Compositional Derivation of Symmetries for Constraint Satisfaction

  • Pascal Van Hentenryck
  • Pierre Flener
  • Justin Pearson
  • Magnus Ågren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3607)

Abstract

This paper reconsiders the problems of discovering symmetries in constraint satisfaction problems (CSPs). It proposes a compositional approach which derives symmetries of the applications from primitive constraints. The key insight is the recognition of the special role of global constraints in symmetry detection. Once the symmetries of global constraints are available, it often becomes much easier to derive symmetries compositionally and efficiently. The paper demonstrates the potential of this approach by studying several classes of value and variable symmetries and applying the resulting techniques to two non-trivial applications. The paper also discusses the potential of reformulations and high-level modeling abstractions to strengthen symmetry discovery.

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References

  1. 1.
    Backofen, R., Will, S.: Excluding symmetries in constraint-based search. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 73–87. Springer, Heidelberg (1999)Google Scholar
  2. 2.
    Bakewell, A., Frisch, A.M., Miguel, I.: Towards automatic modelling of constraint satisfaction problems: A system based on compositional refinement. In: Proceedings of CP 2003 Workshop on Modelling and Reformulating Constraint Satisfaction Problems (2003), Available at http://www-users.cs.york.ac.uk/~frisch/Reformulation/03/
  3. 3.
    Barnier, N., Brisset, P.: Solving the Kirkman’s schoolgirl problem in a few seconds. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 477–491. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Journal of Mathematical and Computer Modelling 20(12), 97–123 (1994)MATHCrossRefGoogle Scholar
  5. 5.
    Choueiry, B.Y., Noubir, G.: On the computation of local interchangeability in discrete constraint satisfaction problems. In: Proceedings of AAAI 1998, pp. 326–333 (1998)Google Scholar
  6. 6.
    Choueiry, B.Y., Davis, A.M.: Dynamic bundling: Less effort for more solutions. In: Koenig, S., Holte, R.C. (eds.) SARA 2002. LNCS (LNAI), vol. 2371, pp. 64–82. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Eriksson, M.: Detecting Symmetries in Relational Models of CSPs. Master’s thesis, Computing Science, Department of Information Technology, Uppsala University, Sweden (2005)Google Scholar
  8. 8.
    Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Flener, P., Frisch, A.M., Hnich, B., Kızıltan, Z., Miguel, I., Pearson, J., Walsh, T.: Breaking row and column symmetries in matrix models. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 462–476. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Focacci, F., Milano, M.: Global cut framework for removing symmetries. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 77–92. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Focacci, F., Lodi, A., Milano, M.: Optimization-oriented global constraints. Constraints 7(3-4), 351–365 (2002)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Fox, M., Long, D.: Extending the exploitation of symmetries in planning. In: Proceedings of AIPS 2002 (2002)Google Scholar
  13. 13.
    Freuder, E.C.: Eliminating interchangeable values in constraint satisfaction problems. In: Proceedings of AAAI 1991, pp. 227–233 (1991)Google Scholar
  14. 14.
    Gent, I.P., Smith, B.M.: Symmetry breaking during search in constraint programming. In: Proceedings of ECAI 2000, pp. 599–603 (2000)Google Scholar
  15. 15.
    Gent, I.P., McDonald, I., Miguel, I., Smith, B.M.: Approaches to conditional symmetry breaking. In: Proceedings of SymCon 2004 (2004)Google Scholar
  16. 16.
    Johnson, E., Nemhauser, G., Savelsbergh, M.: Progress in linear programming-based algorithms for integer programming: An exposition. INFORMS Journal on Computing 12, 2–23 (2000)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Lal, A., Choueiry, B.Y.: Dynamic detection and exploitation of value symmetries for non-binary finite CSPs. In: Proceedings of SymCon 2003 (2003)Google Scholar
  18. 18.
    Michel, L., Van Hentenryck, P.: A constraint-based architecture for local search. In: Proceedings of OOPSLA 2002, ACM SIGPLAN Notices, vol. 37(11), pp. 101–110 (2002)Google Scholar
  19. 19.
    Puget, J.-F.: On the satisfiability of symmetrical constrained satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 350–361. Springer, Heidelberg (1993)Google Scholar
  20. 20.
    Puget, J.-F.: Symmetry breaking revisited. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 446–461. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Puget, J.-F.: Symmetry breaking using stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–599. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  22. 22.
    Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of AAAI 1994 (1994)Google Scholar
  23. 23.
    Régin, J.-C.: Arc consistency for global cardinality constraints with costs. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 390–404. Springer, Heidelberg (1999)Google Scholar
  24. 24.
    Roy, P., Pachet, F.: Using symmetry of global constraints to speed up the resolution of constraint satisfaction problems. In: Proceedings of the ECAI 1998 Workshop on Non-Binary Constraints, pp. 27–33 (1998)Google Scholar
  25. 25.
    Van Hentenryck, P., Flener, P., Pearson, J., Ågren, M.: Tractable symmetry breaking for CSPs with interchangeable values. In: Proceedings of IJCAI 2003, pp. 277–282. Morgan Kaufmann, San Francisco (2003)Google Scholar
  26. 26.
    Van Hentenryck, P.: Constraint and integer programming in OPL. INFORMS Journal on Computing 14(4), 345–372 (2002)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Pascal Van Hentenryck
    • 1
  • Pierre Flener
    • 2
  • Justin Pearson
    • 2
  • Magnus Ågren
    • 2
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Information TechnologyUppsala UniversityUppsalaSweden

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