A Best Fit Relocation Approach for Heterogeneous Sensor Networks

Wireless Pers Commun (2012) 65:733–751DOI 10.1007/s11277-011-0282-y

A Best Fit Relocation Approach for HeterogeneousSensor Networks

Salah Abdel Mageid · Mohamed Zaki

Published online: 2 April 2011© Springer Science+Business Media, LLC. 2011

Abstract The heterogeneity of sensing devices has to be taken into account for increasingthe network performance and lifetime. This paper presents a study for the sensor relocationproblem based on the heterogeneity point of view. A novel approach named Best Fit Relo-cation Approach, BFRA, is proposed for heterogeneous sensors in order to maximize thecoverage of the monitored field and guarantee the connectivity of the deployed sensors. Thisapproach proposes new computational geometry algorithms with perfect complexity to beexploited in small and large-scale sensor networks. A simulation tool is proposed to performa set of experiments to evaluate the proposed algorithms for different sensor characteristicstaking into consideration the curly of field boundaries and the presence of obstacles. Simu-lation results show that near-optimal coverage performance could be achieved in much lessboth running time and average moving distance.

Keywords Heterogeneous sensor networks · Sensor relocation ·Computatinal geometry algorithms · Best Fitting

1 Introduction

A sensing device in Wireless Sensor Networks (WSNs) consists of measuring, processing,and communication models, which enable us to observe and react with events and phe-nomena in specified environments [1,2]. Sensor networks have many applications such asenvironmental monitoring, smart home, disaster relief operations, and ambient monitoring[3–5].

Sensor relocation is a key process in WSNs to reduce the coverage gaps inside the moni-tored field. In most cases, the coverage gaps take place due to unplanned initial deployment

S. A. Mageid · M. Zaki (B)Systems and Computers Department, Faculty of Engineering, Al-Azhar University, Cairo, Egypte-mail: [email protected]

S. A. Mageide-mail: [email protected]

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734 S. A. Mageid, M. Zaki

Table 1 Comparison between OBS and GBS solutions

Item OBS GBS

Time complexity More than or equals O(n3) In order of O (nlogn)

Number of deployed sensors Small Large

Network scale Small Large

Deployment management Centralized Centralized / distributed

Sensor type Heterogeneous/homogeneous Homogeneous only

and/or sensor failure. This process affects different aspects of the sensor network operationssuch as coverage, connectivity, routing, and lifetime. In particular, sensing devices may beheterogeneous nodes in which they have different characteristics such as mobility, energycapability, sensing range and communication range.

Many research solutions have been introduced to solve the problem of sensor relocation.Some solutions have been carried out based on different optimization techniques such asILP, Circle Packing, Genetic Algorithms, Simulated Annealing and Swarm Algorithms [6–8].Here, these types of solutions are named Optimization Based Solutions (OBS). Such solutionsconsider most network parameters such as sensor mobility, lifetime and field dimensions inwhich different optimization techniques have been investigated to obtain the best techniqueachieving high coverage with less running time. Such solutions may achieve higher coverageperformance; however, the time complexity is expected to significantly increase when thenumber of deployed sensors increases. Accordingly, those solutions are recommended forsmall-scale sensor networks to enable a centralized node (i.e., a powerful machine) to deter-mine the final positions for limited number of mobile sensors. On the other hand, differentsolutions have been proposed based on known geometric principles to be decentralized andlightweight; therefore, deploying a large number of sensor nodes is suggested to increasethe coverage performance of large-scale sensor networks. Here, these types of solutions arenamed Geometry Based Solutions (GBS). For example, Voronoi diagrams and Delaunaytriangulation have been exploited to discover the coverage gaps and design simple heuristicsto estimate the sensors’ locations that hail the coverage gaps and increase the coverage per-formance [9–11]. Besides, the potential fields’ concept has been suggested to deploy sensornodes which sensors may repulse or attract according to their current locations to increasethe coverage [12–14]. GBS solutions require homogeneous sensors; for instance, the Voro-noi diagrams are only applied to identical sites, i.e. the sensing range of deployed sensors isidentical. The main items of difference between OBS and GBS solutions are summarized inTable 1.

This paper aims at affording a new design for large-scale sensor networks. This targetcannot be achieved by optimization-based solutions as shown in Table 1. Actually, the pro-posed approach is a geometric oriented solution and designed to overcome the problem ofthe existing geometric solutions to work with heterogeneous sensor nodes. The practicalsignificance of our work arises from the following:

1. It realizes the advantages of the optimization techniques, however, with considerabletime saving, large number of deployed sensors and large-scale network.

2. Using heterogeneous sensors, it achieves the advantages of the geometric techniques ofhomogenous sensors.

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A Best Fit Relocation Approach 735

A set of geometric algorithms is designed to perfectly deal with heterogeneous sensors andsmoothly achieve the sensor relocation requirements. The proposed algorithms are light-weight which are achieving much less time complexity for large-scale sensor networks. Weperfectly deal with different sensor aspects such as sensor mobility, energy, sensing range,and communication range. The mobile sensors are superbly fitted into the coverage gapsachieving low energy consumption and high coverage performance.

