Arc-consistency for continuous variables

doi:10.1016/0004-3702(94)90022-1

Artificial Intelligence

Volume 65, Issue 2, February 1994, Pages 363-376

https://doi.org/10.1016/0004-3702(94)90022-1 Get rights and content

Abstract

Davis [1] has investigated the properties of the Waltz propagation algorithm with interval labels in continuous domains. He shows that in most cases the algorithm does not achieve arc-consistency and furthermore is subject to infinite iterations.

In this paper, I show that the main reason for Davis' negative results lies in the way he formulates the propagation rule for the Waltz algorithm. For binary constraints, I propose a different propagation rule and show that it guarantees arc-consistency upon quiescence of the propagation. Generalizations to n-ary constraints are possible but involve more complex geometry.

Arc-consistency guarantees a minimal network only when the constraint graph is a tree. I show that the new formulation of the propagation algorithm rules out the possibility of infinite iterations for all tree-structured constraint networks, and thus obtain a general and reliable algorithm for arc-consistency in continuous domains.

References (8)

E. Davis
Constraint propagation with interval labels
Artif. Intell.
(1987)
R. Dechter et al.
Temporal constraint networks
Artif. Intell.
(1991)
E. Hyvönen
Constraint reasoning based on interval arithmetic: the tolerance propagation approach
Artif. Intell.
(1992)
A.K. Mackworth
Consistency in networks of relations
Artif. Intell.
(1977)

There are more references available in the full text version of this article.

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Research noteArc-consistency for continuous variables

Abstract

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Research note
Arc-consistency for continuous variables