On-Supporting Energy Balanced K-Barrier Coverage In Wireless Sensor Networks

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1 On-Supporting Energy Balanced K-Barrier Coverage In Wireless Sensor Networks Chih-Yung Chang w Li-Ling Hung Aletheia University Yu-Chieh Chen u.edu.tw Ming-Hsien Li du.tw ABSTRACT The k-barrier coverage problem is known as the problem of detecting the intruders by at least k sensors when the intruders moving along the crossing paths from one boundary to another. This paper proposes decentralized algorithms to cope with the k- barrier coverage problem. For a given value k, the proposed algorithms find out the maximum disjoint sets of sensors such that each set of sensors meets the requirement of k-barrier coverage for users. Three mechanisms, called Basic, Backtracking, and Branch, are proposed for constructing as more as possible the disjoint sets of sensors that satisfy the requirement of k-barrier coverage. Performance study reveals that the proposed algorithms achieve near-optimal performance. Categories and Subject Descriptors C.. [Computer Communication Networks]: Network Architecture and Design Wireless communication General Terms Algorithms, Performance, Design. Keywords Distributed, Barrier Coverage, Wireless Sensor Networks. INTRODUCTION Wireless sensor networks (WSNs) have a wide range of potential applications. One of the most important goals of these applications is to detect intruders as they cross a border or as they penetrate a protected region. This type of coverage is referred to as barrier coverage[-][-], where the sensors form a barrier for detecting the intruders. The k-barrier coverage problem [] aims at determining the minimum number of sensors deployed in the given WSN so that all crossing paths through the region are covered by at least k active sensors, where a crossing path is any path that crosses the width of the region completely. The barrier coverage is the abbreviation of k-barrier coverage when the value of k is one. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. IWCMC 9, June, 9, Leipzig, Germany. Copyright 9 ACM /9/...$. The k-barrier coverage problem is an important issue for many applications, such as intrusion detection, object tracking, and border surveillance. For any crossing path, detecting the intruder by multiple sensors is desired for these applications, because it increases the reliability or security. Such k-barrier coverage minimizes the risk of possibly missed intruders. In the relevant research of k-barrier coverage, Kumar et al. [] discusses the number demanded for sensor nodes from the probability point of view such that the probability that any crossing path is detected by at least k (k is greater or equal to ) sensor nodes is greater than.99. However, given a densely deployed WSN, Kumar et al. [] did not explicitly determine the set of active sensors that guarantee the surveillance quality of k-barrier coverage. Vu et al. [] separately proposes the centralized and distributed algorithm to support the network environment with -barrier coverage. Chen et al. [] proposes a mechanism to measure the barrier coverage degree in the network environment and find out the appropriate number of sensors to maintain -barrier coverage. Chen et al. [] designs a localized algorithm to divide the network environment into several blocks and prove if each block is with k-barrier coverage, then the whole network is also k-barrier coverage. However, the abovementioned previous work didn t find out the specific set of the sensors to achieve the k-barrier coverage purpose. If more sets of sensors with k-barrier coverage capability, we can schedule these sets in turn to extend the network lifetime. Previous study [] presented a centralized mechanism that applies the graph theorem to connect the sensors whose sensing range are overlapping for establishing the maximum number of disjoint paths. Each established path guarantees one-barrier coverage and hence the set of active sensors can be determined for providing k-barrier coverage for a maximal k. However, the centralized mechanism developed in [] has several drawbacks. Firstly, it requires global information. Each sensor in the network needs to flood its location information to sink node. Then the sink node finds the maximum disjoint paths and then floods the result to all sensor nodes. In total, twice flooding operations are applied in the WSN, which consumes a considerable energy of sensors. Moreover, sensor nodes closer to the sink node will die earlier due to the heavy workload for relaying packets. The centralized mechanism also lacks scalability and flexibility. This paper aims to develop a decentralized scheme to cope with the k-barrier coverage problem. The proposed mechanism finds a maximal number of disjoint sets of sensors such that each set is composed of minimum number of sensors but supports k- barrier coverage. The sets of sensors can be active in turn to reduce the energy consumption and achieve load balance purpose.

