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27
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 77 (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
A greedy approach to establish singleton arc consistency
 In Proceedings of IJCAI’05
, 2005
"... In this paper, we propose a new approach to establish Singleton Arc Consistency (SAC) on constraint networks. While the principle of existing SAC algorithms involves performing a breadthfirst search up to a depth equal to 1, the principle of the two algorithms introduced in this paper involves perf ..."
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Cited by 27 (13 self)
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In this paper, we propose a new approach to establish Singleton Arc Consistency (SAC) on constraint networks. While the principle of existing SAC algorithms involves performing a breadthfirst search up to a depth equal to 1, the principle of the two algorithms introduced in this paper involves performing several runs of a greedy search (where at each step, arc consistency is maintained). It is then an original illustration of applying inference (i.e. establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. Furthermore, both space and time complexities are quite competitive. 1
Conservative Dual Consistency
 In Proceedings of AAAI’07
, 2007
"... Consistencies are properties of Constraint Networks (CNs) that can be exploited in order to make inferences. When a significant amount of such inferences can be performed, CNs are much easier to solve. In this paper, we interest ourselves in relation filtering consistencies for binary constraints, i ..."
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Cited by 13 (9 self)
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Consistencies are properties of Constraint Networks (CNs) that can be exploited in order to make inferences. When a significant amount of such inferences can be performed, CNs are much easier to solve. In this paper, we interest ourselves in relation filtering consistencies for binary constraints, i.e. consistencies that allow to identify inconsistent pairs of values. We propose a new consistency called Dual Consistency (DC) and relate it to Path Consistency (PC). We show that Conservative DC (CDC, i.e. DC with only relations associated with the constraints of the network considered) is more powerful, in terms of filtering, than Conservative PC (CPC). Following the approach of Mac Gregor, we introduce an algorithm to establish (strong) CDC with a very low worstcase space complexity. Even if the relative efficiency of the algorithm introduced to establish (strong) CDC partly depends on the density of the constraint graph, the experiments we have conducted show that, on many series of CSP instances, CDC is largely faster than CPC (up to more than one order of magnitude). Besides, we have observed that enforcing CDC in a preprocessing stage can significantly speed up the resolution of hard structured instances.
Lookahead saturation with restriction for SAT
 In Proceedings of 11th CP
, 2005
"... Abstract. We present a new and more efficient heuristic by restricting lookahead saturation (LAS) with NVO (neighbourhood variable ordering) and DEW (dynamic equality weighting). We report on the integration of this heuristic in Satz, a highperformance SAT solver, showing empirically that it signif ..."
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Cited by 9 (1 self)
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Abstract. We present a new and more efficient heuristic by restricting lookahead saturation (LAS) with NVO (neighbourhood variable ordering) and DEW (dynamic equality weighting). We report on the integration of this heuristic in Satz, a highperformance SAT solver, showing empirically that it significantly improves the performance on an extensive range of benchmark problems that exhibit hard structure. 1
Decidable Relationships between Consistency Notions for Constraint Satisfaction Problems
"... Abstract. We define an abstract pebble game that provides game interpretations for essentially all known consistency algorithms for constraint satisfaction problems including arcconsistency, (j, k)consistency, kconsistency, kminimality, and refinements of arcconsistency such as peek arcconsist ..."
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Cited by 5 (0 self)
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Abstract. We define an abstract pebble game that provides game interpretations for essentially all known consistency algorithms for constraint satisfaction problems including arcconsistency, (j, k)consistency, kconsistency, kminimality, and refinements of arcconsistency such as peek arcconsistency and singleton arcconsistency. Our main result is that for any two instances of the abstract pebble game where the first satisfies the additional condition of being stacked, there exists an algorithm to decide whether consistency with respect to the first implies consistency with respect to the second. In particular, there is a decidable criterion to tell whether singleton arcconsistency with respect to a given constraint language implies kconsistency with respect to the same constraint language, for any fixed k. We also offer a new decidable criterion to tell whether arcconsistency implies satisfiability which pulls from methods in Ramsey theory and looks more amenable to generalization. 1
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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Cited by 4 (2 self)
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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.
Efficient Algorithms for Singleton Arc Consistency
"... In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it require ..."
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Cited by 4 (3 self)
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In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it requires far less space and is often more efficient in practice than the optimal algorithm SACOpt. In the second approach, we perform several runs of a greedy search (where at each step, arc consistency is maintained), possibly detecting the singleton arc consistency of several values in one run. It is an original illustration of applying inference (i.e., establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. We present extensive experiments that show the benefit of our two approaches.
Lookahead in Smodels compared to local consistencies in CSP
 In Proceedings of The 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’05), LNCS/LNAI 3662
, 2005
"... Abstract. In answer set programming systems like Smodels and some SAT solvers, constraint propagation is carried out by a mechanism called lookahead. The question arises as what is the pruning power of lookahead, and how such pruning power fares in comparison with the consistency techniques in solvi ..."
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Cited by 2 (2 self)
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Abstract. In answer set programming systems like Smodels and some SAT solvers, constraint propagation is carried out by a mechanism called lookahead. The question arises as what is the pruning power of lookahead, and how such pruning power fares in comparison with the consistency techniques in solving CSPs. In this paper, we study the pruning power of lookahead by relating it to local consistencies under two different encodings from CSPs to answer set programs. This leads to an understanding of how the search space is pruned in an answer set solver with lookahead for solving CSPs. On the other hand, lookahead as a general constraint propagation mechanism provides a uniform algorithm for enforcing a variety of local consistencies. We also study the impact on the search efficiency under these encodings. 1
Bound consistencies for the discrete CSP
 In Proceedings of CPAI’05 workshop held with CP’05
, 2005
"... Abstract. Many works in the area of Constraint Programming have focused on inference, and more precisely, on filtering methods based on properties of constraint networks. Such properties are called domain filtering consistencies when they allow removing some inconsistent values from the domains of v ..."
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Cited by 1 (1 self)
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Abstract. Many works in the area of Constraint Programming have focused on inference, and more precisely, on filtering methods based on properties of constraint networks. Such properties are called domain filtering consistencies when they allow removing some inconsistent values from the domains of variables, and bound consistencies when they focus on bounds of domains. In this paper, we study the relationship between consistencies introduced with respect to discrete and continuous constraint networks, and experiment the effectiveness of exploiting bound consistencies on discrete instances. 1
Abscon 2005
"... Abstract. This paper describes the algorithms, heuristics and strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the first CSP solver competition. Both solvers maintain arc consistency during search, explore the search space using a conflictdirec ..."
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Abstract. This paper describes the algorithms, heuristics and strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the first CSP solver competition. Both solvers maintain arc consistency during search, explore the search space using a conflictdirected variable ordering heuristic and integrate a restart strategy. At preprocessing, the first solver establishes arc consistency whereas the second one establishes a partial form of a consistency which is stronger than singleton arc consistency. 1