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SecondOrder Consistencies
"... In this paper, we propose a comprehensive study of secondorder consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic secondorder consistencies, namely path consistency (PC), ..."
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In this paper, we propose a comprehensive study of secondorder consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic secondorder consistencies, namely path consistency (PC), 3consistency (3C), dual consistency (DC) and 2singleton arc consistency (2SAC), as well as their conservative and strong variants. Interestingly, dual consistency is an original property that can be established by using the outcome of the enforcement of generalized arc consistency (GAC), which makes it rather easy to obtain since constraint solvers typically maintain GAC during search. On binary constraint networks, DC is equivalent to PC, but its restriction to existing constraints, called conservative dual consistency (CDC), is strictly stronger than traditional conservative consistencies derived from path consistency, namely partial path consistency (PPC) and conservative path consistency (CPC). After introducing a general algorithm to enforce strong (C)DC, we present the results of an experimentation over a wide range of benchmarks that demonstrate the interest of (conservative) dual consistency. In particular, we show that enforcing (C)DC before search clearly improves the performance of MAC (the algorithm that maintains GAC during search) on several binary and nonbinary structured problems. 1.
Integrating Strong Local Consistencies into Constraint Solvers
, 2010
"... This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to eventbased constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different le ..."
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This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to eventbased constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how strong consistencies can be applied with different kinds of constraints, including userdefined constraints. We experiment our technique with a coarsegrained algorithm for MaxRPC, called MaxRPC rm, and a variant of it, LMaxRPC rm. Experiments confirm the interest of strong consistencies for Constraint Programming tools.
STRONG DOMAIN FILTERING CONSISTENCIES FOR NONBINARY CONSTRAINT SATISFACTION PROBLEMS
"... Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with nonbinary const ..."
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Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with nonbinary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for nonbinary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in nonbinary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worstcase complexities of the resulting algorithms. Finally, we make a preliminary empirical study. 1.
Strong Inverse Consistencies for Nonbinary CSPs
"... Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with nonbinary const ..."
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Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with nonbinary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong inverse consistencies for nonbinary constraints and compare their pruning power. We show that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for inverse consistencies in nonbinary CSPs and show how it can be instantiated to enforce some of the proposed consistencies. Finally, we make a preliminary empirical study that demonstrates the potential of strong inverse consistencies. 1
A Generic Scheme for Integrating Strong Local Consistencies into Constraint Solvers
"... Abstract. This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to eventbased constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use di ..."
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Abstract. This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to eventbased constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how strong consistencies can be applied with different kinds of constraints, including userdefined constraints. We experiment our technique with a coarsegrained algorithm for MaxRPC, called MaxRPC rm and a variant of it, LMaxRPC rm. Experiments confirm the interest of strong consistencies for Constraint Programming tools. 1
Actes JFPC 2007 Consistance duale conservative
"... Les consistances sont des propriétés de réseaux de contraintes qui peuvent être exploitées afin de générer des inférences. Lorsqu’un nombre important d’inférences peut être effectué, il devient alors plus facile de résoudre les réseaux à l’aide par exemple d’une recherche systématique. Dans ce papie ..."
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Les consistances sont des propriétés de réseaux de contraintes qui peuvent être exploitées afin de générer des inférences. Lorsqu’un nombre important d’inférences peut être effectué, il devient alors plus facile de résoudre les réseaux à l’aide par exemple d’une recherche systématique. Dans ce papier, nous nous intéressons aux consistances de relation, i.e. aux consistances qui permettent d’identifier des couples de valeurs inconsistantes. Nous proposons une nouvelle consistance, appelée consistance duale (DC pour Dual Consistency), et nous la comparons à la consistance de chemin (PC pour Path Consistency). Nous montrons que la DC conservative (CDC), i.e. DC telle que seules les relations associées aux contraintes du réseau soient filtrées, est
Author manuscript, published in "17th International Conference on Principles and Practice of Constraint Programming (CP'11), Perugla: Italy (2011)" A Framework for Decisionbased Consistencies
, 2013
"... Abstract. Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consiste ..."
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Abstract. Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decisionbased consistencies. We identify four general classes (or levels) of decisionbased consistencies, denoted by S φ ∆, E φ ∆, B φ ∆ and D φ ∆, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this general framework provides us with a better insight into decisionbased consistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones. 1
A Framework for Decisionbased Consistencies
"... Abstract. Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consist ..."
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Abstract. Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decisionbased consistencies. We identify four general classes (or levels) of decisionbased consistencies, denoted by Sφ∆, E φ