Set Intersection and Consistency in Constraint Networks

TL;DR

This paper explores the relationship between consistency in constraint networks and set intersection, providing a unifying proof schema and identifying new classes of constraints where local consistency guarantees global consistency.

Contribution

It introduces a generic proof schema linking consistency to set intersection, unifies existing results, and identifies new classes of constraints with guaranteed global consistency.

Findings

Set intersection properties can determine consistency in constraint networks.

A new class of tree convex constraints ensures global consistency from local consistency.

Consistency results extend to networks with only some tight constraints.

Abstract

In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This approach not only simplifies the understanding of and unifies many existing consistency results, but also directs the study of consistency to that of set intersection properties in many situations, as demonstrated by the results on the convexity and tightness of constraints in this paper. Specifically, we identify a new class of tree convex constraints where local consistency ensures global consistency. This generalizes row convex constraints. Various consistency results are also obtained on constraint networks where only some, in contrast to all in the existing work,constraints are tight.