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An Adaptive Prefix-Assignment Technique for Symmetry Reduction

  • Tommi Junttila
  • Matti KarppaEmail author
  • Petteri Kaski
  • Jukka Kohonen
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10491)

Abstract

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay’s canonical extension framework [J. Algorithms 26 (1998), no. 2, 306–324]. Among key features of the technique are (i) adaptability—the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelisability—prefix-assignments can be processed in parallel independently of each other; (iii) versatility—the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability—the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the tentative practical applicability of our technique we have prepared a preliminary implementation and report on a limited set of experiments that demonstrate ability to reduce symmetry on hard instances.

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Notes

Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 338077 “Theory and Practice of Advanced Search and Enumeration” (M.K., P.K., and J.K.). We gratefully acknowledge the use of computational resources provided by the Aalto Science-IT project at Aalto University. We thank Tomi Janhunen for useful discussions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tommi Junttila
    • 1
  • Matti Karppa
    • 1
    Email author
  • Petteri Kaski
    • 1
  • Jukka Kohonen
    • 1
  1. 1.Department of Computer ScienceAalto UniversityEspooFinland

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