---
title: "Multiset Ordering Constraints"
authors:
  - "Alan M. Frisch"
  - "Ian Miguel"
  - "Zeynep Kiziltan"
  - "Brahim Hnich"
  - "Toby Walsh"
doi: ""
url: "https://ijcai.org/proceedings/2003/32"
pdf: "https://ijcai.org/proceedings/2003/0032.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "221-225"
track: ""
keywords:
---

# Multiset Ordering Constraints

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

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 221-225.

## Abstract

We identify a new and important global (or nonbinary) constraint which 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 a linear time algorithm for enforcing generalised arc-consistency on such a multiset ordering constraint. Experimental results show considerable promise.