The symmetric cardinality constraint is described in terms of a set of variables X={x 1,...,x k }, which take their values as subsets of values V={v 1,...,v n }. It constraints the cardinality of the set assigned to each variable to be in an interval [l x i ,c x i ] and at the same time it restricts the number of occurrences of each value v j inV in the sets assigned to variables in X to be in an other interval [l v j ,c v j ]. In this paper we introduce the symmetric cardinality constraint and define set constraint satisfaction problem as a framework for dealing with this type of constraints. Moreover, we present effective filtering methods for the symmetric cardinality constraint.


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  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows. In: Theory, algorithms and applications, Prentice-Hall Inc., Englewood Cliffs (1993)Google Scholar
  2. 2.
    Laurière, J.-L.: A language and a program for stating and solving combinatorial problems. Artificial Intelligence 10, 29–127 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Régin, J.-C.: Generalized Arc Consistency for Global Cardinality Constraint. In: Proc. of the Fourteenth National Conference on Artificial Intelligence (AAAI 1996) (1996) Google Scholar
  4. 4.
    Lawler, E.: Combinatorial Optimization: Network and Matroids. Holt, Rinehart and Winston (1976)zbMATHGoogle Scholar
  5. 5.
    Ahuja, R.K., Kodialam, A., Mishra, A.K., Orlin, J. B.: Computational Investigations of Maximum Flow Algorithms. European Journal of Operational Research, 97 (1997) 509–542 Google Scholar
  6. 6.
    Tarjan, R. E.: Depth–First Search and Linear Graph Algorithms. SIAM J. Computing, 1 (1972) 146–160Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Waldemar Kocjan
    • 1
  • Per Kreuger
    • 2
  1. 1.Mälardalen UniversityVästeråsSweden
  2. 2.Swedish Institute Of Computer ScienceKistaSweden

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