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 Sat- isfaction 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 (ed3), 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 opti- mal worst case time complexity with (ed2). The result is applied to obtain a path consistency algo- rithm which has the same time and space complex- ity as the best known theoretical results. Our exper- imental results show that the new approach to AC-3 is comparable to the traditional AC-3 implementa- tion for simpler problems where AC-3 is more effi- cient than other algorithms and significantly faster on hard instances. simplicity of arc revision in AC-3 makes it convenient for implementation and amenable to various extensions for many constraint systems. Thus while AC-3 is considered as being sub-optimal, it often is the algorithm of choice and can out- perform other theoretically optimal algorithms. In this paper, we show that AC-3 achieves worst case op- timal time complexity of (ed2). This result is surprising since AC-3 being a coarse grained "arc revision" algorithm (Mackworth, 1977), is considered to be non-optimal. The known results for optimal algorithms are all on fine grained "value revision" algorithms. Preliminary experiments show that the new AC-3 is comparable to the traditional implemen- tations on easy CSP instances where AC-3 is known to be substantially better than the optimal fine grained algorithms. In the hard problem instances such as those from the phase transition, the new AC-3 is significantly better and is compa- rable to the best known algorithms such as AC-6. We also show that the results for AC-3 can be applied immediately to obtain a path consistency algorithm which has the same time and space complexity as the best known theoretical results. 1

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: a b s t r a c t This paper concerns project scheduling under resource constraints. Traditionally, the objective is to find a unique solution that minimizes the project makespan, while respecting the precedence constraints and the resource constraints. This work focuses on developing a model and a decision support framework for industrial application of the cumulative global constraint. For a given project scheduling, the proposed approach allows the generation of different optimal solutions relative to the alternate availability of out-sourcing and resources. The objective is to provide a decision-maker an assistance to construct, choose, and define the appropriate scheduling program taking into account the possible capacity resources. The industrial problem under consideration is modeled as a constraint satisfaction problem (CSP). It is imple-mented under the constraint programming language CHIP V5. The provided solutions determine values for the various variables associated to the tasks realized on each resource, as well as the curves with the profile of the total consumption of resources on time.
    Computers & Industrial Engineering 09/2010; 61:357-363. · 1.69 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Les techniques de suppression de symÈtries dÈveloppÈes pour la programmation par contraintes ont pour objectif d'amÈliorer l'efficacitÈ des mÈthodes de rÈsolution en rÈduisant drastiquement la taille de l'espace de recherche. ParallËlement, les mÈthodes de rÈsolution rÈcentes, telles que les mÈthodes rÈtro-prospectives, permettent de s'attaquer ‡ des problËmes de plus en plus grands, que ce soit par la taille des domaines ou le nombre de variables considÈrÈes, et dont l'espace de recherche augmente bien s˚r lui aussi. Il paraÓt donc intÈressant de faire profiter les mÈthodes rÈtro-prospectives des amÈliorations permises par les techniques de suppression de symÈtries qui ont cependant ÈtÈ dÈveloppÈes pour un cadre plus classique d'exploration. Dans cet article, nous proposons donc un algorithme hybridant une mÈthode rÈtro-prospective (textttdecision-repair) et une technique gÈnÈrique de suppression de symÈtries (SBDS). Nous prÈsentons plusieurs approches pour exprimer et traiter efficacement dans ce cadre les contraintes liÈes ‡ la suppression des symÈtries. De premiers rÈsultats expÈrimentaux valident la dÈmarche.
    2Ëmes JournÈes Francophones de Programmation par Contraintes (JFPC'06); 06/2006
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Summary form only given. Our aim is to maintain the global consistency of a constraint satisfaction problem involving temporal constraints any time a new constraint is added. This problem is of practical relevance since it is often required to check whether a solution to a CSP continues to be a solution when a new constraint is added and if not, whether a new solution satisfying the old and new constraints can be found. The two methods that we present are respectively a complete search technique based on constraint propagation and an approximation method based on stochastic local search. The goal of both methods is to check whether the existence of a solution is maintained any time a new constraint is added. The approximation method does not guarantee the completeness of the solution provided, but is of interest for those problems where it is impossible or impractical to find a complete solution. This is the case for real time applications where a solution should be returned within a given deadline and over constrained problems where a complete solution does not exist.
    Computer Systems and Applications, 2003. Book of Abstracts. ACS/IEEE International Conference on; 08/2003


Available from