The constraint NValue 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.


Constraint Satisfaction Problem Intersection Graph Interval Graph Maximal Match Linear Relaxation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christian Bessiere
    • 1
  • Emmanuel Hebrard
    • 2
  • Brahim Hnich
    • 3
  • Zeynep Kiziltan
    • 4
  • Toby Walsh
    • 2
  1. 1.LIRMMCNRS/University of MontpellierFrance
  2. 2.NICTA and UNSWSydneyAustralia
  3. 3.4C and UCCCorkIreland
  4. 4.University of BolognaItaly

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