The coverage problem in three-dimensional wireless sensor networks

One of the fundamental issues in sensor networks is the coverage problem, which reflects how well a sensor network is monitored or tracked by sensors. In this paper, we formulate this problem as a decision problem, whose goal is to determine whether every point in the service area of the sensor network is covered by at least α sensors, where α is a given parameter and the sensing regions of the sensors are modeled by balls (not necessarily of the same radius). This problem in a 2D space is solved in (C. F. Huang et al, ACM Int´l W´kshop on Wireless Sensor Networks and App., p.115-12 1, 2003) with an efficient polynomial-time algorithm (in terms of the number of sensors). In this paper, we show that tackling this problem in a 3D space is still feasible within polynomial time. The proposed solution can be easily translated into an efficient polynomial-time distributed protocol.