2 . Algorithms for Constructing a Defense Barrier with k-barrier Coverage The WSN discussed in this paper is a rectangle region R which is surrounded by borders of two neighboring countries. The four notations L sourth, L north, L left, L right denote the four boundaries of R. Sensor nodes are randomly deployed in the network. Each sensor has a unique ID and is aware of its own location and the boundary information including the coordinates of four points of R. A crossing path is a movement trajectory that starts from L sourth to L north and crosses the width of R. Figures (a) and (b) depict the valid and invalid crossing paths, respectively. Through the exchange of the beacon with one hop neighbors, each sensor can collect the ID and location information of its neighboring sensors. (a) Valid crossing path (b) Invalid crossing path Figure. An example illustrating the valid and invalid crossing paths Figure shows another type of barrier, say c, which initially branches and then merges at some defense circles. Since any crossing path will be detected by at least two sensors of c, defense barrier c supports -barrier coverage. Figure. A branch defense barrier supporting -barrier coverage. One challenge of the k-barrier coverage problem is that there are a huge number of barriers and each Defense Barrier with degree k, says DB-k, is composed of k disjoint barriers. How to locally construct a DB-k that is composed of a minimal number of sensors will be a big challenge... Network Initialization Initially, the network is partitioned into the M N equal-sized grids as shown in Fig. (a). According to the partition, each grid is assigned with a coordinates. The rules for assigning coordinates are described below. The most left-up grid is initially assigned with (, ). As shown in Fig. (a), the x-coordinate and y- coordinate are increased by one if the location of a grid shifts one position toward right and down directions, respectively. To guarantee that any sensor s sensing range can fully cover its grid, the length of each grid is r, as shown in Fig. (b). Since the grid size and the boundaries of R are predefined, each sensor is aware of its coordinates of the located grid. Based on the neighboring information, each sensor can derive the coverage degrees of its own and its neighboring grids. More specifically, a grid is p-covered if there are p sensors in that grid. The partitioning of the network region into grids can simplify the k-barrier coverage problem. By this way, a DB-k can be constructed from L left to L right grid by grid, such that each grid contains k sensors. c r S (,) (,) (,N) (,) (M,) r S Sensor i (a) Topology of the Coarse- (b) Grid size in Coarse-Grain Grain Approach. Approach. Figure. The grid topology and the corresponding grid size. Let notations g(x, y) denote the coordinates of grid g and N(x,y) denote the number of sensor nodes in grid g(x, y). A Weighted Grid Matrix (WGM) is an M N sized matrix where each entry corresponds to a grid and records the number of sensors located at that grid. Figure gives an example of WGM. We emphasize that the WGM is a tool that is used to help understand the proposed mechanisms from the conceptual point of view. The developed mechanisms presented in this paper are totally decentralized. M N Figure. An example of Weighted Grid Matrix (WGM)... Approaches to K-Barrier Coverage Problem In each grid, a Decision Maker (DM) will be elected for executing the proposed mechanism. The DM of a grid is the sensor with the minimum ID since the initial energy of each sensor is equal. Figure defines a priority table where the middle grid of the table is defined as a defense grid. Let sensor A play the role of DM in the defense grid and it has determined to join the DB-k. In Fig., the number labeled on each grid denotes the priority of that grid. The right grid will be the best candidate to join the DB-k because a straight defense barrier will be easily constructed with fewer sensors. The priority of right-up grid is higher than that of right-down grid because that we expect to select sensors to join the DB-k from top to bottom. With this property, sensors located at the top region can be fully utilized. The top and down grids have a higher priority than left grids because that they are closer to the right boundary of R. 8 Figure. A priority table for selecting the neighboring grids to construct a defense barrier. Let the length and width of region R be L W and the length of each grid is e. It implies that region R contains L / e W / e grids. The Decision Maker of g(x,y) is denoted as DM g(x,y). Based on the priority table as shown in Fig., the following proposes three mechanisms to construct a DB-k. r s

