Filtering Algorithms for the NValue Constraint

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.

• Type: Conference
• Year: 2005
• Where: CPAIOR
• Authors: Christian Bessière, Emmanuel Hebrard, Brahim Hnich, Zeynep Kiziltan, Toby Walsh
• Keywords: CPAIOR 2005, Lower Bound, Maximum Independent Set Problem, Tighter Lower Bound