Optimal Placement of Relay Nodes for Energy Efficiency in Sensor Networks

Energy efficient system design in wireless sensor networks has been previously discussed at different levels of the network protocol stack so as to provide the maximum possible lifetime of a given network. This paper proposes a novel idea to save energy through extra re lay nodes by eliminating geometric deficiencies of the given topology. Given the sensing locations, the problem is to determine the optimal locations of relay nodes together with the optimal energy provided to them so that the network is alive during the desired lifetime with minimum total energy. We first formulate the problem as a nonlinear programming problem. We then propose an approximation algorithm based on restricting the locations where the relay nodes are allowed to a square lattice. This algorithm approximates the original problem with performance ratio of as low as 2 by trading complexity. For the parking lot application we consider, the relay nodes provide a significant decrease in the total energy required to achieve a specific lifetime.