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Fast Bound Consistency for the Global Cardinality Constraint

  • Irit Katriel
  • Sven Thiel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2833)

Abstract

We show an algorithm for bound consistency of global cardinality constraints, which runs in time \(O(n+n')\phantom{}\) plus the time required to sort the assignment variables by range endpoints, where n is the number of assignment variables and n′ is the number of values in the union of their ranges. We thus offer a fast alternative to Régin’s arc consistency algorithm [6] which runs in time \(O(n^{3/2}n')\phantom{}\) and space \(O(n \cdot{} n')\phantom{}\). Our algorithm can also narrow the bounds for the number of occurrences of each value, which has not been done before.

Keywords

Bipartite Graph Priority Queue Intersection Graph Count Variable Assignment 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.

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References

  1. 1.
    Aho, A., Hopcroft, J., Ullman, J.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)MATHGoogle Scholar
  2. 2.
    Gabow, H.N., Tarjan, R.E.: A Linear-Time Algorithm for a Special Case of Disjoint Set Union. Journal of Computer and System Sciences 30(2), 209–221 (1985)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ford Jr., L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)MATHGoogle Scholar
  4. 4.
    Katriel, I., Thiel, S.: Fast bound consistency for the global cardinality constraint. Research Report MPI-I-2003-1-013, Max-Planck-Institut für Informatik, Saarbrücken, Germany (2003)Google Scholar
  5. 5.
    Mehlhorn, K., Thiel, S.: Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 306–319. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Régin, J.-C.: Generalized Arc-Consistency for Global Cardinality Constraint. In: Proceedings of the 13th National Conference on Artificial Intelligence (AAAI 1996), pp. 209–215 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Irit Katriel
    • 1
  • Sven Thiel
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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