This paper is organized as follows: Sect. 2 presents the proposed relocation strategy anddescribes the proposed algorithm. The designed procedures for our framework are describedin details in Sect. 3. The simulation results are given in Sect. 4 to evaluate the performancecomparisons of the proposed models. Section 5 concludes this work along with the futurework.

2 The Best Fit Relocation Approach

Given a target field in which heterogeneous sensors are initially deployed. Those sensorshave different sensing ranges, communication ranges, lifespan, and mobility. The sensingarea of a sensor (i) is approximated by a circle with radius ri indicating its sensing range.Each sensor can determine its current position by GPS services or based on a localizationalgorithm, i.e. [15,16]. This information can be shared with all other sensors within the sen-sor’s communication range to reach the centralized node. In particular, either the perimeter ofthe monitored field or the perimeters of the obstacles are curly. Both the monitored field andthe obstacle models are the polygon shapes that approximately represent their perimeters.Accordingly, proper tangents are drawn for a given curly perimeter to construct a polygonin which the number of tangents is sufficient to create a proper polygon. Afterwards, thosemodels are passed to the proposed approach.

The Best Fit Relocation Approach (BFRA) is a geometric oriented solution. Initially,the centralized node (i.e., a base station for WSNs) waits for broadcast messages from thedeployed sensors carrying the identification number (sensor id) and the current location(x, y). After the location information for all sensors are collected, the centralized node (i.e.the base station) runs the BFRA approach. The BFRA Algorithm is illustrated as follows:

ALGORITHM BFRA_Approach()

INPUT n number of heterogeneous sensorsinfo(i) information characteristics for sensor (i)L(i) (x, y) location for sensor (i)B_Tang set of obstacles’ tangentsF_Tang field’s tangents

OUTPUT Best fit distribution of sensorsPROCEDURE1. BEGIN2. initialize list EA; {Exposed Arcs List}3. initialize list EDG; {Edges List}4. initialize list ObsPOL; {Obstacles Polygons List}5. initialize list GapPOL; {Coverage Gap Polygons List}6. initialize list MidPoints; {Midpoints of triangles List}7. initialize polygon FieldPOL; {Field Polygon}8. Construct FieldPOL from F_Tang;

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9. Construct an obstacle’s polygon from the corresponding set of B_Tang,then add into ObsPOL list;

10. For sensor(i) from i = 1 to n DO11. EA(i) = ExposedArcProc (Li, ObsPOL, FieldPOL);

{Li is a subset of L representing the sensor (i) location and its one-hopneighbors’ location}

12. Add EA(i) to EA;13. End Loop14. EDG = EdgeConstructionProc (EA) ;15. Consturct BorderEdge List;16. EDG.Add(BorderEdge);17. GapPOL = EdgeClassificationProc (EDG) ;18. For GapPOL(k) from k = 1 to p DO // p the number of gaps’ polygons19. MidPoints(k) = TriangulateProc (GapPOL(k));20. Add MidPoints(k) to MidPoints;21. End Loop22. For MobileSsensor(k) from k = 1 to m DO23. A(i) = SensorOverlayProc (Li);24. Anew (i) = SensorOverlayProc (MidPoints, newLi);25. BestFitProc (MidPoints, info(MobileSensors));26. Move MobileSensor (m) into selected MidPoint;27. END

The inputs of BFRA algorithm are the number of heterogeneous sensors and their physicalcharacteristics such as sensing range, communication range, lifespan and the mobility sup-port. In addition, the initial locations of heterogeneous sensors, the proper sets of obstacles’tangents and the proper set of field’s tangents are given information for the centralized node(i.e. the base station). At first, from each set of the obstacles’ tangents (B_Tang), the corre-sponding polygon is constructed and stored in Obstacle Polygons (ObsPOL) list as shown inline (9), each polygon represented by circular linked list edges.

Afterwards, from line (10) to line (13), our approach discovers the coverage gaps byextracting the exposed arcs data from each sensor using the Exposed Arc Procedure. A sen-sor may have no exposed arcs. When exposed arcs are discovered for a sensor, they are storedand appended to Exposed Arcs (EA) list. All framework procedures are discussed in details inthe next section. After constructing the EA list that contains all exposed arcs, the exposed arcsare approximated to line segments (edges) to facilitate this geometric work. As illustrated inline (14), the Edge Construction Procedure approximates all exposed arcs into line segments(sensor edges). In addition, the borders of the monitored field and the obstacles are scannedto detect the exposed edges by a method similar to the Exposed Arc Procedure as shown inline (15) and (16). All edges (sensor and border) are handled to assign the next edge for eachedge. Edge (i) is the next edge for edge ( j) when the front point of edge (i) is the rear pointof edge ( j).

Afterwards, the Edge Classification Procedure, illustrated at line (17), runs to classifythe stored edges into groups in which each group forms a circular linked list representing apolygon. The resultant polygons are stored in the Gap Polygons (GapPOL) list.

