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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 112 (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.
Consistency Techniques for Continuous Constraints
 Constraints
, 1996
"... We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constrai ..."
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Cited by 58 (7 self)
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We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.
Comparing Partial Consistencies
, 1999
"... Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The ..."
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Cited by 23 (4 self)
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Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The
Boosting the Interval Narrowing Algorithm
, 1996
"... Interval narrowing techniques are a key issue for handling constraints over real numbers in the logic programming framework. However, the standard fixedpoint algorithm used for interval narrowing may give rise to cyclic phenomena and hence to problems of slow convergence. Analysis of these cyclic p ..."
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Cited by 21 (6 self)
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Interval narrowing techniques are a key issue for handling constraints over real numbers in the logic programming framework. However, the standard fixedpoint algorithm used for interval narrowing may give rise to cyclic phenomena and hence to problems of slow convergence. Analysis of these cyclic phenomena shows: 1) that a large number of operations carried out during a cycle are unnecessary; 2) that many others could be removed from cycles and performed only once when these cycles have been processed. What is proposed here is a revised interval narrowing algorithm for identifying and simplifying such cyclic phenomena dynamically. First experimental results show that this approach improves performance significantly.
Dynamic Optimization Of Interval Narrowing Algorithms
, 1998
"... this paper is on the first problem. It shows that there is a strong connection between the existence of cyclic phenomena and slow convergence. The main goal is to dynamically identify cyclic phenomena while executing algorithm ..."
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Cited by 20 (3 self)
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this paper is on the first problem. It shows that there is a strong connection between the existence of cyclic phenomena and slow convergence. The main goal is to dynamically identify cyclic phenomena while executing algorithm
A Note on Partial Consistencies over Continuous Domains
 In Proc. CP98 (Fourth International Conference on Principles and Practice of Constraint Programming
, 1998
"... . This paper investigates the relations among different partial consistencies which have been proposed for pruning the domains of the variables in constraint systems over the real numbers. We establish several properties of the filtering achieved by the algorithms based upon these partial consistenc ..."
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Cited by 17 (2 self)
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. This paper investigates the relations among different partial consistencies which have been proposed for pruning the domains of the variables in constraint systems over the real numbers. We establish several properties of the filtering achieved by the algorithms based upon these partial consistencies. Especially, we prove that : 1) 2BConsistency (or Hull consistency) algorithms actually yield a weaker pruning than Boxconsistency; 2) 3BConsistency algorithms perform a stronger pruning than Boxconsistency. This paper also provides an analysis of both the capabilities and the inherent limits of the filtering algorithms which achieve these partial consistencies. 1 Introduction Partial consistencies are the cornerstones for solving non linear constraints over the real numbers [5, 21, 3, 14, 13, 1, 26]. A partial consistency is a local property which is enforced in order to prune the sets of possible values of a variable before searching for isolated solutions. Arcconsistency is ...
Adapting CLP(R) To FloatingPoint Arithmetic
 In Proceedings of the International Conference on Fifth Generation Computer Systems
"... As a logic programming language, Prolog has shortcomings. One of the most serious of these is in arithmetic. CLP(R), though a vast improvement, assumes perfect arithmetic on reals, an unrealistic requirement for computers, where there is strong pressure to use floatingpoint arithmetic. We present an ..."
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Cited by 9 (3 self)
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As a logic programming language, Prolog has shortcomings. One of the most serious of these is in arithmetic. CLP(R), though a vast improvement, assumes perfect arithmetic on reals, an unrealistic requirement for computers, where there is strong pressure to use floatingpoint arithmetic. We present an adaptation of CLP(R) where the errors due to floatingpoint computation are absorbed by the use of intervals in such a way that the logical status of answers is not jeopardized. This system is based on Cleary's "squeezing" of floatingpoint intervals, modified to fit into Mackworth's general framework of the ConstraintSatisfaction Problem. Our partial implementation consists of a metainterpreter executed by an existing CLP(R) system. All that stands in the way of correct answers involving real numbers is the planned addition of outward rounding to the current prototype. 1 Introduction Mainstream computing holds that programming should be improved by gradual steps, as exemplified by the m...
