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Breaking Symmetries in Graphs: The Nauty Way

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Principles and Practice of Constraint Programming (CP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9892))

Abstract

Symmetry breaking is an essential component when solving graph search problems as it restricts the search space to that of canonical representations. There are an abundance of powerful tools, such as nauty, which apply to find the canonical representation of a given graph and to test for isomorphisms given a set of graphs. In contrast, for graph search problems, current symmetry breaking techniques are partial and solvers unnecessarily explore an abundance of isomorphic parts of the search space. This paper is novel in that it introduces complete symmetry breaking for graph search problems by modeling, in terms of constraints, the same ideas underlying the algorithm applied in tools like nauty. Whereas nauty tests given graphs, symmetry breaks restrict the search space and apply during generation.

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Notes

  1. 1.

    We restrict our consideration here to static symmetry breaking, rather than dynamic approaches such as SBDS [7] or LDSB [8].

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Michael Codish & Avraham Itzhakov

  2. Department of Computing and Information Systems, The University of Melbourne, Melbourne, Australia

    Graeme Gange & Peter J. Stuckey

  3. Data61 CSIRO, Melbourne, Australia

    Peter J. Stuckey

Authors
  1. Michael Codish
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  2. Graeme Gange
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  3. Avraham Itzhakov
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  4. Peter J. Stuckey
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Corresponding author

Correspondence to Michael Codish .

Editor information

Editors and Affiliations

  1. University of Nice Sophia Antipolis , Sophia Antipolis, France

    Michel Rueher

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© 2016 Springer International Publishing Switzerland

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Codish, M., Gange, G., Itzhakov, A., Stuckey, P.J. (2016). Breaking Symmetries in Graphs: The Nauty Way. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_11

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  • DOI: https://doi.org/10.1007/978-3-319-44953-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44952-4

  • Online ISBN: 978-3-319-44953-1

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