Undirected Unicast Network Capacity: A Partition Bound

TL;DR

This paper introduces a new partition bound technique for estimating the maximum information flow in undirected unicast networks, providing tight bounds for certain network classes and methods to improve the bound's accuracy.

Contribution

It presents a novel partition bound method, characterizes its tightness for specific networks, and offers algorithms to compute and tighten the bound.

Findings

Partition bound accurately estimates network capacity for certain classes.

Routing achieves capacity in networks where the bound is tight.

The bound can be loosened, with methods proposed to improve it.

Abstract

In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in undirected unicast networks and give an algorithm to compute it. Two classes of networks are presented for which the bound is tight and the capacity is achievable by routing thus confirming the undirected unicast conjecture for these classes of networks. We also show that the bound can be loose in general and present an approach to tighten it.