---
title: "Local Consistency for Ternary Numeric Constraints"
authors:
  - "Boi Faltings"
  - "Esther M. Gelle"
doi: ""
url: "https://ijcai.org/proceedings/1997/58"
pdf: "https://ijcai.org/proceedings/1997/0058.pdf"
venue: "Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence"
year: 1997
pages: "392-396"
track: "Constraint Satisfaction"
keywords:
---

# Local Consistency for Ternary Numeric Constraints

Boi Faltings, Esther M. Gelle

*Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence*, pages 392-396.

## Abstract

We consider algorithms of the Waltz type for computing local consistency (also called arcconsistency) for constraints over numeric domains. Many commonly used propagation rules do not in fact enforce local consistency. We extend the propa&ation rule given by Faltings [Faltings, 1994j to the case of ternary constraints. Since any general n-ary continuous constraint can be represented as a collection of ternary ones, this also covers n-ary constraints in general. We show how the propagation can be implemented efficiently. The new algorithm gives significantly tighter labellings than previous propagation algorithms on most problems.