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72
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 76 (5 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
Encodings of NonBinary Constraint Satisfaction Problems
, 1999
"... We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. ..."
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Cited by 47 (10 self)
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We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation
Optimal and Suboptimal Singleton Arc Consistency Algorithms
 Professional Book Center
, 2005
"... Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent after the assignment of a value to a variable. Algorithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give ..."
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Cited by 40 (4 self)
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Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent after the assignment of a value to a variable. Algorithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give a lower bound to the time complexity of enforcing SAC, and we propose an algorithm that achieves this complexity, thus being optimal. However, it can be costly in space on large problems. We then propose another SAC algorithm that trades time optimality for a better space complexity. Nevertheless, this last algorithm has a better worstcase time complexity than previously published SAC algorithms. An experimental study shows the good performance of the new algorithms. 1
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 38 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
Binary vs. nonbinary constraints
 Artificial Intelligence
, 2002
"... Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of the ..."
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Cited by 31 (3 self)
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Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of these two transformations. Our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms. We first compare local consistency techniques such as arc consistency in terms of their inferential power when they are applied to the original (nonbinary) formulation and to each of its binary transformations. For example, we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation. We then extend these results to the two backtracking algorithms. We are able to give either a theoretical bound on how much one formulation is better than another, or examples that show such a bound does not exist. For example, we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem. Our results can be used to help decide if applying one of these transformations to all (or part) of a constraint satisfaction model would be beneficial. 2 1
Theoretical analysis of singleton arc consistency
 Proceedings ECAI’04 Workshop on Modelling and solving problems with constraints
, 2004
"... Singleton arc consistency (SAC) is a consistency property that is simple to specify and is stronger than arc consistency. Algorithms have already been proposed to enforce SAC, but they have a high time complexity. In this paper, we give a lower bound to the worstcase time complexity of enforcing SA ..."
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Cited by 28 (3 self)
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Singleton arc consistency (SAC) is a consistency property that is simple to specify and is stronger than arc consistency. Algorithms have already been proposed to enforce SAC, but they have a high time complexity. In this paper, we give a lower bound to the worstcase time complexity of enforcing SAC on binary constraints. We discuss two interesting features of SAC. The first feature leads us to propose an algorithm for SAC that has optimal time complexity when restricted to binary constraints. The second feature leads us to extend SAC to a stronger level of local consistency that we call Bidirectional SAC (BiSAC). We also show the relationship between SAC and the propagation of disjunctive constraints. 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 27 (11 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.
Optimal basic block instruction scheduling for multipleissue processors using constraint programming
 In: Proceedings of the 18th IEEE International Conference on Tools with Artificial Intelligence
, 2005
"... Instruction scheduling is one of the most important steps for improving the performance of object code produced by a compiler. A fundamental problem that arises in instruction scheduling is to find a minimum length schedule for a basic block—a straightline sequence of code with a single entry point ..."
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Cited by 22 (9 self)
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Instruction scheduling is one of the most important steps for improving the performance of object code produced by a compiler. A fundamental problem that arises in instruction scheduling is to find a minimum length schedule for a basic block—a straightline sequence of code with a single entry point and a single exit point—subject to precedence, latency, and resource constraints. Solving the problem exactly is NPcomplete, and heuristic approaches are currently used in most compilers. In contrast, we present a scheduler that finds provably optimal schedules for basic blocks using techniques from constraint programming. In developing our optimal scheduler, the key to scaling up to large, real problems was in the development of preprocessing techniques for improving the constraint model. We experimentally evaluated our optimal scheduler on the SPEC 2000 integer and floating point benchmarks. On this benchmark suite, the optimal scheduler was very robust—all but a handful of the hundreds of thousands of basic blocks in our benchmark suite were solved optimally within a reasonable time limit—and scaled to the largest basic blocks, including basic blocks with up to 2600 instructions. This compares favorably to the best previous exact approaches. 1.
Random constraint satisfaction: easy generation of hard (satisfiable) instances
 Artificial Intelligence
"... rue de l’université, SP 16 ..."
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