Multiset Ordering Constraints

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.