD packet the loca-tions of the boundary nodes fb0; b1; . . . ; bNg. It selects twonodes bn and bm so that the distance between them is thelongest between any two nodes in the set of boundary nodes

Distanceðbm; bnÞ ¼MaxfDistanceðbj; bkÞ=bj; bk2 fb0; b1; . . . ; bNgg:

Then, it calculates the hole center, which is the mid-point vof segment bmbn

xv ¼ ðxbm þ xbnÞ=2yv ¼ ðybm þ ybnÞ=2:

�

We note that each stuck node sends a HD packet with-out any coordination among stuck nodes. Thus, therewill be redundancy in the discovery process. This willgenerate unnecessary traffic and more packet collisions;the situation may become worse especially for largeholes. To avoid this problem, we use a mechanism toprevent redundancy in the discovery process. The basicidea is to remove redundant HD packets as soon as pos-sible. The criterion for judging whether a HD packet isredundant is as follows: at each node, if a HD packetarrives and discovers that the packet has a Hole-IDgreater than a Hole-ID carried by a packet alreadypassed, the packet will be considered redundant and itwill be deleted.

At the end of this step the node that has the smallestHole-ID removes the HD packet and names itself as ‘HoleManager (HM)’: it will be responsible for the hole-healingannouncement. In another hole manager selection strategy,one can pick the node with the largest residual energyamong all the boundary nodes.

4.1.3 Border Detection

The network boundary nodes (nodes on the limits of theRoI) execute the TENT rule and, as a result, they detect thatthey are stuck nodes, which will launch the hole discoveryand the healing processes even if these nodes are actuallynot stuck nodes (they are the borders of the network). Thatis why we need to carry out the network boundary-nodeidentification to avoid that the hole discovery process belaunched by those nodes.

To discover the network boundary in a distributed way,we follow the following steps:

1. Each node of the network executes the TENT rule;2. Each stuck node launches DHD to identify the nodes

that surround the hole;3. In the HD packet, we define four Boolean variables

to identify the network boundary Xmax; Ymax;Xmin; Ymin. Each stuck node, which receives a HDpacket, compares the coordinates Xmax; Ymax;Xmin; Ymin defined in the packet with its coordinates,and if it finds that it has a higher or a lower valuethan one of these values compared to all its neigh-bors, it sets the corresponding Boolean variable to 1;

4. At the end of this procedure, the largest hole thatdefines the network boundary will be defined by thecoordinates Xmax; Ymax;Xmin; Ymin;

5. We cancel the healing process that will be launchedby the HM node.

The above hole detection steps can be summarized as thepseudo-code depicted in Appendix A, which can be foundon the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TPDS.2013.137.

4.2 Hole Healing

At the end of the hole detection phase the healing phaseis executed. We exploit here nodes locomotion facilitiesto heal detected holes. Our relocation algorithm iscompletely distributed and it is based on the concept ofvirtual forces. To heal the discovered hole we define anattractive force that acts from the hole center and attractsthe nodes towards this center. Similarly, a repulsiveforce is defined among nodes to minimize the overlap-ping in between. We define the HHA in which the forceswill be effective. This allows a local healing where onlythe nodes located at an appropriate distance from thehole will be involved in the healing process.

In this phase, the HM node plays the role of determiningthe HHA and informing nodes on their movement. The HMnode has information about the size of the hole and bound-ary nodes. Details of the healing process are presented inthe following paragraphs.

4.2.1 HHA Determination

The HHA constitutes the basic idea of our algorithm; thedetermination of this area will determine the number ofnodes that must be relocated to ensure a local repair ofthe hole. After the identification of the hole by the DHDalgorithm, the HM node calculates the center and thesize of the hole. As mentioned before, we approximatethe hole by a circle whose radius is the longest distancebetween two hole boundary nodes. Therefore, to deter-mine the HHA, we need to determine the radius of thecircle that defines the HHA.

To find the appropriate radius, we have used an iterativeapproach based on the following formula:

R ¼ r � 1þ bð Þ; b 2 Rþ

where r is the hole radius. b is a positive constant, whichdepends on the nodes density and the sensing range Rs.

