On minimum cost coverage in wireless sensor networks

A solution to the coverage problem in wireless sensor networks provides the total number of sensors that are required to cover a given area of deployment. While prior studies have proposed different formulations and solutions to this problem, these studies have not addressed the problem of minimum cost coverage in which full coverage is achieved by using the minimum number of sensor nodes for an arbitrary geometric shape region. In this paper, we present a geometric solution to the minimum cost coverage problem under a deterministic deployment. Furthermore, we present a probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region. We demonstrate that for virtually 100% probability of coverage, random deployment needs approximately seven times more sensors as compared to a deterministic setup.