Generalized Arc Consistency for Global Cardinality Constraint

نویسنده

  • Jean-Charles Régin
چکیده

A global cardinality constraint (gcc) is speci ed in terms of a set of variables X = fx1; :::; xpg which take their values in a subset of V = fv1; :::; vdg. It constrains the number of times a value vi 2 V is assigned to a variable in X to be in an interval [li; ci]. Cardinality constraints have proved very useful in many real-life problems, such as scheduling, timetabling, or resource allocation. A gcc is more general than a constraint of di erence, which requires each interval to be [0; 1]. In this paper, we present an e cient way of implementing generalized arc consistency for a gcc. The algorithm we propose is based on a new theorem of ow theory. Its space complexity is O(jXj jV j) and its time complexity is O(jXj jV j). We also show how this algorithm can e ciently be combined with other ltering techniques.

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تاریخ انتشار 1996