Multiset Ordering Constraints
Alan M. Frisch, Ian Miguel, Zeynep Kiziltan, Brahim Hnich, Toby Walsh

TL;DR
This paper introduces a new global multiset ordering constraint, along with an efficient linear-time algorithm for enforcing generalized arc consistency, demonstrating promising results across various problem domains.
Contribution
It presents a novel multiset ordering constraint and an efficient linear-time algorithm for its enforcement, expanding the toolkit for symmetry breaking and fuzzy constraint satisfaction.
Findings
Efficient linear-time algorithm for multiset ordering constraints
Effective in symmetry breaking and fuzzy constraint satisfaction
Promising experimental results across multiple domains
Abstract
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised arc consistency on such a multiset ordering constraint. Experimental results on several problem domains show considerable promise.
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Data Management and Algorithms · Rough Sets and Fuzzy Logic
