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Representation and Reasoning with NonBinary Constraints
, 2001
"... Many problems from the \real world" can be eciently expressed as constraint satisfaction problems (CSPs). Most of these can be naturally modelled using nary (or nonbinary) constraints. Representing problems with nary constraints and reasoning with them is therefore very important in constrai ..."
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Many problems from the \real world" can be eciently expressed as constraint satisfaction problems (CSPs). Most of these can be naturally modelled using nary (or nonbinary) constraints. Representing problems with nary constraints and reasoning with them is therefore very important in constraint satisfaction. However, issues regarding nary constraints have been neglected compared to binary constraints. The reasons were the simplicity of dealing with binary constraints compared to nary and the fact that any nonbinary CSP can be encoded into an equivalent binary. This thesis makes an empirical and theoretical study on representation and solution methods for nary CSPs. The results we present demonstrate the importance of the choice of representation and reasoning techniques in nary problems.
Neighborhood Interchangeability for NonBinary CSPs & Application to Databases
, 2005
"... Neighborhood Interchangeability (NI) identifies the equivalent values in the domain of a variable in a Constraint Satisfaction Problem (CSP). We introduce for the first time an algorithm for computing NI sets in the presence of nonbinary constraints. We integrate this mechanism with backtrack searc ..."
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Neighborhood Interchangeability (NI) identifies the equivalent values in the domain of a variable in a Constraint Satisfaction Problem (CSP). We introduce for the first time an algorithm for computing NI sets in the presence of nonbinary constraints. We integrate this mechanism with backtrack search, in a process we call dynamic bundling. We demonstrate that, as for the binary case [Beckwith et al., 2001], dynamic bundling yields multiple robust solutions for less effort than necessary for computing a single solution. We then identify the utility of this mechanism for database applications and introduce a new algorithm based on dynamic bundling for computing a join query, which we model as a CSP. We argue that the algorithm yields a compact solution space and saves memory, diskspace, and/or network bandwidth. Finally, we discuss the application of the join algorithm to materialize views.
Deadend driven learning 3
"... The paper evaluates the e ectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more di cult problem inst ..."
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The paper evaluates the e ectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more di cult problem instances. Our results show that learning can speed up backjumping when using either a xed or dynamic variable ordering. However, the improvement with a dynamic variable ordering is not as great, and for some classes of problems learning is helpful only when a limit is placed on the size of new constraints learned. 1.
Diagnosis as a Constraint Satisfaction Problem
"... this paper was motivated by the desire to evaluate CSP as the basis for consistencybased diagnosis. Much of the work to date in consistencybased diagnosis uses the technique of constraintpropagation [de Kleer 87], [Hamscher 91], but does not use a specific logical system as its basis. Recently, [ ..."
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this paper was motivated by the desire to evaluate CSP as the basis for consistencybased diagnosis. Much of the work to date in consistencybased diagnosis uses the technique of constraintpropagation [de Kleer 87], [Hamscher 91], but does not use a specific logical system as its basis. Recently, [Bond 94] uses LP (logic programming) as the basis for a diagnostic procedure. [Mackworth 92] gives a partially ordered graph which defines a hierarchy of logical systems. Because CSP (Constraint Satisfaction Problem) is both relatively mature and among the simpler logical systems available, it would be highly desirable as a basis for diagnosis. Researchers in CSP, [Dechter 90], [El Fattah 92] and in PCSP (Partial Constraint Satisfaction Problems) [Sabin 94], have addressed the use of CSP for diagnosis. This paper discusses the use of CSP as a logical system for further research in consistencybased diagnosis.
Using the Symmetry of Relations to Establish ArcConsistency in Constraint Networks
"... In [1, 2], Bessière and Cordier said that the AC6 arcconsistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are symmetric. None of the previous algorithms achievin ..."
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In [1, 2], Bessière and Cordier said that the AC6 arcconsistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are symmetric. None of the previous algorithms achieving arcconsistency (AC3 [5, 6], AC4 [7], AC6) use this property. We propose here an improved version of AC6 (the best algorithm for arcconsistency) which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed. 1. Introduction In the last five years, the number of applications using constraint networks has dramatically increased. It appears that the more constraint networks are used, the simpler the constraint satisfaction techniques involved in the applications are. In fact, a great part of reallife applications using constraint networks are limited to a forwardchecking search procedure [4], or use an arcconsistency filtering a...
A Generic Framework for ConstraintDirected Search
"... (For membership information, consult our web page) The material herein is copyrighted material. It may not be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from AAAI. ..."
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(For membership information, consult our web page) The material herein is copyrighted material. It may not be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from AAAI.
4. TITLE AND SUBTITLE S. FUNDING NUMRERS Backtracking Techniques for Hard Scheduling Problems F3060288(L 101
, 1993
"... Approved for public release; P, 1[Distribution unlimited • 13. ABSTRACT,VMaximum200woras) This paper studies a version of the job shop scheduling problem in which 5ome operations have to be scheduled within nonrelaxable time windows i.e. earliest/latest possible start time windows). This problem is ..."
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Approved for public release; P, 1[Distribution unlimited • 13. ABSTRACT,VMaximum200woras) This paper studies a version of the job shop scheduling problem in which 5ome operations have to be scheduled within nonrelaxable time windows i.e. earliest/latest possible start time windows). This problem is a wellknown NPcomplete Constraint,action roblem (CSP). A popular method for solving this type of problems consists in using depthfirst backtrack,rch. Our rier work focused on developing efficient consistency enforcing techniques and efficient variable/value order teuristics to improve the efficiency of this sea. ch procedure. nn this paper, we combine these techniques with new lookback schemes that help the arch procedure recover from socalled deadend search states (i.e. partial solutions that cannot be complec. ithout iolating some constraints). More specifically, we successively describe three intelligent backtracking sci s: (1) Dynamic Consistency Enforcement dynamically identifies critical subproblems and determines how far to o. track by electively enforcing higher levels of consistency among variables participating in these critical subproblen, (2) arning From Failure dynamically modifies the order in which variables are instantiated based on earlier c,,llicts, and I3) Heuristic Backjumping gives up searching areas of the search space that appear too difficult. These sch ",ncs arc