Lines from (18) to (21) show how the GapPOL list is manipulated using the TriangulateProcedure to utilize the new locations that require coverage by mobile sensors. Lines (22)and (24) are assigned for mobile sensors in which a mobile sensor can determine the currentscore and the new score based on the new (estimated) location. The mobile sensor score is

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the portion of the field area that uniquely covered by that sensor. Such procedure enables amobile sensor to move in the direction of increasing its score. Finally, line (25) shows howthe best location for each mobile sensor is selected under certain rules such as appropriatedistance and coverage, the current and estimated scores for mobile sensors and their energylevels.

3 The Proposed Framework

The sensor relocation problem can be summarized as follows. A monitored field has uncov-ered areas so-called “Coverage Gaps”. Mobile sensors can move to those gaps to increasethe coverage performance. Therefore, the first step is how to exactly discover those coveragegaps within the entire field. In fact, the Exposed Arc Procedure is designed to perform thistask.

3.1 The Exposed Arc Procedure

That procedure is the first component in our framework. To determine the exposed arcs fora sensor, at first, the current sensor location and its one-hop neighbors’ locations are known.Assume Si and S j are two heterogeneous sensors with sensing range ri and r j , respectivelyin which S j is a one-hop neighbor to the current sensor Si . The Si and S j sensing areas areoverlapped (intersected) when the distance between Si and S j is less than the sum of ri andr j . An important step in such procedure is to determine the intersection arc belonging to Si

perimeter due to S j .The following example, as illustrated in Fig. 1, shows how a sensor (Si ) determines its

intersection arcs. As shown in figure, the intersection arc belongs to Si perimeter, which startsat p j and ends at q j in anticlockwise. Those points are called “endpoints”, where p j is thelower endpoint and q j is the upper endpoint. Assuming the location of the current sensor,Si (xi , yi ), is the reference point. Let the angle of an intersection point p j is θ(p j ) and theangle of an intersection point q j is θ(q j ).

To determine θ(p j ) and θ(q j ), the angle ϕi j , at first, can be geometrically determined asfollows:

ϕi j = cos−1

(r2

i + d2i j − r2

j

2ri di j

)(1)

The angle φi j is determined in terms of Si and S j locations, (xi , yi ) and (x j , y j ), respectively.

φi j = tan−1(

y j − yi

x j − xi

)(2)

Hence, θ(p j ) and θ(q j ) are determined as follows:

θ(

p j) = 180◦ − (

φi j + ϕi j), and

θ(q j

) = θ(

p j) + 2ϕi j

where

θ(

p j)

and θ(q j

) ∈ [0, 360] (3)

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qj

pj

ϕij

φij

dij

Si (xi, yi)

Sj (xj, yj)

θ(pj)

ri rj

Fig. 1 Sensor (Si ) is intersected by sensor (S j )

Field Boundary

Obstacle Boundary

V1

V2

V3

S

Fig. 2 Virtual sensors are assumed at boundaries

Accordingly, any intersection arc can be described by two angles, the lower angle θ(p j ) andthe upper angle θ(q j ). On the other hand, when a sensor lies near the field boundary or anobstacle boundary, an additional intersection arc may be discovered. As shown above, thefield boundary is a border represented by the field polygon FieldPOL, which constructed fromthe field’s tangents (F_Tang). While an obstacle boundary is a polygon ObsPOL constructedfrom an obstacle’s tangents (B_Tang). As shown in Fig. 2, the sensing area of a sensor Soverlaps with the field boundaries as well as an obstacles boundary.

The Exposed Arc Procedure can discover the intersection arcs similar to the method illus-trated in Fig. 1. When such procedure finds the distance between the position of S and aside of the field polygon or a side of an obstacle polygon is less than its sensing radius, avirtual sensor is assumed. For example, the virtual sensor V1 is assumed behind the side ofthe field boundary in which the line between S and V1 positions is perpendicular with the

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Fig. 3 Sweep radius operation

p4

q4

p2

q2

p3

q3

p1

q1

field polygon side and the line length is the double distance between the position of S and theindicated side. When the Exposed Arc Procedure is applied to S and their virtual neighbors,the intersection arcs are discovered.

Afterwards, a Sweep Radius operation is designed to discover the exposed arcs as shownin Fig. 3. Initially, the endpoints of intersection arcs whether the intersection with sensorneighbors or field/obstacle boundary, represented by dashed arcs, are stored in a priorityqueue, which the priority of its point is its corresponding angle. Highest priority point meansthat the point has minimum angle within a range from zero to 360.

In the Sweep Radius operation, the sweep radius scans the sensing perimeter from the firstpoint in the priority queue anticlockwise. As shown in figure, the first element p1 poppedfrom the priority queue where p1 represents the lower endpoint of Arc1. Arc1 is pushed intoa list S. Afterwards, q4 and q1 are visited respectively. At the point q1, Arc1 is removed fromlist S, and then the list becomes empty. Empty list indicates that an exposed arc is discoveredand starts with q1.

The Exposed Arc Procedure is described as follows:

ALGORITHM. FindExposedArcs (L)

INPUT. A set L of (x, y) points represent a sensor’s location and its neighbors’ locations.OUTPUT. A set E of exposed arcs belongs to one circle circumference and stored in a

queue Q.PROCEDURE

1. Determine a set I of intersection arcs.2. Initialize an empty priority queue PQ. Next, insert the intersection arc endpoints into

PQ in which PQ starts with the smallest lower point and ends with the start point;each endpoint stores the arcs begin from and/or end at itself.

