Relay node placement under budget constraint

The relay node placement problem in the wireless sensor network domain has been studied extensively. But under a fixed budget, it may be impossible to procure the minimum number of relay nodes needed to design a connected network of sensor and relay nodes. Nevertheless, one would still like to design a network with high level of connectedness, or low disconnectedness. In this paper, we introduce the notion of a measure of the “connectedness” of a disconnected graph. We study a family of problems whose goal is to design a network with “maximal connectedness” subject to a fixed budget constraint.