An optimal coarse-grained arc consistency algorithm

Abstract

The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: fine-grained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarse-grained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarse-grained algorithms, like AC-3, over fine-grained algorithms, like AC-4, is the ease of integration when implementing an algorithm in a constraint solver. However, fine-grained algorithms usually have optimal worst case time complexity while coarse-grained algorithms don't. For example, AC-3 is an algorithm with non-optimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarse-grained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best fine-grained algorithms such as AC-6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints.

Planification de chaîne logistique sous incertitude : maintien de solution par satisfaction de contraintes dynamiques

“…Cette résolution est basée sur des techniques de propagation de contraintes (phase de filtrage : réduction de l'espace de recherche en éliminant les valeurs des variables qui n'ont aucune chance d'intervenir dans une solution (Bessière et Régin, 2001 ;Zhang et Yap, 2001 ;Bessière et al, 2005) et sur une stratégie de recherche arborescente (phase de recherche de solutions : énumération des combinaisons de valeurs compatibles entre elles au regard de toutes les contraintes (Real-Full-Look-Ahead, Forward-Checking (Haralick et Elliot, 1980 ;Nadel, 1989), Maintaining Arc-Consistency (Sabin et Freuder, 1994)). …”

Course Scheduling in an Adjustable Constraint Propagation Schema

“…In this context, a propagation algorithms series have been evolved, such as AC-3, AC-5, AC-2001, etc., where 'AC' stands for 'arc-consistency' [19]. There exists a plethora of ways to make one variable of a problem consistent to another, as there are many consistency levels, with the most prominent ones elaborated in Section V.…”

Solving functional constraints by variable substitution

“…(In many of the papers, bifunctional constraints were called functional constraints). The special properties of bi-functional constraints were used to obtain the time complexity better than that of the optimal AC algorithms such as AC2001/3.1 (O(ed 2 )) (Bessiere et al 2005) for arbitrary binary constraints. A fast AC algorithm for a special class of increasing bi-functional constraints was also proposed in (Liu 1995).…”