3 A. Simple Algorithm(SA) The following proposes a Simple Algorithm(SA) for constructing a DB-k. In the Simple CGA Algorithm, DM current denotes the DM who owns the authority to select the DM of the next defense grid. The DM prev denote the previous DM that selects DM current to participate in the DB-k while the DM next denote the DM that is selected to participate in the DB-k by DM current. Let notation N(DM) denote the number of sensors in DM s grid. To clearly describe which neighbor is earlier selected by DM, we refer DM.[Priority=h] to the neighboring DM whose priority is h. Initially, the SA selects a leftmost grid that contains at least k sensors. Then the DM of selected grid has the authority for constructing DB-k and will play the role of DM current. The DM current will be responsible for selecting the best grid to join the DB-k from eight neighboring grids according to their priorities so that the DB-k can be constructed grid by grid. The selected grid should satisfy the criteria that there are at least k sensors in that grid. As soon as the decision has been made, the DM current applies Hand_Over procedure to transfer the authority to the DM next which is the DM of the selected grid. Then the DM current waits for the acknowledgement replied from DM next. The DM next applies Hand_Over procedure again to continuously transfer the authority to the next grid until a selected DM reaches to the right boundary. If it is the case, the DM in the right boundary reports success to sink node and its DM prev. Any DM current that fails to select a valid grid from its neighboring grids will report failure to sink node and its DM prev. Recall that the DM current waits for the result returned from DM next. If the result is success, it simply returns a success message to its DM prev. On the contrary, it returns failed to its DM prev. The DM that receives a success message should further apply the check rule to check if it is a redundant DM. Figure depicts an example for constructing a DB-. The number marked in each grid represents the number of sensors in that grid. Since the sensing range of each sensor can cover the grid where it located, the number in each grid also represents the coverage degree of that grid. Initially, the SA selects a grid from first column and hence the grid (, ) is selected since it contains at least three sensors. At this moment, the DM of grid g(, ) plays the DM current role and has authority to determine the DM next. According to the priority table, DM g(, ) selects the neighboring grid g(, ) to join the DB-, and transfers the authority to DM g(, ) by executing Hand_Over procedure. Then DM g(, ) selects grid g(, ) to join the DB-. The construction of DB- is executed grid by grid until the selected grid reaches to the right boundary. The major advantage of SA is simple and easy to be implemented. However, The SA might be failure in constructing a DB-k. Figure shows a failure example of SA. In Fig., DM g(, ) can not find any grid that contains at least three sensor in its neighboring grids. To explore as more as possible the feasible solutions, the following gives a backtracking mechanism which improves the SA Figure. An example by applying the SA Algorithm B. Backtracking Algorithm(BTA) The basic concept of Backtracking Algorithm(BTA) it is that it allows DM current, say DM x, to transfer the authority to the previous DM, say DM prev =DM y, if the Hand_Over rule is failed at DM x. As soon as the DM y gets the decision authority, it again plays the role of DM current and tries to find the feasible DM next other than DM x to construct a DB-k. The BA mechanism shown below provides more opportunities to construct a feasible DB-k since it allows the construction of DB-k to backtrack the visited grid. The BTA and SA have similar operations if the construction of a defense barrier is successful. However, if a DM current fails to find a feasible grid from its eight neighboring grids, it returns a grid failure message to the DM prev. This message triggers the manager DM prev who stays in the waiting state. Upon receiving the failure message, the DM prev continuously executes and the same procedure as SA and then selects the next grid from the unconsidered grids according to their priorities. This design gives more opportunities for constructing a feasible defense barrier. In the worst case that the authority is backtracked to the leftmost grid, the DM of leftmost grid gives the sink node a final report of path failure. Figure gives an example that SA fails but BA successes to construct a DB-. In this example, the DM g(,) can not find any feasible neighboring grid that satisfies DB-. Applying the proposed BA, the DM g(,) executes the operation depicted in column and hence returns a grid failure message to DM prev =DM (,). Upon receiving the failure message, the DM (,) selects DM g(,) whose priority is next to the DM g(,) but satisfies the requirement of -coverage. Then DM g(,) executes Hand_Over procedure and the DB- is successfully constructed grid by grid Figure. An example by applying the proposed BTA. Although BTA provides more opportunities than SA for constructing a DB-k, however, only those grids which contain at least k sensors will be considered to join the DB-k., The next subsection proposes a BRA algorithm that fully utilizes those grids that contain less than k sensors. C. Branch Mechanism(BRA) The main idea of BRA is to give more opportunities for the neighboring grids to join the DB-k even though each of the neighboring grids contains less than k sensors but the Since the random deployment might cause an imbalanced distribution of sensor nodes, the number of sensors in each grid might be different. Though some grids contain less than k sensors, however, they can contribute their potential coverage for a DB-k. In constructing a DB-k, The BTA and SA did not consider those grids that contain less than k sensors in each grid. Recall that a DB-k can be composed of i curves, say DB-m, DB-m,, DB-m i, where k= m i ++ m i, for all m i <k. That is, a curve with DB-k can have i branches DB-m, DB-m,, DB-m i from some grid. The

