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27
Applying interval arithmetic to real, integer and Boolean constraints
 JOURNAL OF LOGIC PROGRAMMING
, 1997
"... We present in this paper a general narrowing algorithm, based on relational interval arithmetic, which applies to any nary relation on!. The main idea is to define, for every such relation ae, a narrowing function \Gamma! ae based on the approximation of ae by a block which is the cartesian product ..."
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Cited by 168 (19 self)
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We present in this paper a general narrowing algorithm, based on relational interval arithmetic, which applies to any nary relation on!. The main idea is to define, for every such relation ae, a narrowing function \Gamma! ae based on the approximation of ae by a block which is the cartesian product of intervals. We then show how, under certain conditions, one can compute the narrowing function of relations defined in terms of unions and intersections of simpler relations. We apply the use of the narrowing algorithm, which is the core of the CLP language BNRProlog, to integer and disequality constraints, to boolean constraints and to relations mixing numerical and boolean values. The result is a language, called CLP(BNR), where constraints are expressed in a unique structure, allowing the mixing of real numbers, integers and booleans. We end by the presentation of several examples showing the advantages of such approach from the point of view of the expressiveness, and give some computational results from a first prototype
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 67 (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 ...
Configuration as Composite Constraint Satisfaction
 in Proc. Artificial Intelligence and Manufacturing. Research Planning Workshop
, 1996
"... Selecting and arranging parts is the core of a configuration task. The validity of a configuration is defined in terms of constraints. Highly declarative, domain independent and simple to use, the constraint satisfaction problem (CSP) paradigm offers an adequate framework for this task. However, the ..."
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Cited by 65 (5 self)
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Selecting and arranging parts is the core of a configuration task. The validity of a configuration is defined in terms of constraints. Highly declarative, domain independent and simple to use, the constraint satisfaction problem (CSP) paradigm offers an adequate framework for this task. However, the basic paradigm is not powerful enough to capture or to take advantage of essential aspects of configuration, such as the unknown a priori number of constituent parts of a system or the inherent internal structure of these parts. Although notable effort has been spent on extending the basic paradigm to accommodate these issues, we still lack a comprehensive formalism for configuration. This paper presents the main ideas behind a general constraintbased model of configuration tasks represented as a new class of nonstandard constraint satisfaction problems, called composite CSP. Composite CSP unifies several CSP extensions, providing a more comprehensive and efficient basis for formulating and solving configuration problems.
Abstraction via Approximate Symmetry
 In Proc. of the 13 th IJCAI
, 1993
"... Abstraction techniques are important for solving constraint satisfaction problems with global constraints and low solution density. In the presence of global constraints, backtracking search is unable to prune partial solutions. It therefore operates like pure generateandtest. Abstraction improves ..."
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Cited by 40 (4 self)
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Abstraction techniques are important for solving constraint satisfaction problems with global constraints and low solution density. In the presence of global constraints, backtracking search is unable to prune partial solutions. It therefore operates like pure generateandtest. Abstraction improves on generateandtest by enabling entire subsets of the solution space to be pruned early in a search process. This paper describes how abstraction spaces can be characterized in terms of approximate symmetries of the original, concrete search space. It defines two special types of approximate symmetry, called "range symmetry" and "domain symmetry", which apply to function finding problems. It also presents algorithms for automatically synthesizing hierarchic problem solvers based on range or domain symmetry. The algorithms operate by analyzing declarative descriptions of classes of constraint satisfaction problems. Both algorithms have been fully implemented. This paper concludes by presenting data from experiments testing the two synthesis algorithms and the resulting problem solvers on NPhard scheduling and partitioning problems.
On the Computation of Local Interchangeability In Discrete Constraint Satisfaction Problems
, 1998
"... In [4], Freuder defines several types of interchange ability to capture the equivalence among the values of a variable in a discrete constraint satisfaction prob lem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedu ..."
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Cited by 33 (6 self)
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In [4], Freuder defines several types of interchange ability to capture the equivalence among the values of a variable in a discrete constraint satisfaction prob lem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedure for computing a weak form of local interchangeability. Second, we show that the modified procedure can be used to generate a conjunctire decomposition of the CSP by localizing, in the CSP, independent subproblems. Third, for the case of constraints of mutual exclusion, we show that locally interchangeable values can be computed in a straightforward manner, and that the only possible type of local interchangeability is the one that induces locally independent subproblems. Finally, we give hints on how to exploit these results in practice, establish a lattice that relates some types of interchangeability, and identify directions for future research.
The Complexity of Constraint Satisfaction Revisited
 ARTIFICIAL INTELLIGENCE
, 1993
"... This paper is a retrospective account of some of the developments leading up to, and ensuing from, the analysis of the complexity of some polynomial network consistency algorithms for constraint satisfaction problems. ..."
