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Practical Expander Decomposition

Authors Lars Gottesbüren, Nikos Parotsidis, Maximilian Probst Gutenberg

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Lars Gottesbüren
  • Karlsruhe Institute of Technology, Germany
Nikos Parotsidis
  • Google Research, Zürich, Switzerland
Maximilian Probst Gutenberg
  • ETH Zürich, Switzerland

Acknowledgements

We thank Isaac Arvestad for open-sourcing a clean and extensible C++ implementation of the Saranurak-Wang algorithm.

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Lars Gottesbüren, Nikos Parotsidis, and Maximilian Probst Gutenberg. Practical Expander Decomposition. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 61:1-61:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.61

Abstract

The expander decomposition of a graph decomposes the set of vertices into clusters such that the induced subgraph of each cluster is a subgraph with high conductance, and there is only a small number of inter-cluster edges. Expander decompositions are at the forefront of recent theoretical developments in the area of efficient graph algorithms and act as a central component in several state-of-the-art graph algorithms for fundamental problems like maximum flow, min-cost flow, Gomory-Hu trees, global min-cut, and more. Despite this crucial role and the existence of theoretically efficient expander decomposition algorithms, little is known on their behavior in practice.
In this paper we explore the engineering design space in implementations for computing expander decompositions. We base our implementation on the near-linear time algorithm of Saranurak and Wang [SODA'19], and enhance it with practical optimizations that accelerate its running time in practice and at the same time preserve the theoretical runtime and approximation guarantees.
We evaluate our algorithm on real-world graphs with up to tens of millions of edges. We demonstrate significant speedups of up to two orders of magnitude over the only prior implementation. To the best of our knowledge, our implementation is the first to compute expander decompositions at this scale within reasonable time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Expander Decomposition
  • Clustering
  • Graph Algorithms

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