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79
A Generic ArcConsistency Algorithm and its Specializations
 Artificial Intelligence
, 1992
"... Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of ..."
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Cited by 190 (7 self)
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Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of Mohr and Henderson [15]. AC4 runs in O(ed 2 ) in the worst case, where e is the number of arcs (or constraints) and d is the size of the largest domain. Being applicable to the whole class of (binary) CSP, these algorithms do not take into account the semantics of constraints. In this paper, we present a new generic arcconsistency algorithm AC5. This algorithm is parametrized on two specified procedures and can be instantiated to reduce to AC3 and AC4. More important, AC5 can be instantiated to produce an O(ed) algorithm for a number of important classes of constraints: functional, antifunctional, monotonic and their generalization to (functional, antifunctional, and monotonic) piecewise constraints. We also show that AC5 has an important application in constraint logic programming over finite domains [23]. The kernel of the constraint solver for such a programming language is an arcconsistency algorithm for a set of basic constraints. We prove that AC5, in conjunction with node consistency, provides a decision procedure for these constraints running in time O(ed).
Generalized Arc Consistency for Global Cardinality Constraint
"... A global cardinality constraint (gcc) is specified in terms of a set of variables X = fx1 ; :::; xpg which take their values in a subset of V = fv1 ; :::; vdg. It constrains the number of times a value v i 2 V is assigned toavariable in X to be in an interval (l i ;c i ). Cardinality constraints hav ..."
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Cited by 157 (9 self)
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A global cardinality constraint (gcc) is specified in terms of a set of variables X = fx1 ; :::; xpg which take their values in a subset of V = fv1 ; :::; vdg. It constrains the number of times a value v i 2 V is assigned toavariable in X to be in an interval (l i ;c i ). Cardinality constraints have proved very useful in many reallife problems, suchas scheduling, timetabling, or resource allocation. A gcc is more general than a constraint of difference, which requires each interval to be #0; 1#. In this paper, we present an efficient way of implementing generalized arc consistency for a gcc. The algorithm we propose is based on a new theorem of flow theory. Its space complexity is O(#Xj#jVj) and its time complexity is O(jXj 2 #jVj). We also show how this algorithm can efficiently be combined with other filtering techniques.
Practical Applications of Constraint Programming
 CONSTRAINTS
, 1996
"... Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples, ..."
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Cited by 106 (1 self)
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Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,
Automatically configuring constraint satisfaction programs: A case study
 CONSTRAINTS
, 1996
"... Multitac is a learning system that synthesizes heuristic constraint satisfaction programs. The system takes a library of generic algorithms and heuristics and specializes them for a particular application. We present a detailed case study with three different distributions ofa single combinatorial ..."
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Cited by 91 (4 self)
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Multitac is a learning system that synthesizes heuristic constraint satisfaction programs. The system takes a library of generic algorithms and heuristics and specializes them for a particular application. We present a detailed case study with three different distributions ofa single combinatorial problem, "Minimum Maximal Matching", and show that Multitac can synthesize programs for these different distributions that perform on par with handcoded programs and that exceed the performance of some wellknown satisfiability algorithms. In synthesizing a program, Multitac bases its choice of heuristics on an instance distribution, and we demonstrate that this capability has a significant impact on the results.
Constraint satisfaction using constraint logic programming
 Artificial Intelligence
, 1992
"... Constraint logic programming (CLP) is a new class of declarative programming languages whose primitive operations are based on constraints (e.g. constraint solving and constraint entailment). CLP languages naturally combine constraint propagation with nondeterministic choices. As a consequence, the ..."
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Cited by 74 (3 self)
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Constraint logic programming (CLP) is a new class of declarative programming languages whose primitive operations are based on constraints (e.g. constraint solving and constraint entailment). CLP languages naturally combine constraint propagation with nondeterministic choices. As a consequence, they are particularly appropriate for solving a variety of combinatorial search problems, using the global search paradigm, with short development time and efficiency comparable to procedural tools based on the same approach. In this paper, we describe how the CLP language cc(FD), a successor of CHIP using consistency techniques over finite domains, can be used to solve two practical applications: testpattern generation and car sequencing. For both applications, we present the cc(FD) program, describe how constraint solving is performed, report experimental results, and compare the approach with existing tools.
Constraint processing in cc(FD)
, 1992
"... Constraint logic programming languages such as CHIP [26,5] have demonstrated the practicality of declarative languages supporting consistency techniques and nondeterminism. Nevertheless they suffer from the blackbox effect: the programmer must work with a monolithic, unmodifiable, inextensible cons ..."
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Cited by 67 (11 self)
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Constraint logic programming languages such as CHIP [26,5] have demonstrated the practicality of declarative languages supporting consistency techniques and nondeterminism. Nevertheless they suffer from the blackbox effect: the programmer must work with a monolithic, unmodifiable, inextensible constraintsolver. This problem can be overcome within the logically and computationally richer concurrent constraint (cc) programming paradigm [17]. We show that some basic constraintoperations currently hardwired into constraintsolvers can be abstracted and made available as combinators in the programming language. This allows complex constraintsolvers to be decomposed into logically clean and efficiently implementable cc programs over a much simpler constraint system. In particular, we show that the CHIP constraintsolver can be simply programmed in cc(FD), acc language with an extremely simple builtin constraint solver for finite domains.
Solving the Car Sequencing Problem in Constraint Logic Programming
 In European Conference on Artificial Intelligence (ECAI88
, 1988
"... CHIP is a new constraint logic programming language combining the declarative aspect of logic programming with the efficiency of constraint manipulation techniques. In the present paper, we show an application of CHIP to the carsequencing problem which occurs in assembly line scheduling in car manu ..."
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Cited by 60 (5 self)
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CHIP is a new constraint logic programming language combining the declarative aspect of logic programming with the efficiency of constraint manipulation techniques. In the present paper, we show an application of CHIP to the carsequencing problem which occurs in assembly line scheduling in car manufacturing. This problem is highly combinatorial and has been presented recently as a "challenge " lor Artificial Intelligence (Al) systems. We presenthe approach taken to solve this problem in CHIP and give some computational results for different configurations. lt is shown that CHIP provides not only the flexibilitywhich can be expected from an Altoolby simplitying greatly the problem statement but also the efficiency which allows to solve large assembly line problems. This efficiency comes lrom the ability of CHIP to use numerical and symboliconstraints to prune the search space very early. 2 1.
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 53 (4 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
Conjunto: Constraint Logic Programming with Finite Set Domains
 Logic Programming  Proceedings of the 1994 International Symposium, pages 339358, Massachusetts Institute of Technology
, 1994
"... Combinatorial problems involving sets and relations are currently tackled by integer programming and expressed with vectors or matrices of 01 variables. This is efficient but not flexible and unnatural in problem formulation. Toward a natural programming of combinatorial problems based on sets, gra ..."
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Cited by 47 (1 self)
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Combinatorial problems involving sets and relations are currently tackled by integer programming and expressed with vectors or matrices of 01 variables. This is efficient but not flexible and unnatural in problem formulation. Toward a natural programming of combinatorial problems based on sets, graphs or relations, we define a new CLP language with set constraints. This language Conjunto 1 aims at combining the declarative aspect of Prolog with the efficiency of constraint solving techniques. We propose to constrain a set variable to range over finite set domains specified by lower and upper bounds for set inclusion. Conjunto is based on the inclusion and disjointness constraints applied to set expressions which comprise the union, intersection and difference symbols. The main contribution herein is the constraint handler which performs constraint propagation by applying consistency techniques over set constraints. 1 Introduction Various systems of set constraints have been define...