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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 76 (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
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.
An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint
 PROCEEDINGS CP
, 2003
"... Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). ..."
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Cited by 24 (4 self)
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Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). Using a variety of benchmark and random problems, we show that our bounds consistency algorithm is competitive with and can dramatically outperform existing stateoftheart commercial implementations of constraint propagators for the gcc. We also present a new algorithm for domain consistency propagation of the gcc which improves on the worstcase performance of the best previous algorithm for problems that occur often in applications.
The Range and Roots Constraints: Specifying Counting and Occurrence Problems
 In IJCAI
, 2005
"... ..."
Breaking Symmetry of Interchangeable Variables and Values
"... A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, p ..."
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Cited by 18 (13 self)
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A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, pruning all symmetric values is NPhard. We introduce a new global constraint called SIGLEX and its GAC propagator for pruning some (but not necessarily all) symmetric values. We also investigate how different postings of the SIGLEX constraints affect the pruning performance during constraint solving. Finally, we test these static symmetry breaking constraints experimentally for the first time.
Decompositions of All Different, Global Cardinality and Related Constraints
"... We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide ..."
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Cited by 17 (9 self)
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We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudoBoolean solver. 1
Bucket Elimination for Multiobjective Optimization Problems
 JOURNAL OF HEURISTICS
, 2006
"... Multiobjective optimization deals with problems involving multiple measures of performance that should be optimized simultaneously. In this paper we extend bucket elimination (BE), a well known dynamic programming generic algorithm, from monoobjective to multiobjective optimization. We show that t ..."
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Cited by 15 (2 self)
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Multiobjective optimization deals with problems involving multiple measures of performance that should be optimized simultaneously. In this paper we extend bucket elimination (BE), a well known dynamic programming generic algorithm, from monoobjective to multiobjective optimization. We show that the resulting algorithm, MOBE, can be applied to true multiobjective problems as well as monoobjective problems with knapsack (or related) global constraints. We also extend minibucket elimination (MBE), the approximation form of BE, to multiobjective optimization. The new algorithm MOMBE can be used to obtain good quality multiobjective lower bounds or it can be integrated into multiobjective branch and bound in order to increase its pruning efficiency. Its accuracy is empirically evaluated in real scheduling problems, as well as in MaxSATONE and biobjective weighted minimum vertex cover problems.
Enhancing Set Constraint Solvers with Lexicographic Bounds
 JOURNAL OF HEURISTICS
"... Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as binpacking, set partitioning, circuit design, and Combinatorial Design Problems. In this paper we present and evaluate a new means towards improving the practica ..."
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Cited by 12 (1 self)
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Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as binpacking, set partitioning, circuit design, and Combinatorial Design Problems. In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to the challenging symmetrical set problems often cast as Combinatorial Design Problems (CDPs). While CDPs find a natural formulation in the language of sets, in constraint programming literature, alternative models are often used due to a lack of efficiency of traditional FS solvers. We first identify the main structural components of CDPs that render their modeling suitable to set languages but their solving a technical challenge. Our new prototype solver extends the traditional subset variable domain with lexicographic bounds that better approximate a set domain by satisfying the cardinality restrictions applied to the variable, and allow for active symmetry breaking using ordering constraints. Our contribution includes the formal and practical framework of the new solver implemented on top of a traditional set solver, and an empirical evaluation on benchmark CDPs.
Combination of among and cardinality constraints
 Proceedings of the Second International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2005), volume 3524 of Lecture Notes in Computer Science
, 2005
"... Abstract. A cardinality constraint imposes that each value of a set V must be taken a certain number of times by a set of variables X, whereas an among constraint imposes that a certain number of variables of a set X must take a value in the set V. This paper studies several combinations of among co ..."
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Cited by 11 (1 self)
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Abstract. A cardinality constraint imposes that each value of a set V must be taken a certain number of times by a set of variables X, whereas an among constraint imposes that a certain number of variables of a set X must take a value in the set V. This paper studies several combinations of among constraints and several conjunctions of among constraints and cardinality constraints. Some filtering algorithms are proposed and they are characterized when it is possible. Moreover, a weak form of Singleton arc consistency is considered. At last, it is shown how the global sequencing constraint and the global minimum distance constraint can be easily modeled by some conjunctions of cardinality and among constraints. Some results are also given for the global minimum distance constraint. They show that our study outperforms the existing constraints in ILOG Solver. 1
Kernels for Global Constraints
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever b ..."
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Cited by 8 (6 self)
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Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever bound consistency can be enforced in polynomial time; this applies to the global constraints ATMOSTNVALUE and EXTENDED GLOBAL CARDINALITY (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for ATMOSTNVALUE constraints admits a linear time reduction to an equivalent instance on O(k2) variables and domain values. This small kernel can be used to speed up the complete propagation of NVALUE constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.