Breaking symmetry of interchangeable variables and values

  • Authors:

  • Y. C. Law;J. H. M. Lee;Toby Walsh;J. Y. K. Yip

  • Affiliations:

  • Deparment of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Deparment of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;National ICT Australia and School of CSE, University of New South Wales, Sydney, Australia;Deparment of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

  • Venue:
  • CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
  • Year:
  • 2007

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Abstract

A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, pruning all symmetric values is NP-hard. We introduce a new global constraint called SIGLEX and its GAC propagator for pruning some (but not necessarily all) symmetric values. We also investigate how different postings of the SIGLEX constraints affect the pruning performance during constraint solving. Finally, we test these static symmetry breaking constraints experimentally for the first time.