3. Initialize an empty list S.4. Initialize an empty queue Q.5. Visited = false

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6. WHILE PQ is not empty7. DO p = highest priority endpoint (first element) in PQ8. Delete the highest priority endpoint from PQ9. IF not Visited THEN10. temp = p11. Visited = true12. HandleEndpoint(p)13. End Loop

END PROCEDURE

PROCEDURE HandleEndpoint(p)1. IF p is an upper endpoint THEN2. IF list S is not empty THEN3. IF its intersection arc I ′ is not stored in the list S THEN4. clear Q5. ELSE remove an intersection arc I ′ from the list S6. IF list S is empty THEN7. Add new exposed arc E ′ into Q with lower endpoint p8. ELSE Swap (current Q, new exposed arc E ′ with lower endpoint p)9. IF p is a lower endpoint THEN10. IF there is E ′ in Q without an upper limit THEN11. Set p as an upper endpoint of E ′12. insert an intersection arc I ′ into the list S

END PROCEDURE

When p2 is visited where p2 is the lower endpoint of Arc 2, p2 ends the exposed arc andArc2 is pushed into S. Afterwards, the point (q2) is visited, Arc2 is removed from S, and thenthe queue becomes empty again. Therefore, another exposed arc is discovered where startswith q2. When p3 is visited where p3 is the lower endpoint of Arc3, p3 ends the exposed arcand Arc3 is pushed into S. Afterwards, the point p4 is visited, Arc4 is pushed into S. Whenq3 is visited, Arc3 is removed from the list. No exposed arc is detected because the list is notempty. Finally, the sweep radius revisits p1 and terminates the operation.

The time complexity of sweep radius operation is illustrated as follows in details. Thefirst step, as illustrated in line (1), determines the intersection arcs for the current sensordue to the overlapping neighbors, m, using Eqs. (1–3) and the intersection arcs due to themonitored field and the obstacles, d . Hence, the total number of intersection arcs is (m + d);the time complexity of such step is O(m + d). The intersection arcs’ endpoints 2(m + d)

are pushed to a priority queue PQ according to the corresponding angle of each endpointwith complexity O(2(m + d)). Each endpoint is popped from PQ with complexity O(1) andhandled by the HandleEndpoint Procedure with complexity O(1); therefore the complexityof the entire loop is O(2(m +d)), as illustrated in lines from 6 to 13. The proposed frameworkapplies the Exposed Arc Procedure for n sensors; therefore, the total time complexity reachesO(n(m +d)). At random deployment, sensors density in certain region randomly varies. Theexperiments conducted in the next section indicate that the maximum number of intersected(real or virtual) neighbors for any sensor at high-density region is around ten neighbors.Accordingly, the maximum number of intersection arcs (m + d) for any sensor is about 10.In addition, the number of deployed sensors in large-scale networks may reach the order of

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thousands; therefore, the practical total time complexity for the Exposed Arc Procedure isconsidered as O (n) in our work.

3.2 Edge Construction and Classification Procedures

The Edge Construction Procedure manipulates the exposed arcs EA list that contains allexposed arcs of all deployed sensors (n). That procedure comes to sharpen those arcs intoline segments (edges) in which an edge represents an entity in the EDG list and assuming thenumber of edges is u where u > n. The edge entity consists of five attributes: the front point,the rear point, a pointer to the next edge, a Boolean attribute, indicating that it is visited ornot, to help in the classification process, and the last attribute for polygon number. So far, theEDG list contains all edges coming from the exposed arcs of deployed sensors. The ExposedArc Procedure is adopted to discover the exposed line segments of the monitored field andthe obstacles. The adopted procedure scans the field’s border and the obstacles’ borders todetermine the line segments (Border Edges) that are no overlapped by any sensor’s sensingarea. The border edges are appended to EDG list assuming the number of border edges is v.

Two attributes for each edge in the EDG list are initially known: the front point and therear point. The NextEdge attribute can be determined as follows; the edge ( j) is the next edgefor the edge (i) when the rear point of edge (i) is the front point of edge ( j). The NextEdgepointer enables us to classify all edges into groups in which each group represents a coveragegap polygon GapPOL.

The Classification Procedure linearly searches the EDG list, which the index search isthe NextEdge attribute. Initially, the (isVisited) Boolean attribute of the first edge is markedtrue and the polygon number attribute is settled one, and then the procedure moves to theedge indicated by the NextEdge attribute of the first edge. Such action is repeated at thesecond edge, which the edge is marked as visited and the polygon number is one. Whenthe procedure reaches visited edge, such edge will be the first edge and then the first gappolygon is constructed. At this point, the classification procedure visits only the edges of thefirst gap polygon. Accordingly, the procedure moves to the first unvisited edge and repeatthe mentioned steps to determine the edges of the second gap polygon and so on. When alledges are visited, the gap polygons are constructed and stored in GapPOL list.

