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72
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 82 (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.
Efficient CNF encoding of Boolean cardinality constraints
, 2003
"... In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical e ..."
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Cited by 69 (5 self)
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In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardinality constraints. This encoding is also used together with a trivial variable elimination in order to reencode parity learning benchmarks so that a simple Davis and Putnam procedure can solve them.
The alldifferent Constraint: A Survey
, 2001
"... The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several strategies have been designed to solve the alldifferent constraint. This paper surveys the most important developments over the years regarding the alldifferent ..."
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Cited by 49 (1 self)
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The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several strategies have been designed to solve the alldifferent constraint. This paper surveys the most important developments over the years regarding the alldifferent constraint. First we summarize the underlying concepts and results from graph theory and integer programming. Then we give an overview and an abstract comparison of different solution strategies. In addition, the symmetric alldifferent constraint is treated. Finally, we show how to apply costbased filtering to the alldifferent constraint.
Solving small TSPs with constraints
 PROCEEDINGS OF THE 14TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1997
"... This paper presents a set of techniques that makes constraint programming a technique of choice for solving small (up to 30 nodes) traveling salesman problems. These techniques include a propagation scheme to avoid intermediate cycles (a global constraint), a branching scheme and a redundant constra ..."
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Cited by 48 (0 self)
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This paper presents a set of techniques that makes constraint programming a technique of choice for solving small (up to 30 nodes) traveling salesman problems. These techniques include a propagation scheme to avoid intermediate cycles (a global constraint), a branching scheme and a redundant constraint that can be used as a bounding method. The resulting improvement is that we can solve problems twice larger than those solved previously with constraint programming tools. We evaluate the use of Lagrangean Relaxation to narrow the gap between constraint programming and other Operations Research techniques and we show that improved constraint propagation has now a place in the array of techniques that should be used to solve a traveling salesman problem.
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 38 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
A Scheme for Unifying Optimization and Constraint Satisfaction Methods
, 2000
"... Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search a ..."
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Cited by 33 (6 self)
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Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search and inference and the duality of strengthening and relaxation. Optimization as well as constraint satisfaction methods can be seen as exploiting these dualities in their respective ways. Our proposal is that rather than employ either type of method exclusively, one can focus on how these dualities can be exploited in a given problem class. The resulting algorithm is likely to contain elements from both optimization and constraint satisfaction, and perhaps new methods that belong to neither.
Hybrid Benders Decomposition Algorithms in Constraint Logic Programming
 In Procs. of the 7th Intern. Conference on Principles and Practice of Constraint Programming  CP 2001
, 2001
"... Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe ..."
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Cited by 27 (1 self)
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Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe language, that enables it to be used within a constraint programming framework. The programmer is spared from having to write down the dual form of any subproblem, because it is derived by the system. Examples are used to show how problem constraints can be modelled in an undecomposed form. The programmer need only specify which variables belong to which subproblems, and the Benders Decomposition is extracted automatically. A class of minimal perturbation problems is used to illustrate how dierent kinds of algorithms can be used for the dierent subproblems. The implementation is tested on a set of minimal perturbation benchmarks, and the results are analysed.
Constraint and Integer Programming in OPL
 INFORMS Journal on Computing
, 2002
"... In recent years, it has been increasingly recognized that constraint and integer programming have orthogonal and complementary strengths in stating and solving combinatorial optimization applications. In addition, their integration has become an active research topic. The optimization programming la ..."
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Cited by 25 (6 self)
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In recent years, it has been increasingly recognized that constraint and integer programming have orthogonal and complementary strengths in stating and solving combinatorial optimization applications. In addition, their integration has become an active research topic. The optimization programming language opl was a first attempt at integrating these technologies both at the language and at the solver levels. In particular, opl is a modeling language integrating the rich language of constraint programming and the ability to specify search procedures at a high level of abstraction. Its implementation includes both constraint and mathematical programming solvers, as well as some cooperation schemes to make them collaborate on a given problem. The purpose of this paper is to illustrate, using opl, the constraintprogramming approach to combinatorial optimization and the complementary strengths of constraint and integer programming. (Artificial Intelligence; Computer Science; Integer Programming) 1.
Sweep as a Generic Pruning Technique Applied to the NonOverlapping Rectangles Constraint
 Seventh International Conference on Principles and Practice of Constraint Programming, LNCS 2239
, 2001
"... We rst present a generic pruning technique which aggregates several constraints sharing some variables. The method is derived from an idea called sweep which is extensively used in computational geometry. A rst benet of this technique comes from the fact that it can be applied on several familie ..."
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Cited by 24 (7 self)
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We rst present a generic pruning technique which aggregates several constraints sharing some variables. The method is derived from an idea called sweep which is extensively used in computational geometry. A rst benet of this technique comes from the fact that it can be applied on several families of global constraints. A second main advantage is that it does not lead to any memory consumption problem since it only requires temporary memory that can be reclaimed after each invocation of the method.