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An Optimal Filtering Algorithm for Table Constraints
"... Filtering algorithms for table constraints are constraintbased, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient valuebased algorithms for table constraints, meaning that the propagation queue also co ..."
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Filtering algorithms for table constraints are constraintbased, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient valuebased algorithms for table constraints, meaning that the propagation queue also contains information on the removed values. One of these algorithms (AC5TCTr) is proved to have an optimal time complexity of O(r.t + r.d) per table constraint. Experimental results show that, on structured instances, all our algorithms are two or three times faster than the state of the art STR2+ and MDD c algorithms.
Generating Specialpurpose Stateless Propagators for Arbitrary Constraints
"... Abstract. Given an arbitrary constraint c on n variables with domain size d, we show how to generate a custom propagator that establishes GAC in time O(nd) by precomputing the propagation that would be performed on every reachable subdomain of scope(c). Our propagators are stateless: they store no s ..."
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Abstract. Given an arbitrary constraint c on n variables with domain size d, we show how to generate a custom propagator that establishes GAC in time O(nd) by precomputing the propagation that would be performed on every reachable subdomain of scope(c). Our propagators are stateless: they store no state between calls, and so incur no overhead in storing and backtracking state during search. The preprocessing step can take exponential time and the custom propagator is potentially exponential in size. However, for small constraints used repeatedly, in one problem or many, this technique can provide substantial practical gains. Our experimental results show that, compared with optimised implementations of the table constraint, this technique can lead to an order of magnitude speedup, while doing identical search on realistic problems. The technique can also be many times faster than a decomposition into primitive constraints in the Minion solver. Propagation is so fast that, for constraints available in our solver, the generated propagator compares well with a humanoptimised propagator for the same constraint. 1
Sliced Table Constraints: Combining Compression and Tabular Reduction
"... Abstract. Many industrial applications require the use of table constraints (e.g., in configuration problems), sometimes of significant size. During the recent years, researchers have focused on reducing space and time complexities of this type of constraint. Static and dynamic reduction based appro ..."
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Abstract. Many industrial applications require the use of table constraints (e.g., in configuration problems), sometimes of significant size. During the recent years, researchers have focused on reducing space and time complexities of this type of constraint. Static and dynamic reduction based approaches have been proposed giving new compact representations of table constraints and effective filtering algorithms. In this paper, we study the possibility of combining both static and dynamic reduction techniques by proposing a new compressed form of table constraints based on frequent pattern detection, and exploiting it in STR (Simple Tabular Reduction).
Flexible Management of LargeScale Integer Domains in CSPs
 SETN 2010: 6TH HELLENIC CONF. ON ARTIFICIAL INTELLIGENCE
, 2010
"... Most research on Constraint Programming concerns the (exponential) search space of Constraint Satisfaction Problems (CSPs) and intelligent algorithms that reduce and explore it. This work proposes a different way, not of solving a problem, but of storing the domains of its variables, an important—an ..."
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Most research on Constraint Programming concerns the (exponential) search space of Constraint Satisfaction Problems (CSPs) and intelligent algorithms that reduce and explore it. This work proposes a different way, not of solving a problem, but of storing the domains of its variables, an important—and less focused—issue especially when they are large. The new data structures that are used are proved theoretically and empirically to adapt better to large domains, than the commonly used ones. The experiments of this work display the contrast between the most popular Constraint Programming systems and a new system that uses the data structures proposed in order to solve CSP instances with wide domains, such as known Bioinformatics problems.
Domain Consistency with Forbidden Values
, 2010
"... This paper presents a novel domainconsistency algorithm which does not maintain supports dynamically during propagation, but rather maintain forbidden values. It introduces the optimal NAC4 (negative AC4) algorithm based on this idea. It further shows that maintaining forbidden values dynamically ..."
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This paper presents a novel domainconsistency algorithm which does not maintain supports dynamically during propagation, but rather maintain forbidden values. It introduces the optimal NAC4 (negative AC4) algorithm based on this idea. It further shows that maintaining forbidden values dynamically allows the generic algorithm AC5 to achieve domain consistency in time O(ed) for classes of constraints in which the number of supports is O(d 2) but the number of forbidden values is O(d). The paper also shows how forbidden values and supports can be used jointly to achieve domain consistency on logical combinations of constraints and to compute validity as well as entailment of constraints. Experimental results show the benefits of the joint exploitation of supports and forbidden values.
1ILP Modulo Data
"... Abstract—The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could enable advancements in a variety of contexts, from da ..."
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Abstract—The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could enable advancements in a variety of contexts, from databacked decision making to dataintensive scientific research. To this end, we introduce a decidable logic aimed at database analysis. Our logic extends quantifierfree Linear Integer Arithmetic with operators from Relational Algebra, like selection and cross product. We provide a scalable decision procedure that is based on the BC(T) architecture for ILP Modulo Theories. Our decision procedure makes use of database techniques. We also experimentally evaluate our approach, and discuss potential applications. I.
SPIDER: A Basic CSP Solver
"... Abstract. This document provides a short description of a MACbased solver written by the author for the Third International CSP Solver ..."
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Abstract. This document provides a short description of a MACbased solver written by the author for the Third International CSP Solver
Toward more Robustness
, 2013
"... Abstract. This paper describes the three main improvements made to the solver Abscon 109 [9]. The new version, Abscon 112, is able to automatically break some variable symmetries, infer allDifferent constraints from cliques of variables that are pairwise irreflexive, and use an optimized version of ..."
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Abstract. This paper describes the three main improvements made to the solver Abscon 109 [9]. The new version, Abscon 112, is able to automatically break some variable symmetries, infer allDifferent constraints from cliques of variables that are pairwise irreflexive, and use an optimized version of the STR (Simple Tabular Reduction) technique initially introduced by J. Ullmann for table constraints. 1 From Local to Global Variable Symmetries In [10], we have proposed to automatically detect variable symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetrical variables. From this local information that can be obtained in polynomial time, we can build a socalled lsvgraph whose automorphisms correspond to (global) variable symmetries. Interestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constraints. Besides, the size of the lsvgraph is linear wrt the number of constraints (and their arity). To break symmetries from the generators returned by a graph automorphism