As described above, the Edge Construction Procedure is to approximate the exposed arcsof deployed sensors (u) into edges and the Classification Procedure uses linear search forthe EDG list with size (u + v) to classify the edges into gap polygons. Accordingly, thetime complexity of the Edge Construction Procedure and the Classification Procedure are O(u) and O (u + v), respectively. When such complexity is compared with the Exposed ArcProcedure described above, we find the complexity of Classification Procedure is relativelylarger because the (u + v) is greater than n where n the number of deployed sensors, but thetotal complexity of our framework is still linear. Finally, a gap polygon is stored in an arrayof sequenced vertices instead of a circular linked list of edges to facilitate the gap polygonmanipulation.

3.3 Gap Polygons Manipulation

The Triangulate Procedure is used to manipulate the gap polygons in which a polygon areais divided into triangles. Such procedure implements the Monotone Polygon Triangulationalgorithm [17] which its time complexity is O (ti logti ) where ti is the number of gap polygon(i) vertices. Each polygon with ti vertices is divided into (ti −2) triangles. Assume the number

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(a) True sensing areas. (b) Approximated sensing areas.

B

A

C S1

S2

S3

S4

Fig. 4 Boolean operations for 2D polygons

of gap polygons is (g), the total number of edges (u+v) is E , then E = n1+n2+n3+· · ·+ng .Let the average number of vertices are T , then E = gT . The time complexity to triangulate apolygon is O (T logT ), then the total complexity to triangulate g polygons is O (gT logT ) orO (E(logE − logg)). Accordingly, the time complexity of Gap Polygons Manipulation is O(ElogE). Compared with the above procedures, the complexity of such procedure generallyincreases from the order of O (n) to the order of O (nlogn).

Afterwards, the Triangulate Procedure computes each triangle area and its midpoint. Itis impractical to move a mobile sensor to each midpoint in the gap polygon because sometriangles have small areas and moving mobile sensors to them consumes more energy andmay lead to poor coverage performance. Therefore, the total polygon area is determined toestimate the sufficient number of mobile sensors required to fill the gap polygon regardlessof the number of midpoints. The Triangulate Procedure selects the greatest triangles areasto move the mobile sensors to their midpoints (i.e., estimated locations).

3.4 The Sensor Overlay Procedure

As shown above, the coverage gaps are modeled in polygons’ shapes, and the estimatedlocations for the required mobile sensors are determined. The aim of the Sensor OverlayProcedure is to compute the current score of a mobile sensor and its new score at an esti-mated location. Accordingly, the best mobile sensor (i) can be assigned to an estimatedlocation ( j) as shown in the next procedure, the Best Fit Procedure. The following exampleillustrates the Sensor Overlay Procedure. A mobile sensor S1 marked with dashed lines andoverlapping with heterogeneous sensors S2, S3 and S4 as shown in Fig. 4a. The current scoreof S1 is the dashed area that uniquely covered by S1.

To compute such area, all sensing areas of sensors are approximated into hexagon shapesas shown in Fig. 4b. The Sensor Overlay Procedure aims to determine the area of the dashedpolygon, which represents the current score of S1; therefore, the Boolean Operations for2D Polygons algorithm [17] are used. The Boolean operations include union, intersectionand difference between two polygons. The time complexity of a Boolean Operation is O((p + k)logp) where p is the total number of the two polygon vertices and k is the numberof vertices for the resultant polygon.

The Sensor Overlay Procedure initially performs the union operation between S2 and S3

to determine the vertices that represent the union area between S2 and S3 polygons. Such pro-cedure is repeated for the resultant polygon and S4 polygon. The polygon marked with (B) inFig. 4b represents the union of S2, S3 and S4 polygons. Afterwards, the difference operation

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S5

S1 S4

S2

S3

S6

S11

S8

S9

S10

S7S5

S4

S2

S3

S6

S11

S8

S9

S10

S7 S5

S4

S2

S3

S6

S8

S9

S10

S7

(a) S1 is a mobile sensor. 1 (b)S is absent. 1 and S11 are absent. (c) S

Fig. 5 The network connectivity at mobile sensor S1

is performed between S1 polygon marked with (A) and the polygon (B). The difference areamarked with (C) in Fig. 4b represents the S1 current score.

As shown above, the total number of two hexagons’ vertices p is twelve and the numberof resultant polygon’s vertices k is less than p. In addition, the number of Boolean operationsfor one sensor is the number of its neighbors around few tens at most. Accordingly, the totalcomplexity of the Sensor Overlay Procedure is approximately depends on the number ofmobile sensors regardless of the complexity of Boolean operations at each sensor. Therefore,when all deployed sensors are mobile, the complexity is O (n) where n is the number ofdeployed sensors in the monitored field (i.e., thousands sensors for large-scale networks).

On the other hand, a new score is determined for each mobile sensor at each estimatedlocation. The Sensor Overlay Procedure virtually sets a mobile sensor (i) at an estimatedlocation ( j) and discovers the new neighbors. Accordingly, the new score for mobile sensor(i) at an estimated location ( j) can be determined using the Boolean operations algorithmas discussed above. When all deployed sensors are mobile and the number of estimatedlocations is limited around few tens, the time complexity is still O (n).

