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75
Global Constraints for Lexicographic Orderings
, 2002
"... We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show ..."
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Cited by 83 (35 self)
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We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show
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.
Cp(graph): Introducing a graph computation domain in constraint programming
 In CP2005 Proceedings
, 2005
"... Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new co ..."
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Cited by 52 (12 self)
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Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain variables as well as constraints over these variables and their propagators. These constraints are subdivided into kernel constraints and additional constraints formulated as networks of kernel constraints. For some of these constraints a dedicated global constraint and its associated propagator are sketched. CP(Graph) is integrated with finite domain and finite sets computation domains, allowing the combining of constraints of these domains with graph constraints. A prototype of CP(Graph) built over finite domains and finite sets in Oz is presented. And we show that a problem of biochemical network analysis can be very simply described and solved within CP(Graph). 1
Deriving Filtering Algorithms from Constraint Checkers
 Principles and Practice of Constraint Programming (CP’2004), volume 3258 of LNCS
, 2004
"... Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction ..."
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Cited by 51 (11 self)
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Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction of signature and transition constraints we show how to systematically obtain a filtering algorithm. Under some restrictions on the signature and transition constraints this filtering algorithm achieves arcconsistency. An implementation based on some constraints as well as on the metaprogramming facilities of SICStus Prolog is available. For a restricted class of automata we provide a filtering algorithm for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution. Keywords: Constraint Programming,
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.
SALSA: A Language for Search Algorithms
 In CP’98
, 1998
"... Constraint Programming is a technique of choice for solving hard combinatorial optimization problems. However, it is best used in conjunction with other optimization paradigms such as local search, yielding hybrid algorithms with constraints. Such combinations lack a language supporting an elegant d ..."
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Cited by 44 (0 self)
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Constraint Programming is a technique of choice for solving hard combinatorial optimization problems. However, it is best used in conjunction with other optimization paradigms such as local search, yielding hybrid algorithms with constraints. Such combinations lack a language supporting an elegant description and retaining the original declarativity of Constraint Logic Programming. We propose a language, SALSA, dedicated to specifying (local, global or hybrid) search algorithms. We illustrate its use on a few examples from combinatorial optimization for which we specify complex optimization procedures with a few simple lines of code of high ion level. We report preliminary experiments showing that such a language can be implemented on top of CP systems, yielding a powerful environment for combinatorial optimization.
On global warming: Flowbased soft global constraints
, 2006
"... In case a CSP is overconstrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then co ..."
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Cited by 39 (6 self)
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In case a CSP is overconstrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimumweight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint.
Pruning for the minimum constraint family and for the number of distinct values constraint family
 Principles and Practice of Constraint Programming, CP’2001, Paphos, Cyprus, Springer, LNCS 2239
"... The paper presents propagation rules that are common to the minimum constraint family and to the number of distinct values constraint family. One original contribution is to provide a geometrical interpretation of these rules that can be used by a generic sweep pruning algorithm. Finally one practic ..."
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Cited by 37 (7 self)
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The paper presents propagation rules that are common to the minimum constraint family and to the number of distinct values constraint family. One original contribution is to provide a geometrical interpretation of these rules that can be used by a generic sweep pruning algorithm. Finally one practical interest of the paper is to describe an implementation of the number of distinct values constraint. This is a quite common counting constraint that one encounters in many practical applications such as timetabling or frequency allocation problems. The purpose of this paper is to present propagation rules for the minimum constraint family that was introduced in [1]. The minimum constraint family has the form minimum ( M, r,
Global Constraint Catalogue: Past, Present and Future
, 2006
"... The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area. ..."
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Cited by 26 (2 self)
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The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area.