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134
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 82 (12 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].
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 79 (36 self)
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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
Dependency parsing by belief propagation
 In Proceedings of EMNLP
, 2008
"... We formulate dependency parsing as a graphical model with the novel ingredient of global constraints. We show how to apply loopy belief propagation (BP), a simple and effective tool for approximate learning and inference. As a parsing algorithm, BP is both asymptotically and empirically efficient. E ..."
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Cited by 64 (7 self)
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We formulate dependency parsing as a graphical model with the novel ingredient of global constraints. We show how to apply loopy belief propagation (BP), a simple and effective tool for approximate learning and inference. As a parsing algorithm, BP is both asymptotically and empirically efficient. Even with secondorder features or latent variables, which would make exact parsing considerably slower or NPhard, BP needs only O(n3) time with a small constant factor. Furthermore, such features significantly improve parse accuracy over exact firstorder methods. Incorporating additional features would increase the runtime additively rather than multiplicatively. 1
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 64 (23 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.
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 56 (4 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
Efficient Solution Techniques for Disjunctive Temporal Reasoning Problems
, 2002
"... Over the past few years, a new constraintbased formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs). The class of DTPs is significantly more expressive than other problems previously studied in constraintbased temporal reasoning. In ..."
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Cited by 50 (14 self)
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Over the past few years, a new constraintbased formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs). The class of DTPs is significantly more expressive than other problems previously studied in constraintbased temporal reasoning. In this paper we present a new algorithm for DTP solving, called Epilitis, which integrates strategies for efficient DTP solving from the previous literature, including conflictdirected backjumping, removal of subsumed variables, and semantic branching, and further adds nogood recording as a central technique. We discuss the theoretical and technical issues that arise in successfully integrating this range of strategies with one another and with nogood recording in the context of DTP solving. Using an implementation of Epilitis, we explore the effectiveness of various combinations of strategies for solving DTPs, and based on this analysis we demonstrate that Epilitis can achieve a nearly two orderofmagnitude speedup over the previously published algorithms on benchmark problems in the DTP literature.
Encodings of NonBinary Constraint Satisfaction Problems
, 1999
"... We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. ..."
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Cited by 44 (9 self)
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We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation
Singleton Consistencies
, 2000
"... We perform a comprehensive theoretical and empirical study of the bene ts of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the costeffectiven ..."
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Cited by 40 (8 self)
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We perform a comprehensive theoretical and empirical study of the bene ts of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the costeffectiveness of preprocessing with singleton consistency algorithms. Our experiments use both random and structured problems. Whilst preprocessing with singleton consistencies is not in general beneficial for random problems, it starts to pay off when randomness and structure are combined, and it is very worthwhile with structured problems like Golomb rulers. On such problems, preprocessing with consistency techniques as strong as singleton generalized arcconsistency (the singleton extension of generalized arcconsistency) can reduce runtimes. We also show that limiting algorithms that enforce singleton consistencies to a single pass often gives a small reduction in the amount of pruning and improves their costeffectiveness. These experimental results also demonstrate that conclusions from studies on random problems should be treated with caution.
Watched literals for constraint propagation in minion
 In Proc. CP2006, 182–197
, 2006
"... Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three im ..."
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Cited by 35 (14 self)
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Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three important aspects of watched literals as we apply them to constraints, and we describe how they are implemented in the Minion constraint solver. We show three successful applications of watched literals to constraint propagators: the sum of boolean variables; generalised arc consistency for the ‘element ’ constraint; and generalised arc consistency for the ‘table ’ constraint. 1
Modelling the Golomb Ruler Problem
, 1999
"... . The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of different models of this problem, both binary and nonbinary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ..."
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Cited by 31 (9 self)
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. The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of different models of this problem, both binary and nonbinary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ternary constraints gives better results. A binary encoding of the problem gives a smaller search tree, but is impractical because it takes far longer to run. We compare variable ordering heuristics and consider the use of implied constraints to improve propagation. We believe that more case studies such as this are essential to reduce the skill currently required for successful modelling. 1 Introduction In his AAAI98 invited talk, Gene Freuder identified modelling as one of the major hurdles preventing the uptake of constraint satisfaction technology. The availability of nonbinary constraints can increase the number of possible models of a problem amnd so makes modelling still more diffi...