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A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint

Willem Jan van Hoeve
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Abstract

This paper presents an algorithm that achieves hyper-arc consistency for the soft alldifferent constraint. To this end, we prove and exploit the equivalence with a minimum-cost flow problem. Consistency of the constraint can be checked in O(nm) time, and hyper-arc consistency is achieved in O(m) time, where n is the number of variables involved and m is the sum of the cardinalities of the domains. It improves a previous method that did not ensure hyper-arc consistency.

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Willem Jan van Hoeve. 2004-07-16. A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint. https://arxiv.org/abs/cs/0407043

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