Fundamental Results on Target Coverage Problem in Wireless Sensor Networks

The target coverage problem is one of the most fundamental challenges in wireless sensor networks. Due to the complexity of the problem (time-dependent network topology and coverage constraints), previous studies have mainly focused on heuristic algorithms and the theoretical bound remains unknown. In this paper, we aim to fill in this gap by providing fundamental results. First, we investigate the properties of a problem in time domain via an example topology and build a novel transformation to connect a problem in the time domain with a corresponding problem in the space domain while maintaining the same network lifetime. Based on this transformation, we mathematically formulate the problem and build a column-generation based algorithm, which decomposes the original formulation into two sub-formulations and iteratively solves them in a way that approaches the optimal solution. We prove that the network lifetime that can be guaranteed by the proposed algorithm is at least (1-e) of the optimum, where e can be made arbitrarily small depending on the required precision.