A boundary of wireless sensor networks (WSNs) can be used in many fields, for example, to monitor a frontier or a secure place of strategic sensitive sites like oil fields or frontiers of a country. This situation is modeled as the problem of finding a polygon hull in a connected Euclidean graph, which represents a minimal set of connected boundary nodes. In this paper we propose a new algorithm called D-LPCN (Distributed Least Polar-angle Connected Node) which represents the distributed version of the LPCN algorithm introduced in [1]. In each iteration, any boundary node, except the first one, chooses its nearest polar angle node among its neighbors with respect to the node found in the previous iteration. The first starting node can be automatically determined using the Minimum Finding algorithm, which has two main advantages. The first one is that the algorithm works with any type of a connected network, given as planar or not. Furthermore, it takes into account any blocking situation and contains the necessary elements to avoid them. The second advantage is that the algorithm can determine all the boundaries of the different connected parts of the network. The proposed algorithm is validated using the CupCarbon, Tossim and Contiki simulators. It has also been implemented using real sensor nodes based on the TelosB and Arduino/XBee platforms. We have estimated the energy consumption of each node and we have found that the consumption of the network depends on the number of the boundary nodes and their neighbors. The simulation results show that the proposed algorithm is less energy consuming than the existing algorithms and its distributed version is less energy consuming than the centralized version.

Finding the polygon hull in a connected Euclidean graph can be considered as the problem of finding the convex hull with the exception that at any iteration a vertex can be chosen only if it is connected to the vertex chosen at the previous iteration. One of the methods that can be used for this kind of problems is Jarvis' algorithm which allows to find the convex hull and which must be adapted because it does not take into account the connections of the nodes. In this paper, we propose a new algorithm that chooses for a current node and among its neighbors in the graph the nearest polar angle node with respect to the node found in the previous iteration. Its complexity is O(gh 2), where g is the maximum degree of the graph and h the number of the nodes on the hull. For ease of presentation, we first identify some specific graph-structures whose presence may lead a basic version of the algorithm to fail, and we then show how to modify that version to obtain a procedure of the given complexity. Finally, we present some practical applications that can be resolved using the proposed algorithm.

The challenge in the deployment of wireless sensor networks is to ensure the coverage of targets with high energy efficiency, particularly when coverage constraint and energy constraint must be taken into account. Many algorithms have been suggested over the years to enhance network lifetime as sensor nodes are powered by batteries. These algorithms divide a set of sensor nodes into a number of subsets which can monitor all targets. The subsets are either joint or disjoint. In this paper, we propose an efficient method to compute the maximum lifetime target coverage. Our proposed method is centered around a target that is covered by a minimum number of sensor nodes. Based on this approach, we also propose an algorithm to expand the network lifetime which guarantees the monitoring of all targets by forming subsets of sensor nodes. Our obtained results are compared with the work reported in [1]. They are also compared with a method of computing the maximum lifetime target coverage (MLTC). The results obtained by simulation show that the proposed algorithm enhances the network lifetime, which illustrates the efficiency of this algorithm.

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