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An Optimal Coarsegrained Arc Consistency Algorithm
 Artificial Intelligence
"... 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: finegrained algorithms where the removal of a val ..."
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Cited by 93 (16 self)
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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: finegrained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarsegrained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarsegrained algorithms, like AC3, over finegrained algorithms, like AC4, is the ease of integration when implementing an algorithm in a constraint solver. However, finegrained algorithms usually have optimal worst case time complexity while coarsegrained algorithms don’t. For example, AC3 is an algorithm with nonoptimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarsegrained 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 finegrained algorithms such as AC6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the bestknown time and space complexity. The same idea is then extended to nonbinary constraints. Preliminary versions of this paper appeared in [BR01, ZY01].
The Complexity of Global Constraints
, 2004
"... We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular ..."
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Cited by 87 (27 self)
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We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, metaconstraints like the cardinality constraint, and learning nogoods.
Global Constraints for Lexicographic Orderings
, 2002
"... We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show ..."
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Cited by 86 (35 self)
Global Constraints for Lexicographic Orderings
, 2002
"... We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show ..."