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Symmetry-Preserving Graph Compression

Authors Markus Anders , Manuel Penschuck , Pascal Schweitzer

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LIPIcs.ESA.2026.7.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • symmetry detection
  • graph automorphisms
  • preprocessing
  • color refinement
  • approximation hardness
  • mathematical programming

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Abstract

Exploiting symmetry is a well-established technique to eliminate redundant work in combinatorial solvers, yet it often incurs computational overhead that limits its practical impact. In particular, practical instances arising from applications are frequently large and give rise to graphs whose size becomes a major bottleneck for algorithms dealing with symmetry.
We propose a method for symmetry-preserving graph compression that reduces graph size while preserving the symmetries of the original graph in a controlled way. Our approach identifies and merges equivalent vertex colors under conditions that guarantee the recoverability of all symmetries. We provide both a theoretical foundation and efficient practical criteria for such merges, show that computing optimal and approximately optimal compression is intractable, and introduce a linear-time, practical heuristic. Extensive experiments on a vast library of graphs demonstrate that our new technique achieves significant compression ratios. Implemented in the state-of-the-art symmetry detection tool dejavu, we achieve an overall speedup of 1.39, with large modern SAT and MIP benchmarks benefiting the most.

Cite As Get BibTex

Markus Anders, Manuel Penschuck, and Pascal Schweitzer. Symmetry-Preserving Graph Compression. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.7

Author Details

Markus Anders
  • RPTU Kaiserslautern-Landau, Germany
Manuel Penschuck
  • University of Southern Denmark, Odense, Denmark
Pascal Schweitzer
  • TU Darmstadt, Germany

Funding

This work was partially funded by the Novo Nordisk Foundation grant NNF21OC0066551.

Acknowledgements

We thank Christopher Hojny for providing the MIPLIB graphs used in our experiments. A substantial part of the computation for this project was performed on the UCloud interactive HPC system managed by the eScience Center at the University of Southern Denmark.

Supplementary Materials

References

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