Structural Routability of n-Pairs Information Networks

TL;DR

This paper investigates the conditions under which routing alone suffices for data transmission in multi-source, multi-sink networks, introducing the concept of downward dominance to characterize such topologies.

Contribution

It introduces the concept of downward dominance and proves that in such networks, achievability implies the existence of a feasible multicommodity flow.

Findings

Downward dominance characterizes network topologies where routing suffices.

Achievability of source signals implies feasible multicommodity flow in downward dominated networks.

The study applies to cyclic, directed, errorless networks with independent sources.

Abstract

Information does not generally behave like a conservative fluid flow in communication networks with multiple sources and sinks. However, it is often conceptually and practically useful to be able to associate separate data streams with each source-sink pair, with only routing and no coding performed at the network nodes. This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to routability, for any combination of source signals and positive channel capacities. This chapter considers possibly cyclic, directed, errorless networks with n source-sink pairs and mutually independent source signals. The concept of downward dominance is introduced and it is shown that, if the network topology is downward dominated, then the achievability of a given combination of source signals and channel capacities implies the existence of a feasible multicommodity flow.