Advertisement

Consistency and Propagation with Multiset Constraints: A Formal Viewpoint

  • Toby Walsh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2833)

Abstract

We study from a formal perspective the consistency and propagation of constraints involving multiset variables. That is, variables whose values are multisets. These help us model problems more naturally and can, for example, prevent introducing unnecessary symmetry into a model. We identify a number of different representations for multiset variables and compare them. We then propose a definition of local consistency for constraints involving multiset, set and integer variables. This definition is a generalization of the notion of bounds consistency for integer variables. We show how this local consistency property can be enforced by means of some simple inference rules which tighten bounds on the variables. We also study a number of global constraints on set and multiset variables. Surprisingly, unlike finite domain variables, the decomposition of global constraints over set or multiset variables often does not hinder constraint propagation.

Keywords

Inference Rule Constraint Programming Domain Variable Bound Representation Integer Variable 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gervet, C.: Conjunto: constraint logic programming with finite set domains. In: Bruynooghe, M. (ed.) Proc. of the 1994 Int. Symp. on Logic Programming, pp. 339–358. MIT Press, Cambridge (1994)Google Scholar
  2. 2.
    Müller, T., Müller, M.: Finite set constraints in Oz. In: Bry, F., Freitag, B., Seipel, D. (eds.) 13th Logic Programming Workshop, TU München, pp. 104–115 (1997)Google Scholar
  3. 3.
    Proll, L., Smith, B.: Integer linear programming and constraint programming approaches to a template design problem. INFORMS Journal on Computing 10, 265–275 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Gervet, C.: Interval Propagation to Reason about Sets: Definition and Implementation of a Practical Language. Constraints 1, 191–244 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Régin, J.: A filtering algorithm for constraints of difference in CSPs. In: Proc. of the 12th National Conference on AI, American Association for AI, pp. 362–367 (1994)Google Scholar
  6. 6.
    Beldiceanu, N.: Global constraints as graph properties on a structured network of elementary constraints of the same type. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 52–66. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Gent, I., Stergiou, K., Walsh, T.: Decomposable constraints. Artificial Intelligence 123, 133–156 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dovier, A., Piazza, C., Pontelli, E., Rossi, G.: Set and constraint logic programming. ACM Trans. on Programming Languages and Systems 22, 861–931 (2000)CrossRefGoogle Scholar
  9. 9.
    Legeard, B., Legros, E.: Short overview of the CLPS system. In: Małuszyński, J., Wirsing, M. (eds.) PLILP 1991. LNCS, vol. 528, pp. 431–433. Springer, Heidelberg (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Toby Walsh
    • 1
  1. 1.Cork Constraint Computation CenterUniversity College CorkIreland

Personalised recommendations