A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint
<|reference_start|>A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint: 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.<|reference_end|>
@article{van hoeve2004a,
    title={A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint},
    author={Willem Jan van Hoeve},
    journal={arXiv preprint arXiv:cs/0407043},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0407043},
    primaryClass={cs.PL}
}