New optimal solution to disjoint set K-coverage for lifetime extension in wireless sensor networks

Lifetime extension is a fundamental concern in wireless sensor networks (WSNs) owing to the limited energy of each sensor. Random and dense deployment of sensors in many applications impose some coverage redundancy in WSNs, which motivates methods to avoid such redundancy for extending the overall lifetime of the networks. An effective method for this purpose is to divide the sensors into a maximum number of disjoint groups called covers, each of which can cover all targets, so that only one cover is active at any time. The problem of obtaining the maximum number of covers has been proved to be NP-hard. In this study, an optimal method is proposed for the problem. The proposed method is based on the transformation of the problem into the well-known Boolean satisfiability (SAT) problem. Simulation results indicate that the proposed method is superior to existing genetic (GAMDSC) and heuristic (MCMCC) methods. Moreover, as an optimal algorithm, it guarantees obtaining an optimum solution, whereas the existing (meta)heuristic algorithms do not. In addition, we extend the proposed method to the K-coverage problem, where each target is supposed to be covered by at least K number of nodes.