At this point, the proposed framework knows the current score of a mobile sensor (i)and the new score of a mobile sensor (i) when it is decided to move to an estimated loca-tion ( j). Generally, a mobile sensor (i) may move to any estimated location ( j) except thelocations that cannot improve its score. When no estimated location ( j) improves the scoreof a mobile sensor (i), such sensor stays in its current location. In addition, there is anotherreason to prevent a mobile from movement when the network is partitioned due to such move-ment. Accordingly, the breadth first search (BFS) [18] is performed to check the networkconnectivity after moving this mobile sensor.

For example, there are five one-hop neighbors S2, S3, S4, S5 and S6 for a mobile sen-sor S1 as shown in Fig. 5a. Before deciding to move S1, the BFS algorithm is performed inthe absence of S1 for the 2-hop neighbors of S1 to ensure that a spanning tree that connectsall these neighbors can be constructed. Two different scenarios are illustrated in Fig. 5b, c.For Fig. 5b, the BFS procedure returns true because the spanning tree can be constructedwhile it returns false for Fig. 5c. The complexity of BFS procedure for one mobile sensor isO (V + E) where V is the number of 2-hop neighbors and E is the number of edges amongcommunicated sensors. When all sensors are mobile, the total complexity is O ((V + E)n) ∼=O (n) because the number of 2-hop neighbors plus the number of edges for one mobile sensoris a small number around few tens.

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Table 2 ML entity structure

SDR Mobile sensor id (m) Estimated location (l) Connectivity state (c) Energy level (e)

3.5 The Best Fit Procedure

Before discussing the Best Fit Procedure, an important parameter is designed, Score to Dis-tance Ratio (SDR). The SDR is defined as the relative score (Sr ) divided by the relativedistance (Dr ).

SDR(m, l) = Sr (m, l)

Dr (m, l)(4)

where

Sr (m, l) = Snew(m, l) − Sc(m)

Snew(m, l),

and

Dr (m, l) = D(m, l)

r(m)

The parameter Snew(m, l) is the new score of mobile sensor (m) at estimated location(l), Sc(m) is the current score of mobile sensor (m), D(m, l) is the distance between thecurrent position of mobile sensor (m) and the estimated position (l), and r(m) is the mobilesensor (m) sensing range. When SDR ratio is negative, it means that the new score at (l)is less than its current score. Besides, the mobile sensor movement to (l) at such situationleads to decreasing the coverage performance. Otherwise, when the SDR ratio is positive, theestimated location (l) that gives the highest SDR ratio is chosen as a new location for mobilesensor (m). For example, let a mobile sensor (m) at location (10, 14), its sensing rang r(m)

equals 6 m and its current score Sc(m) is 11.2 m2. Let an estimated location l at (17, 20) inwhich the new score of the mobile sensor (m) at that estimated location is 65.4 m2. The SDRratio will be 0.541 or (5.41 ×10−1).

The problem here is one estimated location (l1) may be chosen as a new location for manymobile sensors; accordingly, a procedure is required to assign the estimated location (l1) tothe best mobile sensor. The Best Fit Procedure is performed in which a new data structureis constructed to keep the relationship between mobile sensors and estimated locations; it iscalled ML data structure. Such data structure contains (m ×l) entities where m represents thenumber of mobile sensors and l represents the number of estimated locations. The entity ofML consists of five attributes: SDR ratio, a mobile sensor id (m), an estimated location (l),the connectivity state (c) and a mobile sensor energy level (e) as shown in Table 2.

The ML structure is stored in a priority queue in which the priority is the score rate; thehighest priority entity has largest score rate. The Best Fit Procedure sequentially searchesthe priority queue to fit a best mobile sensor to an estimated location (l). At each positionof the priority queue, three attributes are checked: (1) the score rate should be positive, (2)the connectivity is valid, and (3) the energy level of mobile sensor is appropriate to move.When those conditions are satisfied, the Best Fit Procedure marks the mobile sensor (m) andthe estimated location (l) as visited to avoid the replication. Otherwise, when one of thoseconditions is not satisfied, the Best Fit Procedure discovers that this mobile sensor is notproper for that estimated location and moves to the next row and so on. Table 3 shows anexample for performing the Best Fit Procedure for five mobile sensors and three estimatedlocations (A, B and C) in which the ML size is (m × l = 15).

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Table 3 ML informationIndex SDR (×10−1) M l c e

0 5.33 4 B T 5

1 5.12 4 A T 5

2 4.98 4 C T 5

3 4.63 5 B F 4

4 4.55 5 A F 4

5 4.43 3 B T 5

6 4.22 5 C F 4

7 4.09 2 B T 2

8 3.89 2 A T 2

9 3.81 3 A T 5

10 3.77 3 C T 5

11 3.65 1 B T 4

12 2.14 2 C T 2

13 −1.01 1 A T 4

14 −2.21 1 C T 4

At row (0), the mobile sensor number 4 satisfies the connectively and energy conditionsand has the highest SDR ratio, then such sensor is assigned to estimated location (B). Rows(1) and (2) are skipped because the mobile sensor number 4 is selected. Rows (3), (4) and (6)are skipped because the mobile sensor number 5 is denied to move due to the connectivityissue. Line (5) is skipped because the estimated location (B) is selected. Rows (7), (8) and(12) are skipped because the mobile sensor number 2 is low energy level. At raw (9), themobile sensor number 3 is chosen for the estimated location (A) as a best mobile sensor whichsatisfies the energy and connectivity conditions. Rows (10) and (11) are skipped because thesensor number 3 and location (B) are selected, respectively. Rows (13) and (14) are skippedbecause the sensor number 1 cannot improve its score, which the SDR ratio is negative.

