Global Constraint Catalogue: Past, Present and Future

Beldiceanu, Nicolas; Carlsson, Mats; Demassey, Sophie; Petit, Thierry

doi:10.1007/s10601-006-9010-8

Cited by 69 publications

(74 citation statements)

References 48 publications

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“…Identifying these recurring bits of combinatorial substructure gives us a convenient way to express combinatorial problems. The AllDifferent constraint is but one example of the hundreds of useful constraints that have been identified and are described in the Global Constraint Catalogue [10]. A CSP can be described, in a fully declarative way, as a conjunction of these constraints, which is called a constraint model.…”

Section: Constraint Programmingmentioning

confidence: 99%

Other things besides number: Abstraction, constraint propagation, and string variable types

Scott

2016

Constraints

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Constraint programming (CP) is a technology in which a combinatorial problem is modeled declaratively as a conjunction of constraints, each of which captures some of the combinatorial substructure of the problem. Constraints are more than a modeling convenience: every constraint is partially implemented by an inference algorithm, called a propagator, that rules out some but not necessarily all infeasible candidate values of one or more unknowns in the scope of the constraint. Interleaving propagation with systematic search leads to a powerful and complete solution method, combining a high degree of re-usability with natural, high-level modeling.A propagator can be characterized as a sound approximation of a constraint on an abstraction of sets of candidate values; propagators that share an abstraction are similar in the strength of the inference they perform when identifying infeasible candidate values. In this thesis, we consider abstractions of sets of candidate values that may be described by an elegant mathematical formalism, the Galois connection. We develop a theoretical framework from the correspondence between Galois connections and propagators, unifying two disparate views of the abstractionpropagation connection, namely the oft-overlooked distinction between representational and computational over-approximations. Our framework yields compact definitions of propagator strength, even in complicated cases (i.e., involving several types, or unknowns with internal structure); it also yields a method for the principled derivation of propagators from constraint definitions.We apply this framework to the extension of an existing CP solver to constraints over strings, that is, words of finite length. We define, via a Galois connection, an over-approximation for bounded-length strings, and demonstrate two different methods for implementing this overapproximation in a CP solver. First we use the Galois connection to derive a boundedlength string representation as an aggregation of existing scalar types; propagators for this representation are obtained by manual derivation, or automated synthesis, or a combination. Then we implement a string variable type, motivating design choices with knowledge gained from the construction of the over-approximation. The resulting CP solver extension not only substantially eases modeling for combinatorial string problems, but also leads to substantial efficiency improvements over prior CP methods.

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Section: Constraint Programmingmentioning

confidence: 99%

Other things besides number: Abstraction, constraint propagation, and string variable types

Scott

2016

Constraints

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“…This instance has an empty constraint, and clearly has no solutions, but it is a simple matter (and left as an exercise for the reader) to check that it satisfies the BTP with respect to the variable ordering v 1 < v 2 < v 3 < v 4 .…”

Section: Theorem 5 Let Be An Np-hard Class Of Csp Instances Where Eamentioning

confidence: 99%

“…Similarly, such a set function must map {T rue} to the same value on v 2 and v 3 and on v 3 and v 4 . However, since we also have the constraint v 1 ⇔ v 4 . it must be the case that the set function maps the set {T rue} to different truth values on v 1 and v 4 .…”

Section: Theorem 5 Let Be An Np-hard Class Of Csp Instances Where Eamentioning

confidence: 99%

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The power of propagation: when GAC is enough

Cohen

Jeavons

2016

Constraints

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Considerable effort in constraint programming has focused on the development of efficient propagators for individual constraints. In this paper, we consider the combined power of such propagators when applied to collections of more than one constraint. In particular we identify classes of constraint problems where such propagators can decide the existence of a solution on their own, without the need for any additional search. Sporadic examples of such classes have previously been identified, including classes based on restricting the structure of the problem, restricting the constraint types, and some hybrid examples. However, there has previously been no unifying approach which characterises all of these classes: structural, language-based and hybrid. In this paper we develop such a unifying approach and embed all the known classes into a common framework. We then use this framework to identify a further class of problems that can be solved by propagation alone.

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“…Of these, the most important are cardinality constraints [12,13] and automaton based constraints [8,9,7]. More generally, the reader should refer to the catalogue of constraints [1] to gain a more complete idea of the graph properties used in global constraints. In the same way, difficult problems modeled and solved thanks to graph theory have been successfully tackled in constraint programming and, more particularly, thanks to global constraints.…”

Section: Introductionmentioning

confidence: 99%

Revisiting the tree Constraint

Fages

Lorca

2011

Principles and Practice of Constraint Programming – CP 2011

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Abstract. This paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning.

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Global Constraint Catalogue: Past, Present and Future

Abstract: 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.

Cited by 69 publications

References 48 publications

Other things besides number: Abstraction, constraint propagation, and string variable types

Other things besides number: Abstraction, constraint propagation, and string variable types

The power of propagation: when GAC is enough

Revisiting the tree Constraint

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