A Centralized Algorithm Based on Voronoi Diagram for Hole Detection Problem in Wireless Sensor Networks

One of the challenging problems in wireless sensor networks is detecting and calculating the area of holes which occur because of several reasons such as accidental death of sensors, explosion in the environment or running out of the energy of the sensors that they all disrupt the task of monitoring wireless sensor networks. When the sensors are distributed randomly in some places like dense forests and rugged terrain, it is possible to detect the holes in the environment. Therefore, in this paper we aim to provide a centralized geometric based algorithm to detect and calculate the area of the holes for a given environment. We investigate hole detection problem for a set of sensors with non-identical sensing radii in both cases: (i) when there is no obstacle in the environment and (ii) when there are some polygonal obstacles in the environment. We propose efficient algorithms for detecting holes in both cases. We calculate the amount of holes and report the boundary edges of the holes using computational geometry approaches. The time complexity of algorithm in case (i) is O(n log2n), and in case (ii) is O(n log2n nm2). The results of the simulation show that the provided algorithms exactly detect all holes in a given environment. Also, we compare the algorithm in case (i) with one of state-of-the-art algorithms in the literature. The comparison result shows efficiency of the proposed algorithm.area.