Reducibility of joint relay positioning and flow optimization problem

This paper shows how to reduce the otherwise hard joint relay positioning and flow optimization problem into a sequence a two simpler decoupled problems. We consider a class of wireless multicast hypergraphs not limited by interference and are mainly characterized by their hyperarc rate functions, that are increasing and convex in power, and decreasing in distance between the transmit node and the farthest end node of the hyperarc. The set-up consists of a single multicast flow session involving a source, multiple destinations and a relay that can be positioned freely. The first problem formulates the relay positioning problem in a purely geometric sense, and once the optimal relay position is obtained the second problem addresses the flow optimization. Furthermore, simple and efficient algorithms are presented that solve these problems.