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108
An OpenEnded Finite Domain Constraint Solver
, 1997
"... We describe the design and implementation of a finite domain constraint solver embedded in a Prolog system using an extended unification mechanism via attributed variables as a generic constraint interface. The solver is essentially a scheduler for indexicals, i.e. reactive functional rules encodin ..."
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Cited by 196 (8 self)
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We describe the design and implementation of a finite domain constraint solver embedded in a Prolog system using an extended unification mechanism via attributed variables as a generic constraint interface. The solver is essentially a scheduler for indexicals, i.e. reactive functional rules encoding local consistency methods performing incremental constraint solving or entailment checking, and global constraints, i.e. general propagators which may use specialized algorithms to achieve a higher degree of consistency or better time and space complexity. The solver has an openended design: the user can introduce new constraints, either in terms of indexicals by writing rules in a functional notation, or as global constraints via a Prolog programming interface. Constraints defined in terms of indexicals can be linked to 0/1variables modeling entailment; thus indexicals are used for constraint solving as well as for entailment testing. Constraints can be arbitrarily combined using the ...
Interval propagation to reason about sets: definition and implementation of a practical language
 CONSTRAINTS
, 1997
"... Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficu ..."
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Cited by 121 (8 self)
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Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficult a natural and concise modelling as well as an efficient solving of a class of NPcomplete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by set inclusion. We define the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols ([ � \ � n), and the set inclusion relation (). Set expressions built using the operation symbols are interpreted as relations (s [ s1 = s2,...). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal definition of the language and its design and implementation as a practical language.
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 87 (27 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.
Increasing Constraint Propagation by Redundant Modeling: an Experience Report
 CONSTRAINTS
, 1999
"... This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of ..."
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Cited by 78 (8 self)
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This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as submodels. Channeling constraints allow the submodels to cooperate during constraint solving by propagating constraints freely amongst the submodels. This extra level of pruning and propagation activities becomes the source of execution speedup. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and wellknown nqueens problem, while the second case study applies our method in the design and construction of a reallife ...
Specific Filtering Algorithms for OverConstrained Problems
, 2001
"... In recent years, many constraintspecific filtering algorithms have been introduced. Such algorithms use the semantics of the constraint to perform filtering more eciently than a generic algorithm. The usefulness of such methods has been widely proven for solving constraint satisfaction problems. In ..."
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Cited by 53 (14 self)
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In recent years, many constraintspecific filtering algorithms have been introduced. Such algorithms use the semantics of the constraint to perform filtering more eciently than a generic algorithm. The usefulness of such methods has been widely proven for solving constraint satisfaction problems. In this paper, we extend this concept to overconstrained problems by associating specific filtering algorithms with constraints that may be violated. We present a paradigm that places no restrictions on the constraint filtering algorithms used. We illustrate our method with a complete study of the Alldifferent constraint.
Deriving Filtering Algorithms from Constraint Checkers
 Principles and Practice of Constraint Programming (CP’2004), volume 3258 of LNCS
, 2004
"... Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction ..."
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Cited by 50 (10 self)
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Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction of signature and transition constraints we show how to systematically obtain a filtering algorithm. Under some restrictions on the signature and transition constraints this filtering algorithm achieves arcconsistency. An implementation based on some constraints as well as on the metaprogramming facilities of SICStus Prolog is available. For a restricted class of automata we provide a filtering algorithm for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution. Keywords: Constraint Programming,
Kakuro as a Constraint Problem
"... In this paper we describe models of the logic puzzle Kakuro as a constraint problem with finite domain variables. We show a basic model expressing the constraints of the problem and present various improvements to enhance the constraint propagation, and compare alternatives using MILP and SAT solve ..."
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Cited by 45 (1 self)
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In this paper we describe models of the logic puzzle Kakuro as a constraint problem with finite domain variables. We show a basic model expressing the constraints of the problem and present various improvements to enhance the constraint propagation, and compare alternatives using MILP and SAT solvers. Results for different puzzle collections are given. We also propose a grading scheme predicting the difficulty of a puzzle for a human and show how problems can be tightened by removing hints.
A Unifying Framework for Integer and Finite Domain Constraint Programming
, 1997
"... We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capab ..."
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Cited by 35 (2 self)
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We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capabilities. We introduce symbolic constraint abstractions into integer programming. Finally, we discuss possible combinations of the two approaches.
Revisiting the sequence constraint
 PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP 2006), LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Many combinatorial problems, such as car sequencing and rostering, feature sequence constraints, restricting the number of occurrences of certain values in every subsequence of a given width. To date, none of the filtering algorithms proposed guaranteed domain consistency. In this paper, we presen ..."
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Cited by 35 (4 self)
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Many combinatorial problems, such as car sequencing and rostering, feature sequence constraints, restricting the number of occurrences of certain values in every subsequence of a given width. To date, none of the filtering algorithms proposed guaranteed domain consistency. In this paper, we present three filtering algorithms for the sequence constraint, with complementary strengths. One borrows ideas from dynamic programming; another reformulates it as a regular constraint; the last is customized. The last two algorithms establish domain consistency. Our customized algorithm does so in polynomial time, and can even be applied to a generalized sequence constraint for subsequences of variable widths. Experimental results show the practical usefulness of each.
A Scheme for Unifying Optimization and Constraint Satisfaction Methods
, 2000
"... Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search a ..."
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Cited by 34 (6 self)
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Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search and inference and the duality of strengthening and relaxation. Optimization as well as constraint satisfaction methods can be seen as exploiting these dualities in their respective ways. Our proposal is that rather than employ either type of method exclusively, one can focus on how these dualities can be exploited in a given problem class. The resulting algorithm is likely to contain elements from both optimization and constraint satisfaction, and perhaps new methods that belong to neither.