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Engineering a Preprocessor for Symmetry Detection

Authors Markus Anders, Pascal Schweitzer, Julian Stieß

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Author Details

Markus Anders
  • TU Darmstadt, Germany
Pascal Schweitzer
  • TU Darmstadt, Germany
Julian Stieß
  • University of Koblenz-Landau, Germany

Funding

Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (EngageS: grant No. {820148}).

Acknowledgements

We thank Marc E. Pfetsch and Christopher Hojny for giving us further insights into the user-side of symmetry detection software, as well as providing us with the MIP2017 graphs.

Cite As Get BibTex

Markus Anders, Pascal Schweitzer, and Julian Stieß. Engineering a Preprocessor for Symmetry Detection. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SEA.2023.1

Abstract

State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes.
We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the preprocessor improves the overall running time significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible. 
Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such, the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • graph isomorphism
  • automorphism groups
  • symmetry detection
  • preprocessors

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Supplementary Materials

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