An Analysis on Minimum s-t Cut Capacity of Random Graphs with Specified Degree Distribution

TL;DR

This paper provides a probabilistic analysis and a lower bound for the distribution of minimum s-t cut capacity in random graphs with specified degree distributions, aiding understanding of network flow in uncertain topologies.

Contribution

It introduces a lower bound for the distribution of minimum s-t cut capacity in weighted random graphs with arbitrary degree distributions, validated by experiments.

Findings

Lower bound closely matches empirical data

Distribution analysis aids in network capacity prediction

Applicable to networks with dynamic or unknown topologies

Abstract

The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not so trivial to predict statistical properties on the maximum flow of the network. In this paper, we present a probabilistic analysis for evaluating the accumulate distribution of the minimum s-t cut capacity on random graphs. The graph ensemble treated in this paper consists of weighted graphs with arbitrary specified degree distribution. The main contribution of our work is a lower bound for the accumulate distribution of the minimum s-t cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum s-t cut capacity of random graphs with specified degrees.