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99
Exploiting multidirectionality in coarsegrained arc consistency algorithms
 In Proc. of CP’03
, 2003
"... Abstract. Arc consistency plays a central role in solving Constraint Satisfaction Problems. This is the reason why many algorithms have been proposed to establish it. Recently, an algorithm called AC2001 and AC3.1 has been independently presented by their authors. This algorithm which is considered ..."
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Cited by 23 (12 self)
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Abstract. Arc consistency plays a central role in solving Constraint Satisfaction Problems. This is the reason why many algorithms have been proposed to establish it. Recently, an algorithm called AC2001 and AC3.1 has been independently presented by their authors. This algorithm which is considered as a refinement of the basic algorithm AC3 has the advantage of being simple and competitive. However, it does not take into account constraint bidirectionality as AC7 does. In this paper, we address this issue, and, in particular, introduce two new algorithms called AC3.2 and AC3.3 which benefit from good properties of both AC3 and AC7. Indeed, AC3.2 and AC3.3 are as easy to implement as AC3 and take advantage of bidirectionality as AC7 does. More precisely, AC3.2 is a general algorithm which partially exploits bidirectionality whereas AC3.3 is a binary algorithm which fully exploits bidirectionality. It turns out that, when Maintaining Arc Consistency during search, MAC3.2, due to a memorization effect, is more efficient than MAC3.3 both in terms of constraint checks and cpu time. Compared to MAC2001/3.1, our experimental results show that MAC3.2 saves about 50% of constraint checks and, on average, 15 % of cpu time. 1
GLOBAL CONSTRAINTS AND FILTERING ALGORITHMS
"... Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algor ..."
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Cited by 23 (1 self)
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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Overconstrained problems are also mentioned and global soft constraints are introduced.
Algorithms for quantified constraint satisfaction problems
 In Proceedings of CP2004
, 2004
"... Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reaso ..."
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Cited by 22 (2 self)
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Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reasoning tasks rises from NPcomplete to PSPACEcomplete. Such problems have, so far, been studied mainly in the context of quantified Boolean formulae. Little work has been done on problems with discrete nonBoolean domains. We attempt to fill this gap by extending propagation and search algorithms from standard CSPs to the quantified case. We also show how the notion of value interchangeability can be exploited to break symmetries and speed up search by orders of magnitude. Finally, we test experimentally the algorithms and methods proposed. 1
A fast arc consistency algorithm for nary constraints
 In Proceedings of AAAI’05
, 2005
"... The GACScheme has become a popular general purpose algorithm for solving nary constraints, although it may scan an exponential number of supporting tuples. In this paper, we develop a major improvement of this scheme. When searching for a support, our new algorithm is able to skip over a number ..."
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Cited by 21 (1 self)
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The GACScheme has become a popular general purpose algorithm for solving nary constraints, although it may scan an exponential number of supporting tuples. In this paper, we develop a major improvement of this scheme. When searching for a support, our new algorithm is able to skip over a number of tuples exponential in the arity of the constraint by exploiting knowledge about the current domains of the variables. We demonstrate the effectiveness of the method for large table constraints.
A Global Constraint for Graph Isomorphism Problems
, 2004
"... The graph isomorphism problem consists in deciding if two given graphs have an identical structure. This problem can be modeled as a constraint satisfaction problem in a very straightforward way, so that one can use constraint programming to solve it. However, constraint programming is a generic too ..."
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Cited by 20 (2 self)
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The graph isomorphism problem consists in deciding if two given graphs have an identical structure. This problem can be modeled as a constraint satisfaction problem in a very straightforward way, so that one can use constraint programming to solve it. However, constraint programming is a generic tool that may be less efficient than dedicated algorithms which can take advantage of the global semantic of the original problem. Hence, we
Soft arc consistency revisited
 Artificial Intelligence
"... The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in o ..."
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Cited by 19 (3 self)
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The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in other graphical models (including discrete Markov Random Fields and Bayesian Networks). The incremental lower bounds produced by local consistency filtering are used for pruning inside Branch and Bound search. In this paper, we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously. Over the rationals and allowing simultaneous operations, we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming. This defines Optimal Soft Arc Consistency (OSAC). To reach a more practical algorithm, we show that the existence of a sequence of arc consistency operations which increases the lower bound can be detected by establishing arc consistency in a classical Constraint Satisfaction Problem (CSP) derived from the original cost function network. This leads to a new soft arc consistency method, called,Virtual Arc Consistency which produces improved lower bounds compared with previous techniques and which can solve submodular cost functions. These algorithms have been implemented and evaluated on a variety of problems, including two difficult frequency assignment problems which are solved to optimality for the first time. Our implementation is available in the open source toulbar2 platform.
Arc Consistency in MAC: A New Perspective
 IN PROCEEDINGS OF CPAI’04 WORKSHOP HELD WITH CP’04
, 2004
"... AC refers to algorithms that enforce arc consistency on a constraint network while MAC refers to a backtracking search scheme where after each instantiation of a variable, arc consistency is maintained (or enforced) on the new network. In this paper, we use to denote maintaining arc consisten ..."
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Cited by 14 (2 self)
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AC refers to algorithms that enforce arc consistency on a constraint network while MAC refers to a backtracking search scheme where after each instantiation of a variable, arc consistency is maintained (or enforced) on the new network. In this paper, we use to denote maintaining arc consistency in MAC. In all existing studies, mac is simply taken as an associate of an AC algorithm. In this paper, we argue that it is worth taking as an entity separated from AC. Based on an observation that is invoked many times during a search, we propose three schemes to improve the e#ciency of mac. First, the results of constraint checks are cached. Second, values remained in the auxiliary data structures used by sophisticated AC algorithms are better exploited. Third,
Local Consistencies in SAT
 In Proc. SAT2003
, 2003
"... We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem. ..."
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Cited by 13 (1 self)
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We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem.
Solving Nonbinary CSPs Using the Hidden Variable Encoding
 Proccedings of CP 2001, LNCS 2239
, 2001
"... Nonbinary constraint satisfactionproblfa (CSPs) can be sol ed in two di#erent ways. We can eithertranslzfi theproblH into an equivali t binary one and sol e it using welE7Vo#fiR6V7ol binary CSP techniques or use extended versions of binary techniques directl on the nonbinaryproblin Recentl , it ha ..."
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Cited by 11 (3 self)
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Nonbinary constraint satisfactionproblfa (CSPs) can be sol ed in two di#erent ways. We can eithertranslzfi theproblH into an equivali t binary one and sol e it using welE7Vo#fiR6V7ol binary CSP techniques or use extended versions of binary techniques directl on the nonbinaryproblin Recentl , it has been shown that the hidden variabl encoding is a promising method oftranslo#z6 nonbinary CSPs into binary ones. In this paper we make atheoretical andempirical investigation of arc consistency and searchalxRfio#zH for the hidden variabl encoding. WeanalkE the potential benefits ofapplxzz arc consistency on the hidden encoding compared togeneral#zfi arc consistency on the nonbinary representation. Weal6 show that searchalkHRo#zz for nonbinary constraints can be emulk6x by corresponding binaryalryofixHE that operate on the hidden variabl encoding and onl instantiate original variablo# Empirical resulc on variousimplsoz tations of suchal gorithms reveal that the hidden variabl is competitive and in many cases better than the nonbinary representation for certain cltain of nonbinary constraints. 1