The Optimal Deployment, Coverage, and Connectivity Problems in Wireless Sensor Networks: Revisited

Finding an optimal node deployment strategy in wireless sensor networks (WSNs) that would reduce cost, be robust to node failures, reduce computation, and communication overhead, and guarantee a high level of coverage along with network connectivity is a difficult problem. In fact, sensing coverage and network connectivity are two of the most fundamental problems in WSNs as they can directly impact the network lifetime and operation. In this paper, we consider deriving optimal conditions for connectivity with coverage in WSNs. Most versions of this problem are (NP-complete), while approximation algorithms cannot be developed for some versions of polynomial time, unless P = NP. Hence, we also develop a heuristic for some versions of the problem and the efficacy of the heuristic will be evaluated through extensive simulations. We are also interested in determining the probability of finding a path between a given pair of nodes over a given topology of WSNs. This will serve as a measure of connectivity with coverage of the network. Hence, we derive necessary and sufficient conditions for connectivity with coverage over a clustered structure in WSNs. Then, employing queuing networks modeling techniques, we present a dynamic programming study of the connectivity with coverage of clustered structure and its effect on routing in generalized WSNs. The performance evaluation of the proposed schemes shows that availability of nodes, sensor node coverage, and the connectivity were sufficiently enhanced to maximize network lifetime.