An Optimal Coarse-grained Arc Consistency Algorithm

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An Optimal Coarse-grained Arc Consistency Algorithm

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by Christian Bessiere , Roland H. C. Yap , Yuanlin Zhang

Venue:	Artificial Intelligence
Citations:	92 - 16 self

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@ARTICLE{Bessiere_anoptimal,
    author = {Christian Bessiere and Roland H. C. Yap and Yuanlin Zhang},
    title = {An Optimal Coarse-grained Arc Consistency Algorithm},
    journal = {Artificial Intelligence},
    year = {},
    pages = {2005}
}

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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 effec-tive 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. How-ever, 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 op-timal 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 consis-tency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints. Preliminary versions of this paper appeared in [BR01, ZY01].

Keyphrases

coarse-grained algorithm fine-grained algorithm optimal coarse-grained arc consistency algorithm constraint solver effec-tive fashion path consis-tency algorithm constraint propagation heavy data structure propagation algorithm case time complexity prime importance preliminary version non-optimal worst case complexity general constraint big advantage best-known time worst case corresponding value non-binary constraint new algorithm related variable main feature experimental result space complexity

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