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Partition Search for Nonbinary Constraint Satisfaction
 Information Sciences
, 2007
"... Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Anal ..."
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Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Analytical prediction of quantitative performance of partition search appears to be intractable and evaluation therefore has to be by experimental comparison with reduction search algorithms that represent the state of the art. Instead of working only with available reduction search algorithms, this paper introduces enhancements such as semijoin reduction preprocessing using Bloom filtering.
Extending forward checking
 in Proceedings of CP’00
, 2000
"... Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from ..."
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Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1
Backtracking Search Algorithms
, 2006
"... There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as var ..."
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Cited by 19 (2 self)
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There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stochastic search algorithms are the topic of Chapter 5. An algorithm for solving a constraint satisfaction problem (CSP) can be either complete or incomplete. Complete, or systematic algorithms, come with a guarantee that a solution will be found if one exists, and can be used to show that a CSP does not have a solution and to find a provably optimal solution. Backtracking search algorithms and dynamic programming algorithms are, in general, examples of complete algorithms. Incomplete, or nonsystematic algorithms, cannot be used to show a CSP does not have a solution or to find a provably optimal solution. However, such algorithms are often effective at finding a solution if one exists and can be used to find an approximation to an optimal solution. Local or stochastic search algorithms are examples of incomplete algorithms. Of the two
Theory and practice of constraint propagation
 In Proceedings of the 3rd Workshop on Constraint Programming in Decision and Control
, 2001
"... Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving co ..."
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Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving constraintbased models, the real power engine behind CP is called constraint propagation (domain filtering, pruning or consistency techniques). In the paper we give a survey of common consistency techniques for binary constraints. We describe the main ideas behind them, list their advantages and limitations, and compare their pruning power. Then we briefly explain how these techniques can be extended to nonbinary constraints. Last part of the paper is devoted to modelling issues. We give some hints how the constraint propagation can be exploited more when solving reallife problems. This part is based on our experience with solving reallife programs and it is also supported by empirical observations of other researchers.
SAT v CSP
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP00)
, 2000
"... We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satisfiability (SAT). We analyse four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arcconsistency o ..."
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We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satisfiability (SAT). We analyse four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arcconsistency on the CSP with unit propagation on the SAT problem. We then extend these results to CSP algorithms that maintain (some level of) arcconsistency during search like FC and MAC, and to the DavisPutnam procedure (which performs unit propagation at each search node). Because of differences in the branching structure of their search, a result showing the dominance of achieving arcconsistency on the CSP over unit propagation on the SAT problem does not necessarily translate to the dominance of MAC over the DavisPutnam procedure. These results provide insight into the relationship between propositional satisfiability and constraint satisfaction.
Decomposable Constraints
, 2000
"... Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be repre ..."
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Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be represented by binary constraints on the same set of variables. We compare theoretically the levels of consistency which are achieved on nonbinary constraints to those achieved on their binary decomposition. We present many new results about the level of consistency achieved by the forward checking algorithm and its various generalizations to nonbinary constraints. We also compare the level of consistency achieved by arcconsistency and its generalization to nonbinary constraints, and identify special cases of nonbinary decomposable constraints where weaker or stronger conditions, than in the general case, hold. We also analyze the cost, in consistency checks, required to achieve certain levels of consistency.
The slide metaconstraint
"... We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide ..."
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Cited by 15 (3 self)
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We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide with a global cardinality constraint. We also show how to propagate Slide. Our experiments demonstrate that using Slide to encode constraints can be just as efficient and effective as using specialized propagators.
Local Consistencies in SAT
 In Proc. SAT2003
, 2003
"... We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem. ..."
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Cited by 13 (1 self)
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We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem.
Description and representation of the problems selected for the first international constraint satisfaction solver competition
 In Proceedings of CPAI’05 workshop held with CP’05
, 2005
"... Abstract. In this paper, we present the problems that have been selected for the first international competition of CSP solvers. First, we introduce a succinct description of each problem and then, we present the two formats that have been used to represent the CSP instances. 1 ..."
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Abstract. In this paper, we present the problems that have been selected for the first international competition of CSP solvers. First, we introduce a succinct description of each problem and then, we present the two formats that have been used to represent the CSP instances. 1