Low-complexity non-uniform demand multicast network coding problems

TL;DR

This paper identifies specific non-uniform demand multicast network coding scenarios that can be solved efficiently in polynomial time by relating them to graph coloring problems and leveraging the strong perfect graph theorem.

Contribution

It characterizes non-uniform demand network coding problems that are solvable in polynomial time, linking them to graph coloring and perfect graph theory.

Findings

Polynomial-time solvable demand scenarios identified

Relation established between demand problems and graph coloring

Application of strong perfect graph theorem to network coding

Abstract

The non-uniform demand network coding problem is posed as a single-source and multiple-sink network transmission problem where the sinks may have heterogeneous demands. In contrast with multicast problems, non-uniform demand problems are concerned with the amounts of data received by each sink, rather than the specifics of the received data. In this work, we enumerate non-uniform network demand scenarios under which network coding solutions can be found in polynomial time. This is accomplished by relating the demand problem with the graph coloring problem, and then applying results from the strong perfect graph theorem to identify coloring problems which can be solved in polynomial time. This characterization of efficiently-solvable non-uniform demand problems is an important step in understanding such problems, as it allows us to better understand situations under which the NP-complete problem might be tractable.