ε-Net Approach to Sensor k-Coverage

Wireless sensors rely on battery power, and in many applications it is difficult or prohibitive to replace them. Hence, in order to prolongate the system's lifetime, some sensors can be kept inactive while others perform all the tasks. In this paper, we study the k-coverage problem of activating the minimum number of sensors to ensure that every point in the area is covered by at least k sensors. This ensures higher fault tolerance, robustness, and improves many operations, among which position detection and intrusion detection. The k-coverage problem is trivially NP-complete, and hence we can only provide approximation algorithms. In this paper, we present an algorithm based on an extension of the classical epsilon-net technique. This method gives an O(logM)-approximation, where M is the number of sensors in an optimal solution. We do not make any particular assumption on the shape of the areas covered by each sensor, besides that they must be closed, connected, and without holes.