Optimisation problems based on the maximal breach path measure for wireless sensor network coverage

Abstract

Coverage is a central issue in the design of wireless sensor networks. There are many measures for coverage, based on what aspect of surveillance quality we wish to address. Designing a network that achieves desired standards in terms of the measure chosen is a nontrivial problem. In this paper we take the Maximal Breach Path measure and formulate the sensor-network design problem as a geometric optimization problem. We present improved polynomial time algorithms for computing the aforesaid measure for a given sensor network. Also, as a first step toward solving the optimisation problem posed in this paper, we present a geometric transformation on a given configuration of sensors that brings the maximal breach to a “local optimal”-in the sense that the resulting breach is the best we can get keeping the topology of the starting configuration intact.