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Circle Graph 3-Coloring: Can Simplicity Beat SAT?

Authors Robert Ganian , Philipp Mauve , Vaishali Surianarayanan

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Subject Classification

ACM Subject Classification
  • Human-centered computing → Graph drawings
  • Theory of computation
Keywords
  • Circle graphs
  • 3-coloring
  • book embeddings
  • simplicity in algorithms

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Abstract

We study the practical performance of the very recent quasi-polynomial algorithm for Circle Graph 3-Coloring (SOSA 2026 best paper), a problem of significant relevance to graph drawing due to its close connection to 3-page book embeddings. We implement and optimize this combinatorial algorithm and benchmark it against state-of-the-art SAT-based approaches on three sets of instances, the hardest of which required a new generation procedure to obtain non-trivial benchmarks. Across all three, our implementation outperforms the SAT-based approaches, with the largest gap on the most challenging instances.

Cite As Get BibTex

Robert Ganian, Philipp Mauve, and Vaishali Surianarayanan. Circle Graph 3-Coloring: Can Simplicity Beat SAT?. In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.29

Author Details

Robert Ganian
  • TU Wien, Austria
Philipp Mauve
  • TU Wien, Austria
Vaishali Surianarayanan
  • Yale University, New Haven, CT, USA

Funding

  • Ganian, Robert: Vienna Science and Technology Fund (WWTF, Project 10.47379/ICT22029), Austrian Science Fund (FWF, Project 10.55776/Y1329).
  • Surianarayanan, Vaishali: UCSC Chancellor’s Postdoctoral Fellowship and Yale Toni Massini Postdoctoral Fellowship. Part of this work was carried out while the author was at the University of California, Santa Cruz, CA, USA.

Supplementary Materials

References

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    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.27503
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