For b ¼ 0, we start with a radius equals to the estimatedhole radius r due to the fact that this area may contain a suf-ficient nodes to heal the hole. The area defined by this circle


(denoted HHA-0) is equal to pr2. The number of nodes nec-essary to cover the area HHA-0 is equal to

pr2

pR2s

¼ r2

R2s

:

The HM node calculates the number of nodes present inthe HHA-0. It solicits its direct neighbors to calculate thenumber of their neighbors in this area. It sends a hole heal-ing area Determination packet containing information aboutthe hole. This communication is done over the GG to reducethe number of exchanged messages. If the number of nodesfound by the HM node is less than the required number toheal the hole, the movement of these nodes will create newholes. To avoid this scenario the HM node starts a newround by increasing b, then it repeats this process until itfinds a sufficient number of nodes to recover the hole. Theabove HHA determination step can be summarized asthe pseudo-code depicted in Appendix A, available in theonline supplemental material. Under the assumption of uni-form deployment, in Appendix B, available in the onlinesupplemental material, we devise a relationship betweenthe required number of nodes for a full hole healing and theradius of the HHA.

After determining the HHA, the HM node sends to theconcerned nodes a movement packet containing informa-tion about the hole to heal. The nodes that receive thispacket will enter in the relocation phase presented in thenext section.

4.2.2 Node Relocation

After determining the HHA, the HM informs the nodesinvolved in the healing process. Nodes that receive forcesfrom the hole center, move towards it. We try to balance thetradeoffs between attractive and repulsive forces to recoverthe hole without side effects (see Fig. 3). We describe in thenext sections the concept of virtual forces used within ourHEAL algorithm.

Attractive Force. The hole center v applies an attractiveforce on every node within the HHA and located at a dis-tance greater than dath from v. A node p within the HHAreceives an attractive force ~Fa p; vð Þ form v given by:

~Fa p; vð Þ ¼�ka

d p; vð Þla� e

rdðp;vÞ ua

�!; d p; vð Þ > dath

0; d p; vð Þ � dath

8

<

:

ð1Þ

where ua�! is the unit vector oriented from the point p to the

hole center v; dðp; vÞ is the euclidean distance between thenode p and the hole center located at v x; yð Þ. la is a distancecoefficient, ka is a coefficient that defines the intensity of theattractive force and r is the hole radius.

The exponential factor enables us to control the move-ment of nodes in the HHA, so that the nodes closest tothe hole center will move longer distance than those on theboundary to prevent the creation of new holes during thehealing process. The formulation of the exponential factor isa heuristic that we have proposed and that is based on thelogic of the nodes’ movement, where the distance isinversely proportional to the force.

Repulsive Force. To minimize overlapped coverage, arepulsive force exists among nodes within the range0 < Fr

�!< drth here Fr

�!denotes repulsive force. If the dis-

tance between two nodes p and q is less than drth; thenFr�!ðp; qÞ will separate those nodes to minimize the over-lapped coverage. Fr

�!ðp; qÞ increases as the distance d p; qð Þecreases and is given by:

~Frðp; qÞ ¼kr

dðp; qÞlrur!; 0 < dðp; qÞ < drth

0; dðp; qÞ � drth

8

<

:

ð2Þ

where ur! is the unit vector oriented from node q to p; kr is a

factor that defines the intensity of the repulsive force and lris a distance coefficient such as lr > la.

Movement Equation. The final position of a node p is dic-tated by the resultant force of the composition of all repul-sive forces that sustained the node from its neighbors set(denoted by NS) and the attractive force applied by the holecenter. This force is ~Fp.

~Fp ¼X

q2NS;p#q

~Fr p; qð Þ þ ~Faðp; vÞ:

Note that the magnitude and orientation of ~Fp can be eas-ily calculated, for example, Robomote [14] uses an on-boardcompass combined with localization information for navi-gation purposes. If ~Fp ¼ 0 then the node p remains in itsoriginal position. Otherwise, p moves one time step in thedirection imposed by ~Fp. The final position of p is given by:

~Pp tþDtð Þ ¼~Fp

jj~Fpjj� V þ ~Pp tð Þ (3)

where V is the node velocity and ~PpðtÞ is its position atinstant t.

The above relocation phase can be summarized as thepseudo-code depicted in Appendix A, available in theonline supplemental material. It should be noted that orien-tation and distance measurement errors could affect thehole-detection/hole-healing process and therefore the heal-ing is not complete. A simple approach to overcome thisproblem consists in checking the existence of a hole uponthe termination of the healing process. If a hole is detected,

Fig. 3. Principle of the healing process.


the hole-detection/hole-healing process may be triggered asecond time (we have to trade-off between healing accuracyand energy consumption).

