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On the Reification of Global Constraints
 CONSTRAINTS
"... We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of total function constraints together with a constraint that can be easily reified. ..."
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Cited by 72 (6 self)
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We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of total function constraints together with a constraint that can be easily reified.
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.
Decomposing Global Grammar Constraints
"... Abstract. A wide range of constraints can be specified using automata or formal languages. The GRAMMAR constraint restricts the values taken by a sequence of variables to be a string from a given contextfree language. Based on an AND/OR decomposition, we show that this constraint can be converted i ..."
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Cited by 27 (12 self)
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Abstract. A wide range of constraints can be specified using automata or formal languages. The GRAMMAR constraint restricts the values taken by a sequence of variables to be a string from a given contextfree language. Based on an AND/OR decomposition, we show that this constraint can be converted into clauses in conjunctive normal form without hindering propagation. Using this decomposition, we can propagate the GRAMMAR constraint in O(n 3) time. The decomposition also provides an efficient incremental propagator. Down a branch of the search tree of length k, we can enforce GAC k times in the same O(n 3) time. On specialized languages, running time can be even better. For example, propagation of the decomposition requires just O(nδ) time for regular languages where δ  is the size of the transition table of the automaton recognizing the regular language. Experiments on a shift scheduling problem with a constraint solver and a state of the art SAT solver show that we can solve problems using this decomposition that defeat existing constraint solvers. 1
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.
The theory of grammar constraints
 In: 12th Int. Conf. on Principles and Practice of Constraint Programming (CP2006), LNCS 4204
, 2006
"... Abstract. By introducing the Regular Membership Constraint, Gilles Pesant pioneered the idea of basing constraints on formal languages. The paper presented here is highly motivated by this work, taking the obvious next step, namely to investigate constraints based on grammars higher up in the Chomsk ..."
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Cited by 26 (3 self)
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Abstract. By introducing the Regular Membership Constraint, Gilles Pesant pioneered the idea of basing constraints on formal languages. The paper presented here is highly motivated by this work, taking the obvious next step, namely to investigate constraints based on grammars higher up in the Chomsky hierarchy. We devise an arcconsistency algorithm for contextfree grammars, investigate when logic combinations of grammar constraints are tractable, show how to exploit nonconstant size grammars and reorderings of languages, and study where the boundaries run between regular, contextfree, and contextsensitive grammar filtering.
The Range and Roots Constraints: Specifying Counting and Occurrence Problems
 In IJCAI
, 2005
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Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction
 Constraints
, 2006
"... Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and ..."
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Cited by 17 (2 self)
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Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient ifthen constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals. 1.
The slide metaconstraint
"... We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide ..."
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Cited by 15 (3 self)
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We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide with a global cardinality constraint. We also show how to propagate Slide. Our experiments demonstrate that using Slide to encode constraints can be just as efficient and effective as using specialized propagators.