Relay node placement in wireless sensor networks

A wireless sensor network consists of many low-cost, low-power sensor nodes, which can perform sensing, simple computation, and transmission of sensed information. Long distance transmission by sensor nodes is not energy efficient since energy consumption is a superlinear function of the transmission distance. One approach to prolonging network lifetime while preserving network connectivity is to deploy a small number of costly, but more powerful, relay nodes whose main task is communication with other sensor or relay nodes. In this paper, we assume that sensor nodes have communication range r > 0, while relay nodes have communication range R >= r, and we study two versions of relay node placement problems. In the first version, we want to deploy the minimum number of relay nodes so that, between each pair of sensor nodes, there is a connecting path consisting of relay and/or sensor nodes. In the second version, we want to deploy the minimum number of relay nodes so that, between each pair of sensor nodes, there is a connecting path consisting solely of relay nodes. We present a polynomial time 7-approximation algorithm for the first problem and a polynomial time (5 + epsilon)-approximation algorithm for the second problem, where epsilon > 0 can be any given constant.