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100
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 92 (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].
Solving Weighted CSP by Maintaining Arc Consistency
, 2004
"... Recently, a general definition of arc consistency (AC) for soft constraint frameworks has been proposed [1]. In this paper we specialize this definition to weighted CSP and introduce two O(ed³) enforcing algorithms. Then, we refine the definition and introduce a stronger form of arc consistency (AC* ..."
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Cited by 84 (12 self)
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Recently, a general definition of arc consistency (AC) for soft constraint frameworks has been proposed [1]. In this paper we specialize this definition to weighted CSP and introduce two O(ed³) enforcing algorithms. Then, we refine the definition and introduce a stronger form of arc consistency (AC*) along with two O(n²d² + ed³) algorithms. As in the CSP case, an important application of AC is to combine it with search. We empirically demonstrate that a branch and bound algorithm that maintains either AC or AC* is a stateoftheart general solver for weighted CSP. Our experiments cover binary MaxCSP and MaxSAT problems.
Existential arc consistency: Getting closer to full arc consistency in weighted csps
 In Proc. of the 19 th IJCAI
, 2005
"... The weighted CSP framework is a soft constraint framework with a wide range of applications. Most current stateoftheart complete solvers can be described as a basic depthfirst branch and bound search that maintain some form of arc consistency during the search. In this paper we introduce a new s ..."
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Cited by 78 (19 self)
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The weighted CSP framework is a soft constraint framework with a wide range of applications. Most current stateoftheart complete solvers can be described as a basic depthfirst branch and bound search that maintain some form of arc consistency during the search. In this paper we introduce a new stronger form of arc consistency, that we call existential directional arc consistency and we provide an algorithm to enforce it. The efficiency of the algorithm is empirically demonstrated in a variety of domains. 1
On Forward Checking for Nonbinary Constraint Satisfaction
 ARTIFICIAL INTELLIGENCE
, 1999
"... Solving nonbinary constraint satisfaction problems, a crucial challenge for the next years, can be tackled in two different ways: translating the nonbinary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option rai ..."
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Cited by 78 (5 self)
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Solving nonbinary constraint satisfaction problems, a crucial challenge for the next years, can be tackled in two different ways: translating the nonbinary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option raises some issues when we want to extend denitions written for the binary case. This paper focuses on the wellknown forward checking algorithm, and shows that it can be generalized to several nonbinary versions, all tting its binary denition. The classical version, proposed by Van Hentenryck, is only one of these generalizations.
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 76 (5 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
In the quest of the best form of local consistency for weighted CSP
 In Proc. of the 18 th IJCAI
, 2003
"... The weighted CSP (WCSP) framework is a soft constraint framework with a wide range of applications. In this paper, we consider the problem of maintaining local consistency during search for solving WCSP. We first refine the notions of directional arc consistency (DAC) and full directional arc consis ..."
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Cited by 61 (12 self)
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The weighted CSP (WCSP) framework is a soft constraint framework with a wide range of applications. In this paper, we consider the problem of maintaining local consistency during search for solving WCSP. We first refine the notions of directional arc consistency (DAC) and full directional arc consistency (FDAC) introduced in [Cooper, 2003] for binary WCSP, define algorithms that enforce these properties and study their complexities. We then consider algorithms that maintain either arc consistency (AC), DAC or FDAC during search. The efficiency of these algorithms is empirically studied. It appears that despite its high theoretical cost, the strongest FDAC property is the best choice. 1
Hybrid backtracking bounded by treedecomposition of constraint networks
 ARTIFICIAL INTELLIGENCE
, 2003
"... We propose a framework for solving CSPs based both on backtracking techniques and on the notion of treedecomposition of the constraint networks. This mixed approach permits us to define a new framework for the enumeration, which we expect that it will benefit from the advantages of two approaches: ..."
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Cited by 56 (15 self)
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We propose a framework for solving CSPs based both on backtracking techniques and on the notion of treedecomposition of the constraint networks. This mixed approach permits us to define a new framework for the enumeration, which we expect that it will benefit from the advantages of two approaches: a practical efficiency of enumerative algorithms and a warranty of a limited time complexity by an approximation of the treewidth of the constraint networks. Finally, experimental results allow us to show the advantages of this approach.
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 47 (10 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
Optimal and Suboptimal Singleton Arc Consistency Algorithms
 Professional Book Center
, 2005
"... Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent after the assignment of a value to a variable. Algorithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give ..."
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Cited by 40 (4 self)
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Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent after the assignment of a value to a variable. Algorithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give a lower bound to the time complexity of enforcing SAC, and we propose an algorithm that achieves this complexity, thus being optimal. However, it can be costly in space on large problems. We then propose another SAC algorithm that trades time optimality for a better space complexity. Nevertheless, this last algorithm has a better worstcase time complexity than previously published SAC algorithms. An experimental study shows the good performance of the new algorithms. 1
Backjumpbased techniques versus conflictdirected heuristics
 In Proceedings of ICTAI’04
, 2004
"... In this paper, we present a general algorithm which gives an uniform view of several stateoftheart systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated lookback and lookahead ..."
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Cited by 34 (11 self)
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In this paper, we present a general algorithm which gives an uniform view of several stateoftheart systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated lookback and lookahead schemes. By means of this algorithm, our purpose is then to study the interest of backjumpbased techniques with respect to conflictdirected variable ordering heuristics. 1