4.3 Treatment of Holes

The case of a single hole in the network is the simplest case.In many applications where several holes appear in the net-work at the same time, the proposed protocol must be read-apted so it becomes able to heal the discovered holes asmuch as possible. This re-adaptation is as follows.

4.3.1 Hole Detection

Each stuck node is associated with only one hole in eachdirection it is stuck in. As the TENT rule detects all thedirections where the nodes are stuck [11], the DHD algo-rithm will still work with the presence of many holes. How-ever, a stuck node bi can be on the boundaries of multipleholes. In this case, bi initiates a HD packet in each directionit is stuck in (at most three). The second or the third HDpacket could be considered as redundant and thusremoved. To avoid this behavior, redundant HD packetsdetection is based on the direction of the HD packet in addi-tion to the Hole-ID. At each hop, the direction of a HDpacket is defined by the previous node that forwards thispacket. This allows the detection of multiple adjacent holes.

4.3.2 Node Relocation

For multiple holes, we use the same healing process toheal the discovered holes. However, several HHA mayoverlap; therefore, a node in the overlapping area willbe solicited by more than one HM. In this case, we mustanswer the following question: how a node solicited byseveral HM should move?

We adopted two strategies:

1. Strategy 1: distance-based. The purpose of this strat-egy is to minimize the distance traveled by nodesin the healing process to preserve nodes’ energy.A node considers only the first movement packetthat it receives.

2. Strategy 2: hole-based. In this strategy, when a nodereceives a movement packet, it waits for a certainperiod of time. After that it compares the receivedmovement packets and moves towards the biggesthole. The purpose of this strategy is to prioritize thehealing of the large holes based on the assumptionthat a large hole constitutes a much serious threat incomparison to a small one. In addition, unlike large

holes, small holes can be covered by running a sim-ple algorithm likes DSSA [18].

A complete HEAL complexity analysis is reported inAppendix C, available in the online supplemental material.

5 EXPERIMENTS

For validation, we have implemented HEAL in the ns2 sim-ulator [31]. We have carried out a two-stage simulation. Thefirst scenario points out the effectiveness of HEAL in termsof hole detection and healing. This is done by varying thesize, the shape and the number of holes created within theRoI. We also compare our approach with that of Wang et al.[10], in terms of bounded holes discovery, while varying thenode density. In the second scenario, we compare HEAL toDSSA [18] and SMART [20] using a random deploymentstrategy. That is to say that the protocols will operatedirectly on the holes resulting from the initial deployment.

5.1 Scenario 1: Validation of HEAL

This scenario contains two sub-scenarios. In the first one, wevary the radius of the hole created within the RoI. We use adeterministic deployment strategy with holes of differentradii. The purpose of this sub-scenario is the evaluation ofHEAL in terms of hole detection and healing. In the secondsub-scenario, we analyze the behavior of HEAL in the pres-ence of several holes in the network. We vary the numberand the size of holes and we analyze the rate of detectionand healing provided by HEAL. Tests will be conducted ondeterministic and random scenes. Parameters of the firstscenario are described in Table 3.

5.1.1 Sub-scenario A: Varying the size of hole

In this sub-scenario we vary the size of the hole. Theresult of the healing process depends on the forcesparameters ka and kr. These parameters are not fixed butdepend on the size of the hole. We proposed adaptivevalues for ka and kr depending on the size of the hole.So after receiving the movement packet, each nodedecides, independently, on ka and kr based on the esti-mated radius of the hole. The simulation results are pre-sented by displaying the network state (sensing disks)before and after the execution of HEAL (see Fig. 4).

By varying the hole radius form 20 to 60 m we obtainalmost the same results. The repair rate is thereabouts

TABLE 3Scenario 1 Parameters

Fig. 4. Result for radius of 58 m. (a) original network, (b) repairednetwork.


100 percent, nodes were able to detect and heal the hole. Thehole with a radius of 38 m (resp. 48 m, 58 m) requires themovement of 50 nodes (resp. 62, 82). We notice that thenodes closest to the hole have moved longer distance thanthose on the border of the HHA (see Fig. 4).

We have analyzed the total distance traveled by nodesaccording to the radius of the hole. As depicted on Fig. 5,this distance is proportional to the hole radius. This distanceincreases from 66 m for a radius of 27 to 840 m for a radius of58 m. This is due to the density of nodes required to heal thehole and the distance between the nodes and the hole cen-ter. The distance traveled is not uniformly distributed onthe nodes. Since according to our relocation model, thenodes near the hole will travel a longer distance comparedto those far from the hole, and thus ensure the connectivityof the network after the movement.

