Optimal relay placement in Wireless Sensor networks using node cut inequalities

Optimal relay placement problem arises in wireless sensor network designs, where additional relay nodes are to be placed at a subset of given potential relay locations in order to transmit data from already existing source nodes to a base station known as root node. The relay nodes have a certain specified transmission radius and cannot transmit data beyond it. In this paper, we consider the projection of original problem onto the sub-space of relay node variables and identify a set of strong inequalities called node cut inequalities. We also propose an integer programming based approach for solving the problem using these inequalities. The computational results show that the node cut inequality based formulation provides a very tight lower bound for the problem, and can be helpful in solving the problem optimally under a branch-and-cut approach.