Finally, the centralized node sends to the best mobile sensors their targets to move. Thecomplexity of the Best Fit Procedure is O(ml), and when all deployed sensors are mobile,the complexity is O(nl) ∼= O(n) where l is limited number around few tens. As shownabove, the proposed procedures are lightweight because the total complexity of the proposedsolution is O (nlogn) where n is the total number of gap polygons’ edges that is relativelylarger than the number of deployed sensors. Therefore, the proposed framework is consideredlightweight compared with the complexity of evolutionary algorithms or swarm algorithms.The next section introduces a comparative study to verify that the proposed solution is aproper centralized solution to deploy heterogeneous sensors in large-scale networks.

4 Performance Comparison and Simulation Results

A C# simulation tool is developed to implement the proposed geometric algorithms and toexamine the effectiveness of the Best Fit Relocation Approach (BFRA). This simulation toolis used to perform several experiments to understand the behavior of heterogeneous sen-sor networks. In these experiments, the sensors deployment in a field of squared shape is

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considered for simplicity. The field dimensions are 60 × 60 m giving a total area of 3.6 km2.The current sensor prototypes, such as Smart Dust (UC Berkeley), CTOS dust, and Wins(Rockwell) have a sensing range around 6 m [19]; therefore, three sensing ranges for thedeployed sensors are assumed (i.e., 4, 5 and 6 m). The communication range for the currentsensor prototypes equals 20 m [20]; so that such value is chosen for all deployed sensors inour simulation.

Figure 6 illustrates the different views of the tool’s interface when twenty-five sensors areused from each sensor type giving a total of 75 sensors.

Such number is chosen to clarify the gap polygons’ construction as shown in Fig. 6. Suchnumber will increase in our experiments to show how the number of deployed sensors affectsthe network performance. Figures 6a, b show the sensing footprint for each sensor in caseof obstacles’ existence and absence, while Fig. 6c, d illustrate the gap polygons in case ofobstacles’ existence and absence. Fig. 6e shows the output of the Triangulate Procedure andthe selected midpoints. The output of the Best Fit Procedure is to fit the best mobile sensorsto the corresponding estimated locations as shown in Fig. 6f. Among the deployed heteroge-neous sensors, we assign a percentage of sensors to be mobile. This percentage varies fromzero percent to 50%, with an increment of 10%, and the mobile sensors are chosen randomly.

To evaluate the proposed approach performance under different parameter settings, werun 50 experiments based on different initial distributions for the obstacles’ absence andexistence, and then calculate the average results. Initially, we choose to increase the numberof deployed sensors into thirty sensors from each sensor type giving a total of 90 sensors.The average initial coverage for those experiments is 83.84% at no movements (0% ofmobile sensors). In this work, three fitting methods are compared. First, Fitting by Distance(Fit-Dis) in which the nearest mobile sensor for an estimated location is chosen regardlessof the percentage of coverage improvement. Second, Fitting by Coverage (Fit-Cov) in whichthe mobile sensor with lower score that achieve a higher score at estimated location is cho-sen regardless of the distance between the mobile sensor and the estimated location. Thelast method is Fitting by Score to Distance Ratio (Fit-SDR); as mentioned above, the scoreimprovement percentage and the lowest distances are considered in the SDR ratio.

Figure 7 shows the coverage performance for those fitting methods under different mobilesensor percentage. Two observations are discovered from the figure. One is that the threemethods can increase the coverage significantly. The other is that the Fit-SDR method slightlyimproves the coverage more than the Fit-Cov but obviously more than the Fit-Dis. As shownin figure, when the mobile sensor percentage changes from 0 to 10%; all of them rela-tively achieve the same coverage improvement from 83.84 to 91.6% because the number ofrequired mobile sensors is larger than the offered. When the number of mobile sensor per-centage increases, there are sufficient sensors to move to the estimated locations inside thegap polygons. Consequently, the nearest sensors are not necessary achieving higher coverage.

In addition, the sensors with lowest scores are not necessary achieving higher coveragewhen they move to the locations with highest score. The figure shows that when the scoreand distance are considered, this leads to the better coverage performance as illustrated inthe Fit-SDR method.

Figure 8 shows the average moving distance in terms of energy consumption under differ-ent mobile sensor percentage. It’s clear that the Fit-Cov method achieves the worst averagemoving distance because the distance between a mobile sensor and an estimated location isnot considered. This may lead to move a mobile sensor long distance and consume muchenergy. However, such problem is solved in Fit-Dis and Fit-SDR because the distance isconsidered. The Fit-Dis method is slightly better than the Fit-SDR method in saving themovement energy.

