A Hyper-Arc Consistency Algorithm for the Soft Alldifferent Constraint

TL;DR

This paper introduces a new algorithm that enforces hyper-arc consistency for the soft alldifferent constraint efficiently by leveraging a minimum-cost flow problem, improving upon previous methods.

Contribution

The paper presents a novel hyper-arc consistency algorithm for the soft alldifferent constraint, with proven equivalence to a minimum-cost flow problem and improved computational complexity.

Findings

Consistency check in O(nm) time

Hyper-arc consistency achieved in O(m) time

Outperforms previous methods that lacked hyper-arc consistency

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.