Expander Hierarchies for Normalized Cuts on Graphs

TL;DR

This paper presents the first practical algorithm for expander decompositions and hierarchies, improving normalized cut clustering solutions significantly on large graphs while maintaining competitive runtimes.

Contribution

It introduces an efficient algorithm for expander hierarchies and demonstrates its effectiveness in a new normalized cut solver with superior solution quality.

Findings

Outperforms state-of-the-art solvers in solution quality on various graph types.

Remains competitive in running time despite improved solution quality.

Effectively applied to large real-world graphs like social and web networks.

Abstract

Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their inherent intricacies and large hidden factors in their asymptotic running times. Here, we introduce the first practically efficient algorithm for computing expander decompositions and their hierarchies and demonstrate its effectiveness and utility by incorporating it as the core component in a novel solver for the normalized cut graph clustering objective. Our extensive experiments on a variety of large graphs show that our expander-based algorithm outperforms state-of-the-art solvers for normalized cut with respect to solution quality by a large margin on a variety of graph classes such as citation, e-mail, and social networks or web graphs while remaining competitive in running time.