Conference Paper

Making AC-3 an Optimal Algorithm.

Conference: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Seattle, Washington, USA, August 4-10, 2001
Source: DBLP

ABSTRACT

The AC-3 algorithm is a basic and widely used arc consistency enforcing algorithm in Constraint Satisfaction Problems (CSP). Its strength lies in that it is simple, empirically efficient and extensible. However its worst case time complexity was not considered optimal since the first complexity result for AC-3 [Mackworth and Freuder, 1985] with the bound O(ed 3), where e is the number of constraints and d the size of the largest domain. In this paper, we show suprisingly that AC-3 achieves the optimal worst case time complexity with O(ed 2). The result is applied to obtain a path consistency algorithm which has the same time and space complexity as the best known theoretical results. Our experimental results show that the new approach to AC-3 is comparable to the traditional AC-3 implementation for simpler problems where AC-3 is more efficient than other algorithms and significantly faster on hard instances. 1

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    • "De façon plus formelle (Montanari, 1974), (Mackworth, 1977), (Tsang, 1993), on définit un CSP par un triplet (X, D, C) tel que : Étant donné un CSP (X, D, C), sa résolution consiste à affecter des valeurs aux variables de telle sorte que toutes les contraintes soient simultanément satisfaites. 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 & Régin, 2001), (Zhang &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 & Elliot, 1980), (Nadel, 1989), Maintaining Arc-Consistency (Sabin & Freuder, 1994Dechter & Dechter, 1988). "
    Preview · Article · Nov 2014
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    • "Résoudre un CSP est un problème NP-complet. La 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]). "
    Preview · Article · Jun 2012
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    • "In this section, we evaluate the behavior of 2-C4 with wellknown arc-consistency algorithms used in the CSP community: AC3 [25], AC2001/3.1 [10] [31]; AC4 [26] 2 ; AC6 [8], AC7 [9] and 2-consistency algorithms: 2-C3OPL [4] and AC3NH [3]. The algorithms AC4-NN and 2-C4 look for all the supports of each value, while other algorithms (AC3, AC2001/3.1, "
    [Show abstract] [Hide abstract] ABSTRACT: Arc-Consistency algorithms are the most commonly used filtering techniques to prune the search space in Constraint Satisfaction Problems (CSPs). 2-consistency is a similar technique that guarantees that any instantiation of a value to a variable can be consistently extended to any second variable. Thus, 2-consistency can be stronger than arc-consistency in binary CSPs. In this work we present a new algorithm to achieve 2-consistency called 2-C4. This algorithm is a reformulation of AC4 algorithm that is able to reduce unnecessary checking and prune more search space than AC4. The experimental results show that 2-C4 was able to prune more search space than arc-consistency algo-rithms in non-normalized instances. Furthermore, 2-C4 was more efficient than other 2-consistency algorithms presented in the literature.
    Full-text · Article · Jun 2012 · International journal of innovative computing, information & control: IJICIC
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