Fig. 6 shows the number of movements performed bynodes to heal the hole. This number reflects the number ofnodes within the HHA. It is proportional to the size of thehole, which is logical because when the hole is large itsrecovery needs more nodes. For a large hole with a radiusof 58 m, 82 nodes have moved among 169 nodes; thus 87nodes remained fixed, which represents half of the nodes.These results confirm that the principle of local healing thatwe proposed is functional.

5.1.2 Sub-Scenario B: Varying the Number and Size of

Hole

In this sub-scenario we vary the number and the size ofholes created in the RoI, and we analyze the behavior ofHEAL. Using deterministic deployment, we created twoholes with different shapes (44 and 32 m). Detection as wellas the healing of the holes were made successfully with a

very high percentage of healing. We have checked that thepresence of both large and small holes did not affect the cor-rectness of HEAL. We have checked also that HEAL is stilleffective for small holes.

Some results for stochastic deployment are depicted inFigs. 7 and 8. As we can see, HEAL is still effective and theholes were detected and repaired successfully. In Fig. 7 thehealing of the two holes required the movement of only 86nodes among 400 nodes. We varied the number of holesand their sizes. With two, four and even seven holes (seeFig. 8), detection as well as healing are always functionaland the healing is almost complete. More extensive evalua-tion results can be found in Appendix D, available in theonline supplemental material.

5.2 Scenario 2: Comparing HEAL to SMART andDSSA

In this scenario, we vary the network density and we com-pare the performances of HEAL to those of DSSA [18] andSMART [20]. On one hand, DSSA [18] is a centralized move-ment-assisted virtual forces-based algorithm, this allow usto compare HEAL to a competitive approach based on thesame concept, i.e., virtual forces. On the other hand, SMART[20] is a grid-quorum based movement-assisted localizedalgorithm, this allow us to compare HEAL to a competitiveapproach based on a different principle. The performancesof the three algorithms are evaluated in terms of traveleddistance, number of movements and rate of improvementin network coverage. The three algorithms will operate

Fig. 5. Total traveled distance versus hole radius.

Fig. 6. Number of movements versus hole radius.

Fig. 7. Result for two holes. (a) Original network, (b) repaired network.

Fig. 8. Result for seven holes. (a) Original network, (b) repaired network.


directly on the holes resulting from the initial randomdeployment. The presented results are the average of20 runs. Parameters of the second scenario are shown inTable 4. We note that SMART and DSSA are movement-assisted deployment protocols that try to improve the net-work coverage by exploiting nodes mobility, which is notthe case of our protocol. The purpose of this comparison isto see the performance of HEAL when it is used to improvethe network coverage of the initial deployment.

Fig. 9 shows the improvement in coverage realized byHEAL, DSSA and SMART. For a deployment of 200 nodes,we see that HEAL gives the worst results compared toothers; this is explained by the fact that the random deploy-ment of 200 nodes in the RoI of 200 m � 200 m may produceimportant holes within the RoI and on its borders. HEALwill detect holes and repair some of them since the nodesdensity is not enough for a complete healing. Moreover, ifthe node density increases, the performance of HEALincreases; the mechanism of healing becomes more effectivewith a large number of nodes. The performances of HEALexceed those of DSSA and SMART when the number ofnodes reaches 350.

In Fig. 10, the total distance traveled by the nodes isshown as a function of nodes density. In the interval [200,300] the distance traveled by the nodes in HEAL increaseswith the nodes density, this is due to the significant numberof holes which HEAL detects and tries to repair. Further-more, the number of holes resulting from the initial deploy-ment decreases with the increase of the nodes density,consequently the traveled distance is stabilized beforedecreasing. Compared with SMART, the total distance

traversed in HEAL is much lower whereas the rate of cover-age improvement is equal or better than that presented bySMART. We note that SAMRT is supposed to be more effec-tive with dense topologies [20]. The performances of DSSAdecrease for dense topologies. The traveled distancedecreases with the increase in the number of nodes becausethe inter-nodal force is increasingly weak, thus the displace-ment of the nodes is small and the rate of coverage improve-ment is weak.

