Graph Invariants as Necessary Conditions for Global Constraints

  • Nicolas Beldiceanu
  • Mats Carlsson
  • Jean-Xavier Rampon
  • Charlotte Truchet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3709)


This article presents a database of about 200 graph invariants for deriving systematically necessary conditions from the graph properties based representation of global constraints. This scheme is based on invariants on the graph characteristics used in the description of a global constraint. A SICStus Prolog implementation based on arithmetic and logical constraints as well as on indexicals is available.




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  1. 1.
    Dincbas, M., Simonis, H., Van Hentenryck, P.: Solving the car-sequencing problem in constraint logic programming. In: Kodratoff, Y. (ed.) 8th European Conference on Artificial Intelligence, ECAI 1988, Munich, Germany, August 1988, pp. 290–295. Pitmann Publishing, London (1988)Google Scholar
  2. 2.
    Frisch, A., Miguel, I., Walsh, T.: Extensions to proof planning for generating implied constraints. In: Proceedings of Calculemus (2001)Google Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical Report T2005-06, Swedish Institute of Computer Science (2005)Google Scholar
  4. 4.
    Beldiceanu, N.: Pruning for the Minimum Constraint Family and for the Number of Distinct Values Constraint Family. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 211–224. Springer, Heidelberg (2001); Preprint available as SICS Tech Report T2000-10CrossRefGoogle Scholar
  5. 5.
    Bessière, C., Hebrard, E., Hnich, B., Kızıltan, Z., Walsh, T.: Filtering algorithms for the nvalue constraint. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 79–93. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Turán, P.: On an extremal problem in graph theory. Mat. Fiz. Lapok 48, 436–452 (1941) (In Hungarian)MATHMathSciNetGoogle Scholar
  7. 7.
    COSYTEC. CHIP Reference Manual, release 5.1 edition (1997)Google Scholar
  8. 8.
    Régin, J.-C.: A filtering algorithm for constraints of difference in CSP. In: 12th National Conference on Artificial Intelligence (AAAI 1994), pp. 362–367 (1994)Google Scholar
  9. 9.
    Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Mathl. Comput. Modelling 20(12), 97–123 (1994)MATHCrossRefGoogle Scholar
  10. 10.
    Beldiceanu, N., Flener, P., Lorca, X.: The tree constraint. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 64–78. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Carlsson, M., et al.: SICStus Prolog User’s Manual. Swedish Institute of Computer Science, 3.11.1 edition (February 2004),
  12. 12.
    Van Hentenryck, P., Saraswat, V., Deville, Y.: Constraint processing in cc(FD) (Manuscript 1991)Google Scholar
  13. 13.
    Carlson, B., Carlsson, M., Diaz, D.: Entailment of finite domain constraints. In: Van Hentenryck, P. (ed.) ICLP 1994, Int. Conf. on Logic Programming, S. Margherita Ligure, Italy. MIT Press Series in Logic Programming. The MIT Press, Cambridge (1994)Google Scholar
  14. 14.
    Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Beldiceanu, N., Petit, T., Rochart, G.: Bounds of graph characteristics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 742–746. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Mats Carlsson
    • 2
  • Jean-Xavier Rampon
    • 3
  • Charlotte Truchet
    • 3
  1. 1.LINA FRE CNRS 2729Nantes Cedex 3France
  2. 2.SICSKistaSweden
  3. 3.LINA FRE CNRS 2729Nantes Cedex 3France

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