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Breaking symmetries in graph search with canonizing sets

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Abstract

There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration. We also demonstrate the application of a generalization of our approach to fully-interchangeable matrix search problems.

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Acknowledgments

We thank the anonymous reviewers of this paper for their constructive suggestions. In particular the addition of Section 5 is in view of the comments of the reviewers.

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Authors and Affiliations

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

    Avraham Itzhakov & Michael Codish

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  1. Avraham Itzhakov
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  2. Michael Codish
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Correspondence to Michael Codish.

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Supported by the Israel Science Foundation, grant 182/13.

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Itzhakov, A., Codish, M. Breaking symmetries in graph search with canonizing sets. Constraints 21, 357–374 (2016). https://doi.org/10.1007/s10601-016-9244-z

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