We note that the distance traveled by the nodes in HEALand DSSA is much lower than that of SMART. This is due tothe fact that for SMART, as the nodes density increasesthere will be more nodes regrouping in some parts of thenetwork; so to balance the number of nodes in each cluster,SMART requires the movement of more nodes and thus thetraveled distance increases.

In Fig. 11, we see clearly that SMART and HEAL havealmost the same performances in terms of number ofmovements for a number of nodes between 200 and 300nodes; but HEAL outperforms SMART after that. Thenumber of relocated nodes by the two algorithms in this

Fig. 11. Comparison in terms of number of movements.Fig. 9. Comparison in terms of coverage improvement.

Fig. 10. Comparison in terms of total distance traveled by nodes.

TABLE 4Scenario 2 Parameters


interval is between 40 and 160 nodes for an improve-ment in coverage of 7 percent. DSSA, in this interval,gives a greater coverage improvement but with a veryexcessive number of movements (1,200-1,600). This isdue to the fact that the movements of the nodes inHEAL and SMART is a selective movement at only onetime step (few nodes only are concerned by the move-ment from a source towards a destination).

For DSSA, all the nodes are concerned by the movementaccording to the principle of virtual forces, a node maymove several times before the algorithm converges. In theinterval [350, 450] nodes, HEAL gives the best results incomparison to those of DSSA and SMART.

Finally, the obtained results allow us to assert thatalthough HEAL is a hole healing protocol but it is still effec-tive for the improvement of network coverage by healingholes resulting from the initial random deployment.

6 CONCLUSION

This paper has proposed and implemented a lightweightand comprehensive two-phase protocol, HEAL, for ensur-ing area coverage employing a mobile WSN. The protocoluses a distributed DHD to detect holes in the network. Thecomputation complexity of DHD is Oðv2Þ, where v is theaverage number of 1-hop neighbors. Compared to the exist-ing schemes, DHD has a very low complexity and dealswith holes of various forms and sizes despite the nodes dis-tribution and density. By exploiting the virtual forces con-cept, our approach relocates only the adequate nodeswithin the shortest time and at the lowest cost.

Through the performance evaluation, we validatedHEAL, using different criteria and showed that it detectsand heals the holes despite their number or size with lessmobility in various situations. The evaluation results dem-onstrate that HEAL provides a cost-effective and an accu-rate solution for hole detection and healing in mobile WSNs.

In the future, we plan to investigate the interactionbetween HEAL and the network layer for on-demand holedetection and healing. We are currently working on openholes located at the network boundary. We also plan toinvestigate a special case of holes with obstacles.

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Mustapha Reda Senouci is currently workingtoward the Ph.D. degree in co-supervisionbetween the University of Paris-Est (UPEC,France) and the University of Science and Tech-nology (USTHB, Houari Boumediene, Algeria).He received the Master’s degree in mobile com-puter science from USTHB in 2009 (with distinc-tion) and the engineer degree in computerscience from the Polytechnic School of Algiers(EMP) in 2005 (with distinction), where he is cur-rently a teacher-researcher. His research inter-

ests include mobile ad-hoc networks, wireless sensor networks, andwireless sensor/actor networks.

Abdelhamid Mellouk graduated in computernetwork engineering from the University of ParisSud XI Orsay (with distinction), and received thePhD degree in informatics engineering from thesame university and the doctorat of sciences(Habilitation) diploma from the Paris-Est Univer-sity (UPEC). He is a full professor at Universityof Paris-Est (UPEC), Networks and Telecommu-nication (N&T), France, and the founder andleader of Network Control research activity withextensive international academic and industrial

collaborations. His research interests include high-speed new genera-tion wired/wireless networking and quality of service/experience foradded value services. Currently, he is working on routing and switchingoptimization in dynamic traffic networks; human and bio-inspired artifi-cial intelligence approaches; wireless sensor networks; multimedia andhigh-speed communications. He is an active member of the IEEE Com-munications Society and held several offices including leadership posi-tions in IEEE Communications Society Technical Committees (TheTechnical Committee on Communications Software, The TechnicalCommittee on Switching and Routing), in addition to numerous keynotesand plenary talks in flagship venues.

Khalid Assnoun received the diploma-engineerin computer science from the Polytechnic Schoolof Algiers (EMP) in 2010. He is currently workingtoward the PhD degree in computer science atthe USTHB University in Algiers. His researchinterests include wireless sensor networks.

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Localized movement assisted sensor deployment algorithm for hole detection and healing

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