Constraints

, Volume 11, Issue 4, pp 271–293 | Cite as

Filtering Algorithms for the NValue Constraint

  • Christian Bessiere
  • Emmanuel Hebrard
  • Brahim Hnich
  • Zeynep Kiziltan
  • Toby Walsh
Article

Abstract

The NValue constraint counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NP-hard. We show that computing even the lower bound on the number of values is NP-hard. We therefore study different approximation heuristics for this problem. We introduce three new methods for computing a lower bound on the number of values. The first two are based on the maximum independent set problem and are incomparable to a previous approach based on intervals. The last method is a linear relaxation of the problem. This gives a tighter lower bound than all other methods, but at a greater asymptotic cost.

Keywords

NValue constraint NP-hard AtleastNValue AtMostNValue pruning linear relaxation global constraints 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Christian Bessiere
    • 1
  • Emmanuel Hebrard
    • 2
  • Brahim Hnich
    • 3
  • Zeynep Kiziltan
    • 4
  • Toby Walsh
    • 2
  1. 1.LIRMM-CNRSMontpellierFrance
  2. 2.National ICT Australia LtdThe University of New South WalesSydneyAustralia
  3. 3.Izmir University of EconomicsIzmirTurkey
  4. 4.University of BolognaBolognaItaly

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