Reducibility of joint relay positioning and flow optimization problem

TL;DR

This paper introduces a method to simplify the complex joint relay positioning and flow optimization problem in wireless multicast networks by decoupling it into two manageable problems, with efficient algorithms for each.

Contribution

It presents a novel reduction approach that transforms a hard joint problem into two simpler problems, along with efficient algorithms for solving them.

Findings

Reduction of the joint problem into two simpler problems

Development of efficient algorithms for relay positioning and flow optimization

Demonstration of the approach's effectiveness in wireless multicast hypergraphs

Abstract

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.