Reasoning by Dominance in Not-Equals Binary Constraint Networks

  • Belaïd Benhamou
  • Mohamed Réda Saïdi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4204)


In this paper, we extend the principle of symmetry to dominance in Not-Equals Constraint Networks and show how dominated values are detected and eliminated efficiently at each node of the search tree.


Search Tree Constraint Satisfaction Problem Graph Coloring Constraint Network Graph Coloring Problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Krishnamurty, B.: Short proofs for tricky formulas. Acta informatica (22), 253–275 (1985)Google Scholar
  2. 2.
    Benhamou, B., Sais, L.: Theoretical study of symmetries in propositional calculus and application. In: CADE-11, Saratoga Springs, NY, USA (1992)Google Scholar
  3. 3.
    Puget, J.F.: On the satisfiability of symmetrical constrained satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689. Springer, Heidelberg (1993)Google Scholar
  4. 4.
    Benhamou, B.: Study of symmetry in constraint satisfaction problems. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Puget, J.F.: Breaking symmetries in all different problems. In: Proceedings of IJCAI, pp. 272–277 (2005)Google Scholar
  6. 6.
    Puget, J.-F.: Breaking all value symmetries in surjection problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 490–504. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Cohen, D., et al.: Symmetry definitions for constraint satisfaction problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 17–31. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Freuder, E.: Eliminating interchangeable values in constraints satisfaction problems. In: Proc AAAI 1991, pp. 227–233 (1991)Google Scholar
  9. 9.
    Benhamou, B.: Theoretical study of dominance in constraint satisfaction problems. In: 6th International Conference on Artificial Intelligence: Methodology, Systems and Applications (AIMSA 1994), Sofia, Bulgaria, September 1994, pp. 91–97 (1994)Google Scholar
  10. 10.
    Benhamou, B., Saïdi, M.R.: Reasoning by dominance in not-equals binary constraint networks. Technical report, LSIS (2006),
  11. 11.
    Benhamou, B.: Symmetry in not-equals binary constraint networks. In: SymCon 2004: 4th International Workshop on Symmetry and Constraint Satisfaction Problems (2004)Google Scholar
  12. 12.
    Sewell, E.C.: An improved algorithm for exact graph coloring. DIMACS series on Discrete Mathematics and Theortical Computer Science (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Belaïd Benhamou
    • 1
  • Mohamed Réda Saïdi
    • 1
  1. 1.Laboratoire des Sciences de l’Information et des Systèmes (LSIS)Centre de Mathématiques et d’InformatiqueMarseilleFrance

Personalised recommendations