  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 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, we present simple and efficient
algorithms to solve these problems.