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(c) Gap polygons at obstacles’ existence (d) Gap polygons at obstacles’ absence

(e) Triangulation at obstacles’ absence (f) Mobile sensors’ movements at obstacles’ absence

(a) Sensor footprint at obstacles’ existence (b) Sensor footprint at obstacles’ absence

Fig. 6 Different views of the simulation tool’s interface

As a simulation result, three scenarios are expected depending on the application require-ments. When higher coverage percentage is required at the existence of sufficient energy forsensor movement, the Fit-SDR method is the best choice. Another scenario is that when themovement energy is considered regardless of the optimal coverage, the Fit-Dis method ismore suitable. The last scenario is that when the optimal coverage with minimum movement

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0% 10% 20% 30% 40% 50%

84

86

88

90

92

94

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98

Percentage of mobile sensors

%C

over

age

Fit−Dis

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Fig. 7 Coverage performance under different mobile sensor percentage

0% 10% 20% 30% 40% 50%0

1

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rage

mov

ing

dist

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eter

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Fig. 8 Average moving distance under different mobile sensor percentage

energy as much as possible is required. In this case the Fit-SDR method is chosen because itachieves higher coverage percentage compared with the others along with appropriate mov-ing distance (approximately equal to the smaller moving distance achieved at the Fit-Dismethod).

Another set of experiments is considered, we assume a monitored field with obstacles’existence. For the sake of comparison, the same field dimensions are chosen and 75 hetero-geneous sensors are initially deployed. After applying the fitting methods, Fit-Dis, Fit-Covand Fit-SDR, we noticed that the Fit-Cov has the worst performance because the averagemoving distance obviously increases because some mobile sensors takes long distances toreach their targets due to the obstacles. The shortest path algorithm is applied to choose the

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0 180 360 540 720 900 1080 1260 1440 1620 18000

10

20

30

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Number of deployed sensors (n)

Nor

mal

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run

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tim

e

n

nlog(n)

EA−LeadingOnes

SwarmLeadingOnes

EA−Plateau

BFRA

Fig. 9 Running time comparison

path from a mobile sensor and an estimated location. The Fit-SDR still achieves the betternetwork performance with obstacles’ existence.

Finally, the proposed approach BFRA is compared with the evolutionary algorithms (EA)and swarm algorithms to evaluate the effectiveness of BFRA for large-scale sensor networks.A set of experiments are performed at different numbers of deployed sensors varying from90 to 1,800 with increment of 90. The monitored field dimensions are gradually expanded toreach 300 by 300 m at 1,800 sensors to give a total area of 90 km2. The Fit-SDR is used andthe running time at 90 sensors is taken as a reference to normalize the running time of otherexperiments.

As shown in Fig. 9, the normalized running time for BFRA increases when the numberof deployed sensors increases in which the values (indicated by cross marks) is less than theorder of n log (n) and larger than the order of n. Therefore, the results of such experimentsverify the analysis of our algorithms. On the other hand, when the evolutionary algorithmsare used such as LeadingOnes [21] and Plateau [22], the time complexity is in order of O(n3/2) and O (n3), respectively. The Plateau function improves the drawbacks of Leadin-gOnes function and improves the coverage optimality. However, the complexity of Plateaufunction is larger than the LeadingOnes function. In addition, the time complexity of swarmalgorithms, such as LeadingOnes [23], is in order of O (n2). As shown above, the proposedapproach as a centralized solution is appropriate to work with large-scale sensor networks.

5 Conclusion and Further Work

A new geometric approach for relocation of heterogeneous sensor networks is introduced.As part of this work, new geometric algorithms are proposed. Such algorithms allow the basestation to move mobile sensors achieving an efficient relocation approach that maximizesthe overall field coverage at proper average moving distance. Several simulation experimentsare performed to examine the effectiveness of the designed approach. Based on the results ofsuch experiments, the proposed approach enhances the sensors distribution in the field which

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improves the coverage performance in much less running time and less average moving dis-tance. Several extensions are considered for this research. For example, effort is underwayto develop this work for autonomous sensor networks.

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http://dx.doi.org/10.1155/2007/54731

http://wins.rsc.rockwell.com

http://www.bsac.eecs.berkeley.edu


Author Biographies

Salah Abdel Mageid is assistant professor, Faculty of Engineering,Al-Azhar University. He received the M.S. and Ph.D. degrees in2002 and 2005, respectively from Computers Engineering Department,Al-Azhar University, Cairo, Egypt. He performed Post Doc research in2007 and 2008 at SMU University in Dallas, Texas, USA. His researchinterests include Ad-hoc and Sensor Networks, Network Traffic Man-agement, Routing Protocols and Network Security.

Mohamed Zaki is the professor of software engineering, Com-puter and System Engineering Department, Faculty of Engineering,Al-Azhar University at Cairo. He received his B.Sc. and M.Sc.degrees in electrical engineering from Cairo University in 1968 and1973 respectively. He received his Ph.D. degrees in Computer Engi-neering from Warsaw Technical University, Poland in 1977. His fieldsof interest include artificial intelligence, soft computing, and distrib-uted systems.

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A Best Fit Relocation Approach for Heterogeneous Sensor Networks

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