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23
Encodings of NonBinary Constraint Satisfaction Problems
, 1999
"... We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. ..."
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Cited by 41 (8 self)
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We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation
A fast and simple algorithm for bounds consistency of the alldifferent constraint
 IN PROCEEDINGS OF THE 18TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2003
"... In constraint programming one models a problem by stating constraints on acceptable solutions. The constraint model is then usually solved by interleaving backtracking search and constraint propagation. Previous studies have demonstrated that designing special purpose constraint propagators for comm ..."
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Cited by 38 (10 self)
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In constraint programming one models a problem by stating constraints on acceptable solutions. The constraint model is then usually solved by interleaving backtracking search and constraint propagation. Previous studies have demonstrated that designing special purpose constraint propagators for commonly occurring constraints can significantly improve the efficiency of a constraint programming approach. In this paper we present a fast, simple algorithm for bounds consistency propagation of the alldifferent constraint. The algorithm has the same worst case behavior as the previous best algorithm but is much faster in practice. Using a variety of benchmark and random problems, we show that our algorithm outperforms existing bounds consistency algorithms and also outperforms—on problems with an easily identifiable property—stateoftheart commercial implementations of propagators for stronger forms of local consistency.
Singleton Consistencies
, 2000
"... We perform a comprehensive theoretical and empirical study of the bene ts of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the costeffectiven ..."
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Cited by 37 (8 self)
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We perform a comprehensive theoretical and empirical study of the bene ts of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the costeffectiveness of preprocessing with singleton consistency algorithms. Our experiments use both random and structured problems. Whilst preprocessing with singleton consistencies is not in general beneficial for random problems, it starts to pay off when randomness and structure are combined, and it is very worthwhile with structured problems like Golomb rulers. On such problems, preprocessing with consistency techniques as strong as singleton generalized arcconsistency (the singleton extension of generalized arcconsistency) can reduce runtimes. We also show that limiting algorithms that enforce singleton consistencies to a single pass often gives a small reduction in the amount of pruning and improves their costeffectiveness. These experimental results also demonstrate that conclusions from studies on random problems should be treated with caution.
Permutation Problems and Channelling Constraints
 TR 26, APES Group
, 2001
"... When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual ..."
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Cited by 33 (1 self)
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When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual representation. In the dual representation, dual variables stand for the primal values, whilst dual values stand for the primal variables. By means of channelling constraints, a combined model can have both primal and dual variables. In this paper, we perform an extensive theoretical and empirical study of these different models. Our results will aid constraint programmers to choose a model for a permutation problem. They also illustrate a general methodology for comparing different constraint models.
Dual Modelling of Permutation and Injection Problems
 Journal of Artificial Intelligence Research
, 2004
"... When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many ..."
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Cited by 30 (9 self)
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general...
CGRASS: A System for Transforming Constraint Satisfaction Problems
 Recent Advances in Constraints, 1530, LNCS 2627
, 2002
"... Abstract. Experts at modelling constraint satisfaction problems (CSPs) carefully choose model transformations to reduce greatly the amount of effort that is required to solve a problem by systematic search. It is a considerable challenge to automate such transformations and to identify which transfo ..."
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Cited by 26 (9 self)
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Abstract. Experts at modelling constraint satisfaction problems (CSPs) carefully choose model transformations to reduce greatly the amount of effort that is required to solve a problem by systematic search. It is a considerable challenge to automate such transformations and to identify which transformations are useful. Transformations include adding constraints that are implied by other constraints, adding constraints that eliminate symmetrical solutions, removing redundant constraints and replacing constraints with their logical equivalents. This paper describes the CGRASS (Constraint Generation And Symmetrybreaking) system that can improve a problem model by automatically performing transformations of these kinds. We focus here on transforming individual CSP instances. Experiments on the Golomb ruler problem suggest that producing good problem formulations solely by transforming problem instances is, generally, infeasible. We argue that, in certain cases, it is better to transform the problem class than individual instances and, furthermore, it can sometimes be better to transform formulations of a problem that are more abstract than a CSP. 1
Automated reformulation of specifications by safe delay of constraints
 Proceedings of the 2nd International Workshop on Modelling and Reformulating Constraint Satisfaction Problems
, 2003
"... In this paper we propose a form of reasoning on specifications of combinatorial problems, with the goal of reformulating them so that they are more efficiently solvable. The reformulation technique highlights constraints that can be safely “delayed”, and solved afterwards. Our main contribution is t ..."
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Cited by 18 (7 self)
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In this paper we propose a form of reasoning on specifications of combinatorial problems, with the goal of reformulating them so that they are more efficiently solvable. The reformulation technique highlights constraints that can be safely “delayed”, and solved afterwards. Our main contribution is the characterization (with soundness proof) of safedelay constraints with respect to a criterion on the specification, thus obtaining a mechanism for the automated reformulation of specifications applicable to a great variety of problems, e.g., graph coloring and jobshop scheduling. This is an advancement with respect to the forms of reasoning done by stateoftheartsystems, which typically just detect linearity of specifications. Another contribution is a preliminary experimentation on the effectiveness of the proposed technique, which reveals promising time savings.
Theory and practice of constraint propagation
 In Proceedings of the 3rd Workshop on Constraint Programming in Decision and Control
, 2001
"... Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving co ..."
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Cited by 17 (1 self)
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Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving constraintbased models, the real power engine behind CP is called constraint propagation (domain filtering, pruning or consistency techniques). In the paper we give a survey of common consistency techniques for binary constraints. We describe the main ideas behind them, list their advantages and limitations, and compare their pruning power. Then we briefly explain how these techniques can be extended to nonbinary constraints. Last part of the paper is devoted to modelling issues. We give some hints how the constraint propagation can be exploited more when solving reallife problems. This part is based on our experience with solving reallife programs and it is also supported by empirical observations of other researchers.
Exploiting functional dependencies in declarative problem specifications
 In Proceedings of the Ninth European Conference on Logics in Artificial Intelligence (JELIA 2004
, 2004
"... Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed ..."
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Cited by 12 (7 self)
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Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed in order to express some of the constraints, or due to precise modelling choices, e.g., to provide multiple viewpoints of the search space in order to increase propagation. In either way, the recognition of dependencies greatly helps solvers, letting them avoid spending search on unfruitful branches, while maintaining the highest degree of declarativeness. By modelling constraint problem specifications as secondorder formulae, we provide a characterization of functional dependencies in terms of semantic properties of firstorder ones. Additionally, we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies. We present opl examples of various problems, from bioinformatics, planning and resource allocation fields, and show how in many cases opl greatly benefits from the addition of such search procedures. 1
Extensions to Proof Planning for Generating Implied Constraints
 In Proceedings of Calculemus01
, 2001
"... . We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about al ..."
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Cited by 11 (7 self)
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. We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about algebraic constraints. For example, the eliminate method performs Gaussianlike elimination of variables and terms. We are also reusing proof methods from the PRESS equation solving system like (variable) isolation. 1