Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Kirchweger, Markus; Szeider, Stefan https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-153257
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SAT Modulo Symmetries for Graph Generation

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Abstract

We propose a novel constraint-based approach to graph generation. Our approach utilizes the interaction between a CDCL SAT solver and a special symmetry propagator where the SAT solver runs on an encoding of the desired graph property. The symmetry propagator checks partially generated graphs for minimality w.r.t. a lexicographic ordering during the solving process. This approach has several advantages over a static symmetry breaking: (i) symmetries are detected early in the generation process, (ii) symmetry breaking is seamlessly integrated into the CDCL procedure, and (iii) the propagator can perform a complete symmetry breaking without causing a prohibitively large initial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of girth and diameter. With our approach, we could confirm the Simon-Murty Conjecture (1979) on diameter-2-critical graphs for graphs up to 18 vertices.

BibTeX - Entry

@InProceedings{kirchweger_et_al:LIPIcs.CP.2021.34,
  author =	{Kirchweger, Markus and Szeider, Stefan},
  title =	{{SAT Modulo Symmetries for Graph Generation}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15325},
  URN =		{urn:nbn:de:0030-drops-153257},
  doi =		{10.4230/LIPIcs.CP.2021.34},
  annote =	{Keywords: symmetry breaking, SAT encodings, graph generation, combinatorial search, extremal graphs, CDCL}
}

Keywords: symmetry breaking, SAT encodings, graph generation, combinatorial search, extremal graphs, CDCL
Seminar: 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)
Issue date: 2021
Date of publication: 15.10.2021
Supplementary Material: Software (Source Code): https://doi.org/10.5281/zenodo.5170575


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