2008 Enhancing Set Constraint Solvers with Lexicographic Bounds
 Journal of Heuristics
"... Abstract. Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as binpacking, set partitioning, circuit design, and Combinatorial Design Problems. In this paper we present and evaluate a new means towards improving the ..."
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Cited by 7 (1 self)
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Abstract. Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as binpacking, set partitioning, circuit design, and Combinatorial Design Problems. In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to the challenging symmetrical set problems often cast as Combinatorial Design Problems (CDPs). While CDPs find a natural formulation in the language of sets, in constraint programming literature, alternative models are often used due to a lack of efficiency of traditional FS solvers. We first identify the main structural components of CDPs that render their modeling suitable to set languages but their solving a technical challenge. Our new prototype solver extends the traditional subset variable domain with lexicographic bounds that better approximate a set domain by satisfying the cardinality restrictions applied to the variable, and allow for active symmetry breaking using ordering constraints. Our contribution includes the formal and practical framework of the new solver implemented on top of a traditional set solver, and an empirical evaluation on benchmark CDPs.
Abstracting Numerical Values in CLP(H,N)
, 1994
"... ing Numerical Values in CLP(H,N) Gerda Janssens 1 , Maurice Bruynooghe 1 , Vincent Englebert 2 1 Department of Computer Science, K.U. Leuven Celestijnenlaan 200A, B3001 Heverlee, Belgium 2 Institut d'Informatique, Facult'es Universitaires Notre Dame de la Paix rue GrandGagnage 21, ..."
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Cited by 6 (2 self)
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ing Numerical Values in CLP(H,N) Gerda Janssens 1 , Maurice Bruynooghe 1 , Vincent Englebert 2 1 Department of Computer Science, K.U. Leuven Celestijnenlaan 200A, B3001 Heverlee, Belgium 2 Institut d'Informatique, Facult'es Universitaires Notre Dame de la Paix rue GrandGagnage 21, B5000 Namur, Belgium Abstract. The paper defines approximations for the numerical leaves of variables in CLP(H,N) constraint systems. The abstractions are based on intervals which are computed by narrowing rules. The novelty of this approach lays in the fact that intervals are used as abstraction and that narrowing rules do not only correspond to numerical constraints but also to unification constraints. In the first abstraction the impact of the narrowing rules is limited. A prototype implementation has been developed and the obtained results are sufficiently precise to recognise (future) redundant constraints. The abstraction can be extended (1) by incorporating the narrowing rules more globally (...
Interval Computations On The Spreadsheet
 Applications of Interval Computations
, 1996
"... This paper reviews work on using interval arithmetic as the basis for next generation spreadsheet programs capable of dealing with rounding errors, imprecise data, and numerical constraints. A series of ever more versatile computational models for spreadsheets are presented beginning from classical ..."
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Cited by 6 (1 self)
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This paper reviews work on using interval arithmetic as the basis for next generation spreadsheet programs capable of dealing with rounding errors, imprecise data, and numerical constraints. A series of ever more versatile computational models for spreadsheets are presented beginning from classical interval arithmetic and ending up with interval constraint satisfaction. In order to demonstrate the ideas, an actual implementation of each model as a class library is presented and its integration with a commercial spreadsheet program is explained. 1 LIMITATIONS OF SPREADSHEET COMPUTING Spreadsheet programs, such as MS Excel, Quattro Pro, Lotus 123, etc., are among the most widely used applications of computer science. Since the pioneering days of VisiCalc and others, spreadsheet programs have been enhanced immensely with new features. However, the underlying computational paradigm of evaluating arithmetical functions by using ordinary machine arithmetic has remained the same. The wor...