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Principles of Constraint Programming
, 2000
"... Introduction 1.1 Preliminaries Constraint programming is an alternative approach to programming in which the programming process is limited to a generation of requirements (constraints) and a solution of these requirements by means of general or domain specific methods. The general methods are us ..."
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Cited by 168 (3 self)
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Introduction 1.1 Preliminaries Constraint programming is an alternative approach to programming in which the programming process is limited to a generation of requirements (constraints) and a solution of these requirements by means of general or domain specific methods. The general methods are usually concerned with techniques of reducing the search space and with specific search methods. In contrast, the domain specific methods are usually provided in the form of special purpose algorithms or specialised packages, usually called constraint solvers. Typical examples of constraint solvers are: ffl a program that solves systems of linear equations, ffl a package for linear programming, ffl an implementation of the unification algorithm, a cornerstone of automated theorem proving. Problems that can be solved in a natural way by means of constraint programming are usually those for which efficient algorithms are
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
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Cited by 132 (13 self)
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Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
The Complexity of Global Constraints
, 2004
"... We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular ..."
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Cited by 67 (26 self)
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We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, metaconstraints like the cardinality constraint, and learning nogoods.
On Forward Checking for Nonbinary Constraint Satisfaction
 ARTIFICIAL INTELLIGENCE
, 1999
"... Solving nonbinary constraint satisfaction problems, a crucial challenge for the next years, can be tackled in two different ways: translating the nonbinary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option rai ..."
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Cited by 66 (4 self)
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Solving nonbinary constraint satisfaction problems, a crucial challenge for the next years, can be tackled in two different ways: translating the nonbinary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option raises some issues when we want to extend denitions written for the binary case. This paper focuses on the wellknown forward checking algorithm, and shows that it can be generalized to several nonbinary versions, all tting its binary denition. The classical version, proposed by Van Hentenryck, is only one of these generalizations.
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
The Difference AllDifference Makes
 IN PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1999
"... We perform a comprehensive theoretical and experimental analysis of the use of alldifferent constraints. We prove that generalized arcconsistency on such constraints lies between neighborhood inverse consistency and, under a simple restriction, path inverse consistency on the binary represent ..."
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Cited by 34 (9 self)
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We perform a comprehensive theoretical and experimental analysis of the use of alldifferent constraints. We prove that generalized arcconsistency on such constraints lies between neighborhood inverse consistency and, under a simple restriction, path inverse consistency on the binary representation of the problem. By generalizing the arguments of Kondrak and van Beek, we prove that a search algorithm that maintains generalized arcconsistency on alldifferent constraints dominates a search algorithm that maintains arcconsistency on the binary representation. Our experiments show the practical value of achieving these high levels of consistency. For example, we can solve almost all benchmark quasigroup completion problems up to order 25 with just a few branches of search. These results demonstrate the benefits of using nonbinary constraints like alldifferent to identify structure in problems.
Using Auxiliary Variables and Implied Constraints to Model NonBinary Problems
, 2000
"... We perform an extensive theoretical and empirical analysis of the use of auxiliary variables and implied constraints in modelling a class of nonbinary constraint satisfaction problems called problems of distance. This class of problems include 1d, 2d and circular Golomb rulers. We identify a larg ..."
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Cited by 31 (15 self)
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We perform an extensive theoretical and empirical analysis of the use of auxiliary variables and implied constraints in modelling a class of nonbinary constraint satisfaction problems called problems of distance. This class of problems include 1d, 2d and circular Golomb rulers. We identify a large number of different models, both binary and nonbinary, and compare theoretically the level of consistency achieved by generalized arc consistency on them. Our experiments show that the introduction of auxiliary variables and implied constraints can significantly reduce the size of the search space. For instance, our final models reduce the time to find an optimal 10mark Golomb ruler 50fold.
Modelling the Golomb Ruler Problem
, 1999
"... . The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of different models of this problem, both binary and nonbinary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ..."
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Cited by 29 (10 self)
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. The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of different models of this problem, both binary and nonbinary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ternary constraints gives better results. A binary encoding of the problem gives a smaller search tree, but is impractical because it takes far longer to run. We compare variable ordering heuristics and consider the use of implied constraints to improve propagation. We believe that more case studies such as this are essential to reduce the skill currently required for successful modelling. 1 Introduction In his AAAI98 invited talk, Gene Freuder identified modelling as one of the major hurdles preventing the uptake of constraint satisfaction technology. The availability of nonbinary constraints can increase the number of possible models of a problem amnd so makes modelling still more diffi...
Solving binary constraint satisfaction problems using evolutionary algorithms with an adaptive tness function
 In Eiben et al
"... Abstract. This paper presents a comparative study of Evolutionary Algorithms (EAs) for Constraint Satisfaction Problems (CSPs). We focus on EAs where fitness is based on penalization of constraint violations and the penalties are adapted during the execution. Three different EAs based on this approa ..."
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Cited by 26 (13 self)
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Abstract. This paper presents a comparative study of Evolutionary Algorithms (EAs) for Constraint Satisfaction Problems (CSPs). We focus on EAs where fitness is based on penalization of constraint violations and the penalties are adapted during the execution. Three different EAs based on this approach are implemented. For highly connected constraint networks, the results provide further empirical support to the theoretical prediction of the phase transition in binary CSPs. 1
Binary vs. nonbinary constraints
 Artificial Intelligence
, 2002
"... Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of the ..."
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Cited by 23 (2 self)
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Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of these two transformations. Our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms. We first compare local consistency techniques such as arc consistency in terms of their inferential power when they are applied to the original (nonbinary) formulation and to each of its binary transformations. For example, we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation. We then extend these results to the two backtracking algorithms. We are able to give either a theoretical bound on how much one formulation is better than another, or examples that show such a bound does not exist. For example, we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem. Our results can be used to help decide if applying one of these transformations to all (or part) of a constraint satisfaction model would be beneficial. 2 1