Best and worst-case coverage problems for arbitrary paths in wireless sensor networks

The path-based coverage of a wireless sensor network is to analyze how well the network covers the sensor field in terms of paths. Known results prior to this research, however, considered only a single source–destination pair and thus do not provide a global outlook at the given network but a local feature for the given source–destination pair. In this paper, we propose a new coverage measure of sensor networks that considers arbitrary source–destination pairs. Our novel measure naturally extends the previous concept of the best and the worst-case path-based coverage to evaluate the coverage of a given network from a global point of view, taking arbitrary paths into account. In terms of the present coverage measure, we pose the evaluation and the deployment problems for give a network; the former is to evaluate the new coverage measure of a given sensor network, and the latter is to find an optimal placement of k additional sensor nodes to improve the coverage for a given positive integer k. We present several algorithms that are either centralized or localized that solve the problems with theoretical proofs and simulation results, thus showing that our algorithms are efficient and easy to implement in practice while the quality of their outputs is guaranteed by formal proofs. For the purpose, we show an interesting relation between the present coverage measure and a certain quantity of a point set, called the bottleneck, which has been relatively well studied in other disciplines such as computational geometry and operations research.