Reliability of wireless sensor grids

Wireless sensor networks (WSNs) have many applications in industry and environmental monitoring where sensor nodes are deployed at fixed places for monitoring some phenomena. One of the commonly used deterministic deployment topologies is a rectangular grid. In a WSN reliability measure that considers the aggregate flow of sensor data into a sink node is formulated, and it has been shown that computing this measure for an arbitrary WSN is #P-hard. Thus, it is unlikely that efficient algorithms for solving the problem exist. In this paper we consider a WSN deployed on rectangular W times L grid (WSG) and show that the problem remains #P-hard even when restricted to the grid graph model. We then present a routing scheme upon which we develop an O(nL2^W) algorithm to compute the exact WSG reliability. Therefore, for W << L (thin grid or strip area) the algorithm is polynomial in n, while for a rectangle with arbitrary dimensions the running time is O(nradicn2^radicn). We also present numerical results that demonstrate some of the potential applications of the algorithm. A noteworthy finding is that significant improvement in the WSG reliability can be achieved using more reliable sensors at the two boundaries adjacent to the sink node.