Coverage in wireless ad hoc sensor networks

Sensor networks pose a number of challenging conceptual and optimization problems such as location; deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. We provide efficient distributed algorithms to optimally solve the best-coverage problem raised in [1]. In addition, we consider a more general sensing model: The sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption and how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.