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. The authors consider a class of wireless multicast hyper-graphs not limited by interference and are mainly characterized by their hyper-arc rate functions, that are increasing and convex in power, and decreasing in distance between the transmit node and the farthest end node of the hyper-arc. 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.