License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CP.2022.26
URN: urn:nbn:de:0030-drops-166558
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16655/
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Heule, Marijn J. H. ; Karahalios, Anthony ; van Hoeve, Willem-Jan

From Cliques to Colorings and Back Again

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LIPIcs-CP-2022-26.pdf (0.6 MB)

Abstract

We present an exact algorithm for graph coloring and maximum clique problems based on SAT technology. It relies on four sub-algorithms that alternatingly compute cliques of larger size and colorings with fewer colors. We show how these techniques can mutually help each other: larger cliques facilitate finding smaller colorings, which in turn can boost finding larger cliques. We evaluate our approach on the DIMACS graph coloring suite. For finding maximum cliques, we show that our algorithm can improve the state-of-the-art MaxSAT-based solver IncMaxCLQ, and for the graph coloring problem, we close two open instances, decrease two upper bounds, and increase one lower bound.

BibTeX - Entry

@InProceedings{heule_et_al:LIPIcs.CP.2022.26,
  author =	{Heule, Marijn J. H. and Karahalios, Anthony and van Hoeve, Willem-Jan},
  title =	{{From Cliques to Colorings and Back Again}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{26:1--26:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16655},
  URN =		{urn:nbn:de:0030-drops-166558},
  doi =		{10.4230/LIPIcs.CP.2022.26},
  annote =	{Keywords: Graph coloring, maximum clique, Boolean satisfiability}
}

Keywords: Graph coloring, maximum clique, Boolean satisfiability
Collection: 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)
Issue Date: 2022
Date of publication: 23.07.2022
Supplementary Material: Software (Source Code and Log Files of Experiments): https://github.com/marijnheule/clicolcom

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