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


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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    • "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]). "
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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, "
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    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.
    International journal of innovative computing, information & control: IJICIC 06/2012; 8(6). · 1.66 Impact Factor
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    • "MAC suppresses inconsistent values in the domain of all uninstantiated variables. Although CB-FC was considered as the best instantiation algorithm for a long time [29], MAC is now recognized as one of the most performing existing method [36]. "
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    ABSTRACT: In this paper, we propose mechanisms to improve instantiation heuristics by incorporating weighted factors on variables. The proposed weight-based heuristics are evaluated on several tree search methods such as chronological backtracking and discrepancy-based search for both constraint satisfaction and optimization problems. Experiments are carried out on random constraint satisfaction problems, car sequencing problems, and jobshop scheduling with time-lags, considering various parameter settings and variants of the methods. The results show that weighting mechanisms reduce the tree size and then speed up the solving time, especially for the discrepancy-based search method.
    Journal of Mathematical Modelling and Algorithms 06/2012; 11(2). DOI:10.1007/s10852-012-9174-8
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