Efficiently Computing Maximum Flows in Scale-Free Networks

TL;DR

This paper introduces a new algorithm for maximum flow problems in scale-free networks that significantly outperforms existing methods in speed and efficiency, especially on real-world large-scale networks.

Contribution

The authors propose a simple, efficient algorithm combining Dinitz's method with bidirectional search, optimized for scale-free networks, achieving sublinear run times and easier cut extraction.

Findings

Achieves up to 100x faster performance than Push-Relabel on real-world networks.

Reduces search space by a factor of 275 compared to original Dinitz's algorithm.

Computes Gomory-Hu trees in seconds on large social networks.

Abstract

We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz's algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz's original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph. Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.