Groups and Constraints: Symmetry Breaking During Search

  • Gent I
  • Harvey W
  • Kelsey T
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Abstract

We present an interface between the ECLiPSe constraint logic programming system and the GAPcomputational abstract algebra system- The interface provides a method for efficiently dealing with large numbers of symmetries of constraint satisfaction problems for minimal programming effort- We also report an implementation of SBDS using the GAP-ECLiPSe interface which is capable of handling many more symmetries than previous implementations and provides improved search performance for symmetric constraint satisfaction problems1 Introduction Dealing with symmetries in constraint satisfaction problems has become quitea popular topic for research in recent years. One of the main areas of recent study has been the modification of backtracking search procedures so that theyonly return unique solutions. Such techniques currently broadly fall into two main categories. The first involves adding constraints whenever backtrackingoccurs, so that symmetric versions of the failed part of the search tree will not be considered in future [1, 12]; we will collectively refer to these techniquesas SBDS (Symmetry Breaking During Search). The second category involves performing checks at nodes in the search tree to see whether they are dominatedby the symmetric equivalent of some state already considered [7, 9]. Note that these two kinds of approaches are closely related; the main difference is whenand how the symmetry-breaking conditions are enforced.

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Authors

  • Ian P Gent

  • Warwick Harvey

  • Tom Kelsey

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