An Approximate Approach for Area Coverage in Wireless Sensor Networks

In Wireless Sensor Networks (WSNs), coverage is a critical issue that has a major bearing on the quality of sensing over the target region. In this paper, we study the coverage of a region P with a transparent boundary and transparent obstacles. A transparent obstacle is an area in which a sensor cannot be deployed but through which sensing signals can pass. For cost-effectiveness, our problem is to deploy the minimum number of sensors to cover P excluding the obstacles. This problem is challenging mainly due to the fact that the target region is continuous. A straight-forward idea is to sample a finite set of crucial coverage points in P, thus making the coverage space discrete. Most existing approaches, however, tend to either require too many sampled points, which leads to increased running time, or have an inferior coverage of the region. We propose a discretization approach which converts the area coverage problem into the problem of Minimum Geometric Disk Cover with Candidate Positions (MGDCCP) which is proved to be strongly NP-hard. We present a polynomial-time approximation scheme (PTAS) based on the shifting strategy for the MGDCCP problem. Specifically, our approach guarantees covering a (1 − ε) fraction of the region with probability no less than (1 − ε h ) using at most (1 + l ) 2h sensors, where h is the theoretical minimal number of sensors needed to cover the region P, l is a positive integer parameter in the shifting strategy, and ε ∈ (0, 1) is the covering tolerance. Furthermore, we show that our proposed approach is output-sensitive with time complexity that is polynomial in the input size and the optimal solution size. Therefore, for any fixed parameter l and ε, the coverage accuracy, the running time, the approximation ratio and the success probability are all bounded. c © 2011 Published by Elsevier Ltd.