Deriving Filtering Algorithms from Constraint Checkers

Beldiceanu, Nicolas; Carlsson, Mats; Petit, Thierry

doi:10.1007/978-3-540-30201-8_11

Cited by 71 publications

(96 citation statements)

References 20 publications

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“…Such a representation allows the modeler to take advantage of the large number of global constraints made available by existing CP solvers. Of particular interest for solving string problems are constraints for membership in regular [11,75] and context-free [78,90] languages. For example, the propagator in [75] for Regular L works by maintaining a layered graph: the regular language is specified by a finite automaton, and each layer of the graph replicates the nodes of the automaton but with each transition connecting to a node in the next layer.…”

Section: Fixed-length String Variablesmentioning

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: Fixed-length String Variablesmentioning

confidence: 99%

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

Scott

2016

Constraints

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“…This is especially useful if A is a product automaton for several constraints. For this purpose, we use the automaton constraint introduced in [2], which (unlike the regular constraint [12]) allows us to associate counters to a transition. Each string property requires (i) a counter variable whose final value reflects the value of that string property, (ii) possibly some auxiliary counter variables, (iii) initial values of the counter variables, and (iv) update formulae in the automaton transitions for the counter variables.…”

Section: Extracting Occurrence Word and Stretch Constraints From Anmentioning

confidence: 99%

“…, R}. Each row r (with 0 ≤ r < R) of M is subject to a constraint defined by a finite-state automaton A [2,12]. For simplicity, we assume that each row is subject to the same constraint.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Matrices, Automata, and Double Counting

Beldiceanu¹,

Carlsson²,

Flener³

et al. 2010

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finitestate automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances.

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“…Hence it is interesting to integrate the two methods, and design a hybrid neighbourhood, namely a variable-directed and constraint-directed neighbourhood, so that we can benefit from the advantages of both. We address how to design a hybrid neighbourhood for the very useful automaton constraint [3], a particular case of which is also known as the regular constraint [5].…”

Section: Introductionmentioning

confidence: 99%

Solution neighbourhoods for constraint-directed local search

Flener

Pearson

2012

Proceedings of the 27th Annual ACM Symposium on Applied Computing

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We propose solution neighbourhoods, which contain only solutions to a chosen constraint, as the solutions to a constraint capture the structure of the constraint. We save the time needed for neighbourhood evaluation of that constraint by using a solution neighbourhood. This may be useful especially for constraints for which there exists no known constanttime algorithm for neighbour evaluation. We design a solution neighbourhood for the very useful automaton constraint, and demonstrate the practicality of our approach on a library of nurse scheduling instances. We show the feasibility of designing solution neighbourhoods for other constraints.

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Deriving Filtering Algorithms from Constraint Checkers

Cited by 71 publications

References 20 publications

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

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

On Matrices, Automata, and Double Counting

Solution neighbourhoods for constraint-directed local search

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