Budget constrained relay node placement problem for maximal “connectedness”

The relay node placement problem in the wireless sensor network have been studied extensively in the last few years. The goal of most of these problems is to place the fewest number of relay nodes in the deployment area so that the network formed by the sensors nodes and the relay nodes is connected. Most of these studies are conducted for the unconstrained budget scenario, in the sense that there is an underlying assumption that no matter however many relay nodes are needed to make the network connected, they can be procured and deployed. However, in a fixed budget scenario, the expenses involved in procuring the minimum number of relay nodes to make the network connected may exceed the budget. Although in this scenario, one has to give up the idea of having a network connecting all the sensor nodes, one would still like to have a network with high level of “connectedness”. In the paper we introduce two metrics for measuring “connectedness” of a disconnected graph and study the problem whose goal is to design a network with maximal “connectedness”, subject to a fixed budget constraint. We show that both versions of the problem are NP-complete and provide heuristics for their solution. We show that the problem is non-trivial even when the number of sensor nodes is as few as three. We evaluate the performance of heuristics through simulation.