J. Parallel Distrib. Comput. 72 (2012) 1654–1663 Contents lists available at SciVerse ScienceDirect J. Parallel Distrib. Comput. journal homepage: www.elsevier.com/locate/jpdc Constructing sensor barriers with minimum cost in wireless sensor networks Jun He a,∗ , Hongchi Shi b a College of Optical Sciences, University of Arizona, 1630 E. University Boulevard, Tucson, AZ 85721, United States b Department of Computer Science, Texas State University-San Marcos, 601 University Drive, San Marcos, TX 78666, United States article info Article history: Received 24 September 2010 Received in revised form 1 June 2012 Accepted 24 July 2012 Available online 1 August 2012 Keywords: Wireless sensor network Barrier coverage Minimum cost flow Distributed algorithm Complexity analysis Asynchronous communications abstract One major application category for wireless sensor networks is to detect intruders entering protected areas. Early research has studied the barrier coverage problem for intruder detection. However, an open problem is to build sensor barriers with minimum cost in wireless sensor networks. This is a critical problem (called minimum-cost barrier coverage), and its solution can be widely used in sensor barrier applications, such as border security and intruder detection. In this paper, we present a complete solution to the minimum-cost barrier coverage problem. The cost here can be any performance measurement and normally is defined as the resource consumed or occupied by the sensor barriers. Our algorithm, called the PUSH–PULL-IMPROVE algorithm, is the first one that provides a distributed solution to the minimum-cost barrier coverage problem in asynchronous wireless sensor networks. It can be used for protected areas of any size and shape with homogeneous or heterogeneous networks. In our algorithm, each node does not necessarily know its exact location and only needs to communicate with its neighbors. For a deployment of n sensors and a cost measurement with maximum value C max , our algorithm has O(n 2 log(nC max )) message complexity and O(n 2 log(nC max )) time complexity to find K barriers. Simulation results verify the performance of the algorithm. We observe that the actual number of messages sent in the simulations is much less than n 2 . © 2012 Elsevier Inc. All rights reserved. 1. Introduction One of the major application categories for wireless sensor networks (WSNs) is to detect intrusion in protected areas. For example, in border surveillance and homeland security, sensor barriers are used to detect intruders illegally crossing the protected border. A sensor barrier is formed by sensing areas of a set of active wireless sensor nodes. In order to detect all intrusion events, the barrier cannot contain any gap, and this is referred to as a strong barrier [15]. In this paper, we only consider the scenario of strong barriers. Sensors are usually dropped by airplanes or launched by artilleries onto a field. It is quite hard to determine sensor locations and network topology before the deployment. Thus, the deployed sensor nodes usually have to self-organize to set up the barriers in a distributed manner. Also, it is impractical to designate a sink to collect all sensor nodes’ information and centrally configure the network because it has a high communication cost and requires a powerful super-node which is usually unavailable. So, a distributed algorithm is more desirable, which reduces the chance of network failure and improves the network survivability ∗ Corresponding author. E-mail addresses: junhe@ieee.org (J. He), hs15@txstate.edu (H. Shi). and reliability. Furthermore, due to unreliable communication channels in wireless sensor networks, the algorithm has to be able to work asynchronously. Normally, sensor nodes are only equipped with weak computa- tion processors with little memory space and powered by batter- ies with limited energy. Therefore, an effective algorithm should build barriers with low message complexity to preserve the energy in each node and only activate the sensor nodes with minimum cost to form the barriers to extend the lifetime of the wireless sen- sor network. Here, the cost can be any performance measurement, and normally it is defined as the resource consumed or occupied by the sensor barriers. For example, it can be the energy cost (such as communication and sensing energy consumption) of the barrier coverage, a cost associated with the residual battery level in each sensor, or the number of sensor nodes activated for the barrier cov- erage. Any non-negative integer cost function can be incorporated into our algorithm. In case of non-integer costs, we can discretize the costs and then scale them into non-negative integer numbers so that the algorithm can handle them. In recent years, the barrier coverage problem has become an emerging subject of research [15,8,3,17,4,22,24,23,16,18,13, 5,19,20]. The concept of barrier coverage was first introduced in a robotic system [8]. More details of barrier coverage were given in [15]. Kumar et al. defined the notion of barrier coverage using wireless sensors and proposed a centralized algorithm to 0743-7315/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jpdc.2012.07.004