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Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 50 (3 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
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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Cited by 16 (4 self)
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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
Domain filtering consistencies for nonbinary constraints
 ARTIFICIAL INTELLIGENCE
, 2008
"... In nonbinary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering ..."
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Cited by 15 (5 self)
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In nonbinary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering consistencies have been proposed. In this paper we present a detailed theoretical, algorithmic and empirical study of domain filtering consistencies for nonbinary problems. We study three domain filtering consistencies that are inspired by corresponding variable based domain filtering consistencies for binary problems. These consistencies are stronger than generalized arc consistency, but weaker than pairwise consistency, which is a strong consistency that removes tuples from constraint relations. Among other theoretical results, and contrary to expectations, we prove that these new consistencies do not reduce to the variable based definitions of their counterparts on binary constraints. We propose a number of algorithms to achieve the three consistencies. One of these algorithms has a time complexity comparable to that for generalized arc consistency despite performing more pruning. Experiments demonstrate that our new consistencies are promising as they can be more efficient than generalized arc consistency on certain nonbinary problems.
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 11 (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.
Inverse Consistencies for Nonbinary Constraints
, 2006
"... We present a detailed study of two inverse consistencies for nonbinary constraints: relational path inverse consistency (rel PIC) and pairwise inverse consistency (PWIC). These are stronger than generalized arc consistency (GAC), even though they also only prune domain values. We propose algorith ..."
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Cited by 6 (1 self)
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We present a detailed study of two inverse consistencies for nonbinary constraints: relational path inverse consistency (rel PIC) and pairwise inverse consistency (PWIC). These are stronger than generalized arc consistency (GAC), even though they also only prune domain values. We propose algorithms to achieve rel PIC and PWIC, that have a time complexity better than the previous generic algorithm for inverse consistencies. One of our algorithms for PWIC has a complexity comparable to that for GAC despite doing more pruning. Our experiments demonstrate that inverse consistencies can be more efficient than GAC on a range of nonbinary problems.
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 constraint sa ..."
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Cited by 3 (0 self)
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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.
Relational Consistencies
 Research Report APES282001, APES Research Group
, 2001
"... We perform an extensive comparison of relational consistencies along four dimensions: on binary constraints, on nonbinary constraints, on encodings of nonbinary constraints, and on decomposable nonbinary constraints. Our results contain some surprises. For example, on binary constraints, re ..."
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Cited by 2 (0 self)
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We perform an extensive comparison of relational consistencies along four dimensions: on binary constraints, on nonbinary constraints, on encodings of nonbinary constraints, and on decomposable nonbinary constraints. Our results contain some surprises. For example, on binary constraints, relational pathconsistency does not reduce to pathconsistency. On nonbinary constraints, relational arcconsistency is incomparable to generalized arcconsistency, whilst strong relational arcconsistency dominates generalized arcconsistency.