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Cited by 26 (3 self)
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This paper is a retrospective account of some of the developments leading up to, and ensuing from, the analysis of the complexity of some polynomial network consistency algorithms for constraint satisfaction problems.
Knowledge Structuring and Constraint Satisfaction: The Mapsee Approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1988
"... AbstractSchemabased representations for visual knowledge are integrated with constraint satisfaction techniques. This integration is discussed in a progression of three sketch map interpretation programs: Mapsee1, Mapsee2, and Mapsee3. The programs are evaluated by the criteria of descriptive ..."
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Cited by 20 (0 self)
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AbstractSchemabased representations for visual knowledge are integrated with constraint satisfaction techniques. This integration is discussed in a progression of three sketch map interpretation programs: Mapsee1, Mapsee2, and Mapsee3. The programs are evaluated by the criteria of descriptive and procedural adequacy. The evaluation indicates that a schemabased representation used in combination with a hierarchical arc consistency algorithm constitutes a modular, efficient, and effective approach to the structured representation of visual knowledge. The schemata used in this representation are embedded in composition and specialization hierarchies. Specialization hierarchies are further expanded into discrimination graphs. Index TermsConstraint satisfaction, discrimination graphs, hierarchical arc consistency, modelbased vision, recognition, schema representations, sketch maps. I.
Hierarchical Arc Consistency for Disjoint Real Intervals in Constraint Logic Programming
 COMPUTATIONAL INTELLIGENCE
, 1992
"... There have been many proposals for adding sound implementations of numeric processing to Prolog. This paper describes an approach to numeric constraint processing which has been implemented in Echidna, a new constraint logic programming (CLP) language. Echidna uses consistency algorithms which can a ..."
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Cited by 19 (0 self)
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There have been many proposals for adding sound implementations of numeric processing to Prolog. This paper describes an approach to numeric constraint processing which has been implemented in Echidna, a new constraint logic programming (CLP) language. Echidna uses consistency algorithms which can actively process a wider variety of numeric constraints than most other CLP systems, including constraints containing some common nonlinear functions. A unique feature of Echidna is that it implements domains for realvalued variables with hierarchical data structures and exploits this structure using a hierarchical arc consistency algorithm specialized for numeric constraints. This gives Echidna two advantages over other systems. First, the union of disjoint intervals can be represented directly. Other approaches require trying each disjoint interval in turn during backtrack search. Second, the hierarchical structure facilitates varying the precision of constraint processing. Consequently...
A Nurse Rostering System Using Constraint Programming and Redundant Modeling
 IEEE Transactions in Information Technology in Biomedicine
, 1997
"... This paper describes the design and implementation of a constraintbased nurse rostering system using a redundant modeling approach. Nurse rostering is defined as the process of generating timetables for specifying the work shifts of nurses over a given period of time. This process is difficult beca ..."
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Cited by 17 (2 self)
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This paper describes the design and implementation of a constraintbased nurse rostering system using a redundant modeling approach. Nurse rostering is defined as the process of generating timetables for specifying the work shifts of nurses over a given period of time. This process is difficult because the human roster planner has to ensure that every rostering decision made complies with a mixture of hard hospital rules and soft nurse preference rules. Moreover, some nurse shift preassignments often break the regularity of wanted (or unwanted) shifts and reduce the choices for other unfilled slots. Soft constraints amount to disjunction, which can be modeled as choices in the search space. This approach, although straightforward, incurs overhead in the search of solution. To reduce search time, we propose redundant modeling, an effective way to increase constraint propagation through cooperations among different models for the same problem. Our problem domain involves around twentyf...
Interval Computation as Deduction in CHIP
 Journal of Logic Programming
, 1993
"... Logic programming realizes the ideal of "computation is deduction," but not when floatingpoint numbers are involved. In that respect logic programming languages are as careless as conventional computation: they ignore the fact that floatingpoint operations are only approximate and that it is not e ..."
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Cited by 16 (3 self)
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Logic programming realizes the ideal of "computation is deduction," but not when floatingpoint numbers are involved. In that respect logic programming languages are as careless as conventional computation: they ignore the fact that floatingpoint operations are only approximate and that it is not easy to tell how good the approximation is. It is our aim to extend the benefits of logic programming to computation involving floatingpoint arithmetic. Our starting points are the ideas of Cleary and the CHIP programming language. Cleary proposed a relational form of interval arithmetic which was incorporated in BNR Prolog in such a way that variables already bound can be bound again. In this way the usual logical interpretation of computation no longer holds. In this paper we develop a technique for narrowing intervals that we relate both to Cleary's work and to the constraintsatisfaction techniques of artificial intelligence. We then modify CHIP by allowing domains to be intervals of rea...