We propose an adaptive heuristic for model restarts that aligns symmetry breaking with the dynamic branching heuristic. Experiments show that this method performs very well compared to other symmetry breaking methods.


Symmetry Breaking Constraint Programming Precedence Constraint Constraint Satisfaction Problem Dynamic Symmetry Breaking 
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.
    Puget, J.F.: On the satisfiability of symmetrical constrained satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS (LNAI), vol. 689, pp. 350–361. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  2. 2.
    Shlyakhter, I.: Generating effective symmetry-breaking predicates for search problems. In: Proc. of Workshop on Theory and Applications of Satisfiability Testing, SAT 2001 (2001)Google Scholar
  3. 3.
    Flener, P., Frisch, A.M., Hnich, B., Kiziltan, 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. 462–477. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Law, Y., Lee, J.: Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction. Constraints 11(2-3), 221–267 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Walsh, T.: Symmetry breaking using value precedence. In: Proc. of ECAI 2006, pp. 168–172 (2006)Google Scholar
  6. 6.
    Walsh, T.: General Symmetry Breaking Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 650–664. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Walsh, T.: Breaking value symmetry. In: Proc. of the 23rd National Conf. on AI, pp. 1585–1588. AAAI (2008)Google Scholar
  8. 8.
    Gent, I., Smith, B.: Symmetry breaking in constraint programming. In: Proc. of ECAI 2000, pp. 599–603 (2000)Google Scholar
  9. 9.
    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
  10. 10.
    Hentenryck, P.V., Agren, M., Flener, P., Pearson, J.: Tractable symmetry breaking for CSPs with interchangeable values. In: Proc. of the 18th IJCAI (2003)Google Scholar
  11. 11.
    Flener, P., Pearson, J., Sellmann, M., Van Hentenryck, P.: Static and dynamic structural symmetry breaking. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 695–699. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Heller, D., Panda, A., Sellmann, M., Yip, J.: Model restarts for structural symmetry breaking. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 539–544. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    ChocoTeam: Documentation. CHOCO is a java library for constraint satisfaction problems (CSP) and constraint programming (CP),
  14. 14.
    Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Katsirelos, G., Walsh, T.: Symmetries of symmetry breaking constraints. In: Proc. of ECAI 2010 (2010)Google Scholar
  16. 16.
    Walsh, T.: Breaking value symmetry. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 880–887. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Crawford, J., Luks, G., Ginsberg, M., Roy, A.: Symmetry breaking predicates for search problems. In: Proc. of the 5th Int. Conf. on Knowledge Representation and Reasoning (KR 1996), pp. 148–159 (1996)Google Scholar
  18. 18.
    Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Information Processing Letters 47, 173–180 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: Proc. of the 16th ECAI 2004, pp. 146–150 (2004)Google Scholar
  20. 20.
    Gomes, C., Selman, B., Crato, N.: Heavy-tailed distributions in combinatorial search. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 121–135. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Frisch, A.M., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Global constraints for lexicographic orderings. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 93–108. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  22. 22.
    Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Propagation algorithms for lexicographic ordering constraints. Artificial Intelligence 170(10), 803–908 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Law, Y.C., Lee, J.H.M., Walsh, T., Yip, J.Y.K.: Breaking symmetry of interchangeable variables and values. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 423–437. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Katsirelos, G., Narodytska, N., Walsh, T.: Combining symmetry breaking and global constraints. In: Oddi, A., Fages, F., Rossi, F. (eds.) CSCLP 2008. LNCS, vol. 5655, pp. 84–98. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  25. 25.
    Jefferson, C., Kelsey, T., Linton, S., Petrie, K.: GAPLex: Generalised static symmetry breaking. In: Proc. of 6th Int. Workshop on Symmetry in Constraint Satisfaction Problems, SymCon 2006 (2006)Google Scholar
  26. 26.
    Puget, J.-F.: Symmetry breaking using stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–599. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nina Narodytska
    • 1
  • Toby Walsh
    • 1
  1. 1.NICTA and UNSWSydneyAustralia

Personalised recommendations