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An Adaptive Prefix-Assignment Technique for Symmetry Reduction

  • Tommi Junttila
  • Matti KarppaEmail author
  • Petteri Kaski
  • Jukka Kohonen
Conference paper
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.

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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