Ad Hoc Networking Under Limitations on Sum Power Interference to an External Node

The purpose of this work is to connect wireless nodes to form an ad hoc network, while trying to limit the interference to a node or device that is external to the network. Specifically, we consider two forms of the problem of limiting interference caused by the emitted power required to form the connections within a network. First, we consider a case where the interference at the external node cannot exceed some power threshold, and we would like to connect as many nodes together to form a tree without exceeding that threshold. We call this the Largest Constrained Tree (LCT) problem, which we model as a graph where the cost to connect a pair of nodes is the sum of the interference caused by transmitting in each direction. The second form of the problem we consider is the case where the power incident on the external node must be minimized, and we would like to connect nodes to form a network backbone, specifically a connected dominating set (CDS). As an approximation, we model the power emitted by the leaf nodes to the CDS as a smaller fixed amount, due to the transmission being out of band or having directionality gain. To solve these problems, we formulate them as mixed integer linear programs, and we demonstrate their performance through Monte Carlo simulation for various network sizes, node densities, external node distances, and network activity levels.