While several powerful methods exist for automatically detecting symmetries in instances of constraint satisfaction problems (CSPs), current methods for detecting symmetries in CSP models are limited to the kind of symmetries that can be inferred from the global constraints present in the model. Herein, a new approach for detecting symmetries in CSP models is presented. The approach is based on first applying powerful methods to a sequence of problem instances, and then reasoning on the resulting instance symmetries to infer symmetries of the model. Our results show that this approach deserves further exploration.


Constraint Satisfaction Problem Global Constraint Board Size Solution Symmetry Parameterised Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cohen, D., Jeavons, P., Jefferson, C., Petrie, K.E., Smith, B.M.: Symmetry Definitions for Constraint Satisfaction Problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 17–31. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting Structure in Symmetry Generation for CNF. In: 41st Design Automation Conference, pp. 530–534 (2004)Google Scholar
  3. 3.
    Frisch, A.M., Miguel, I., Walsh, T.: CGRASS: A System for Transforming Constraint Satisfaction Problems. In: O’Sullivan, B. (ed.) CologNet 2002. LNCS (LNAI), vol. 2627, pp. 15–30. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.4.9 (2006)Google Scholar
  5. 5.
    Gent, I.P., Harvey, W., Kelsey, T., Linton, S.: Generic SBDD using Computational Group Theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Gent, I.P., Smith, B.M.: Symmetry Breaking in Constraint Programming. In: ECAI 2000. 14th European Conference on Artificial Intelligence (2000)Google Scholar
  7. 7.
    Haselböck, A.: Exploiting Interchangeabilities in Constraint-Satisfaction Problems. In: IJCAI 1993, pp. 282–289 (1993)Google Scholar
  8. 8.
    Mancini, T., Cadoli, M.: Detecting and Breaking Symmetries by Reasoning on Problem Specifications. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Mears, C., de la Banda, M.G., Wallace, M.: On Implementing Symmetry Detection. In: SymCon 2006 (2006)Google Scholar
  10. 10.
    Puget, J.-F.: Symmetry Breaking Revisited. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 446–461. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Puget, J.-F.: Automatic Detection of Variable and Value Symmetries. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 475–489. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Romani, A., Markov, I.L.: Automatically Exploiting Symmetries in Constraint Programming. In: Danelutto, M., Vanneschi, M., Laforenza, D. (eds.) Euro-Par 2004. LNCS, vol. 3149, pp. 98–112. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Roney-Dougal, C.M., Gent, I.P., Kelsey, T., Linton, S.: Tractable Symmetry Breaking using Restricted Search Trees. In: ECAI 2004 (2004)Google Scholar
  14. 14.
    Roy, P., Pachet, F.: Using Symmetry of Global Constraints to Speed Up the Resolution of Constraint Satisfaction Problems. In: ECAI 1998 Workshop on Non-binary Constraints, pp. 27–33 (1998)Google Scholar
  15. 15.
    Sellmann, M., Van Hentenryck, P.: Structural Symmetry Breaking. In: IJCAI 2005 (2005)Google Scholar
  16. 16.
    Van Hentenryck, P., Flener, P., Pearson, J., Ågren, M.: Compositional Derivation of Symmetries for Constraint Satisfaction. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, Springer, Heidelberg (2005)Google Scholar
  17. 17.
    Walsh, T.: General Symmetry Breaking Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christopher Mears
    • 1
  • Maria Garcia de la Banda
    • 1
  • Mark Wallace
    • 1
  • Bart Demoen
    • 2
  1. 1.Monash UniversityAustralia
  2. 2.Katholieke Universiteit LeuvenBelgium

Personalised recommendations