4 following proposes a algorithm BRA to improve the utilization of those grids that contain less than k sensors. Let weak grid represents the grid contains less than k sensors. A grid contains at least k sensors is called qualified grid. The BRA can construct more defense barriers with the DB-k than SA and BTA by inviting weak grids when all neighboring grids of DM current are weak grids. That is, the BRA gives more opportunities for the weak grids to join the DB-k and hence balances the energy consumption of sensors and prolongs the network lifetime. Similar to SA and BTA, the BRA selects a qualified grid from the leftmost column to the rightmost column. As soon as a DM current fails to find a qualified grid, it tries to select some weak grids that the total number of sensors in the selected weak grids is equal to or lager than k. The BRA Mechanism calls the Branch procedure that aims to find a set of neighboring grids so that the sensors in these grids can cooperatively contribute k- barrier coverage. In the Branch procedure, the DMs of the selected grids will play the role of DM current and then further execute the Branch procedure until the right boundary is reached. In BRA, if DM current receives a success message from the Branch procedure, it further replies a success message to the DM prev. Figure 8 gives an example for constructing a DB- by applying BRA. Initially, the BRA selects grid g(,) to be the starting grid. Different from the SA and BTA, when the BRA fails to find a qualified grid from its neighboring girds, it considers the weak grids for constructing as more as possible DB-k. Herein, the weak grid located in the upper row has higher priority to be selected. Hence the priority table is changed as shown in Fig. 9. As shown in Fig. 8, according to the new priority table, DM g(,) selects a qualified grid g(, ) which contains sensor nodes to join the DB- and then transfers the authority to DM g(,) by sending a selection message. The selection message contains the location information of DM g(,) and the required coverage degree k. Based on the new priority table, the selected DM will further select the DM next in the qualified grid until DM g(,) is selected. However, DM g(,) can not find any qualified grid from its neighboring grids. Therefore, DM g(,) will initiate a branch message trying to select weak grids DM g(,) and DM g(,) to construct a DB- according to the priority table shown in Fig. 9. The branch message sent by DM g(,) contains the location information of DM g(,) and the required coverage degree for each weak grid. In this example, DM g(,) and DM g(,) will be notified that the required coverage degrees are and, respectively. On obtaining the authority, DM g(,) and DM g(,) individually apply the same BRA Mechanism to construct the -coverage and -coverage branches, respectively. By applying the BRA, a branched DB- can be successfully constructed as shown in Fig. 8. The BRA approach not only improves the defense strength of barrier coverage but also balances the energy consumption of sensors in the network. The BTA mechanism presented in previous subsection can be further integrated with the BRA Mechanism when the BRA fails to find satisfied weak grids at some DM current. In the experiment, we will investigate the performance improvement of the mechanism by integrating Branch and Backtracking schemes Cover -Cover -Cover Figure 8. An example of BRA. Simulation Results 8 Figure 9. The priority table of BRA This section studies the performance of the proposed SA, BTA, and BRA mechanisms and their combinations against the Maximum Disjoint Paths (MDP) mechanism which is a centralized algorithm proposed in []. Table lists the simulation parameters and their corresponding values referred to the typical Berkeley motes. Sensing Range m Comm. Range m Table. Simulation Parameters Simulation Parameters Monitoring Number of Grid Size Area Sensors m (m),,, Deployment Random In addition to the theoretical analysis of the communication complexity, Fig. further investigates the control overhead of MDP and the three proposed mechanisms. Since the control overhead of MDP is exponentially increased with the value k, the three proposed mechanisms outperform MDP in terms of control overhead. Whenever the DM current fails to find the qualified grid, the BTA applies the backtracking policy to find the next grid backward and thus creates more control overheads than the other two proposed mechanisms. Though the BRA does not consider the backward grids, however, it applies branch policy aiming to give more opportunities for the weak grids. Hence the BRA creates more control overhead than SA. Figure. The communication overheads of SA, BTA, BRA, and MDP in the monitoring area with sensor nodes. Table compares the SA, BTA, BRA and MDP mechanisms in terms of the maximum k of the constructed DB-k, the utilization of sensors as well as the average number of sensors per DB-. It is known that the strength of the constructed DB-k increases with the value of k. Since the centralized MDP tries all possible paths, it constructs a DB-k with the maximal k and the result can be treated as the optimal solution. The SA has a poor

