---
title: "Decompositions of All Different, Global Cardinality and Related Constraints"
authors:
  - "Christian Bessière"
  - "George Katsirelos"
  - "Nina Narodytska"
  - "Claude-Guy Quimper"
  - "Toby Walsh"
doi: ""
url: "https://ijcai.org/proceedings/2009/77"
pdf: "https://ijcai.org/proceedings/2009/0077.pdf"
venue: "Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence"
year: 2009
pages: "419-423"
track: ""
keywords:
---

# Decompositions of All Different, Global Cardinality and Related Constraints

Christian Bessière, George Katsirelos, Nina Narodytska, Claude-Guy Quimper, Toby Walsh

*Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence*, pages 419-423.

## Abstract

We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver. Christian Bessiere, George Katsirelos, Nina Narodytska, Claude-Guy Quimper, Toby Walsh