5 performance because that the DM current in SA only looks forward to find DM next without applying branch and backtracking policies. As soon as a DM current fails to find the next qualified grid, the construction of DB-k is failure. As a result, it constructs a DB-k with smallest k (degree of barrier coverage) and results in the lowest utilization of the sensor nodes. Nevertheless, the SA always looks forward to construct a DB-k and the constructed DBk is composed of several straight line segments. Hence its average number of sensors per DB- outperforms the other three compared mechanisms. The BTA constructs higher degree of defense barrier than the SA because it adopts backtracking policy whenever a dead end grid is encountered. Therefore, BTA gives more opportunities to construct a DB-k with higher degree than SA. The BRA adopts the branch policy to construct the DB-k and hence further utilize the weak grids.consequently, the BRA outperforms SA and BTA in terms of the maximal value of defense degree. branch policy to utilize the weak grids first and then applies SA to construct DB- as more as possible. Whenever the DM current fails to find the next qualified grid, the backtracking policy is further applied. In Fig., the two combination mechanisms outperform the other three compared mechanisms. In comparison, BRA+SA+BTA mechanism has a better performance than SA+BRA+BTA mechanism in terms of the number of constructed DB-. This is because that the branch policy applied first in the BRA+SA+BTA mechanism help to utilize the weak grids and thus gives more opportunities to construct a successful DB-. Table. The comparison of SA, BTA, BRA and MDP in terms of k, utilization, and average number of active sensor per DB-. SA BTA BRA (Branch at first) MDP Maximum k (coverage degree of defense barrier) 9 Utilization of sensors in the Network 8.% 9.%.%.% Average number of waked up sensors per DB Figure investigates the numbers of DB- and DB- constructed by applying SA, BTA, BRA and MDP by varying the number of deployed sensors ranging from to. The BRA adopts branch policy to further invite the weak grids participating in the defense barrier. Therefore, the BRA outperforms BTA and SA and approaches to the optimal performance produced by MDP. Figure. The numbers of DB- and DB- constructed by applying SA, BTA, BRA and MDP It is interesting that the backtracking and branch policies can be integrated to obtain a better performance in constructing a DBk. Figure investigates the performance improvement by integrating the SA, BTA, BRA with different orders. The individual SA, BTA and BRA are compared with the combinational mechanisms in terms of the number of constructed DB-. The SA+BRA+BTA mechanism applies SA algorithm first and then further applies branch and backtracking policies whenever the DM current fails to find the next qualified grid. Unlike SA+BRA+BTA mechanism, the BRA+SA+BTA mechanism adopts Figure. The comparison of SA, BTA, BRA and their combinations in terms of the different order for constructing DB-. Conclusions Barrier Coverage is an important application for country s boundary defense and intruder detection. This paper initially partitions the network region into grids to simplify the problem. Then we propose a decentralized SA mechanism to cope with the k-barrier coverage problem. In addition, the BTA and BRA mechanisms that adopt branch and backtracking policies are proposed to further improve the performance of SA. Simulation study shows that the proposed BRA outperforms SA and BTA and likely approaches to the optimal performance of constructing DBk in case of k. In addition, the combinational mechanism BRA+SA+BTA outperforms the other compared mechanisms in terms of the number of constructed DB-k.. References []. S. Kumar, T. H. Lai, and A. Arora, Barrier Coverage with Wireless Sensors, in MobiCom, pp. 8-98,. []. A. Schrijver. Combinatorial Optimization : Polyhedra and efficiency, Springer, ISBN ,. []. Changxiang Shen, Weifang Cheng, Xiangke Liao, and Shaoliang Peng, Barrier Coverage with Mobile Sensors, in ISPAN 8, pp. 99-, 8. []. Ai Chen, Ten H. Lai, and Dong Xuan, Measuring and Guaranteeing Quality of Barrier-Coverage in Wireless Sensor Networks, in ACM MobiHoc, pp. -, 8. []. Ai Chen, Santosh Kumor, and Ten H. Lai, Designing Localized Algorithms for Barrier Coverage, in ACM MobiCom, pp. -,. 8