Efficient algorithms for singleton arc consistency

Bessière, Christian; Cardon, Stéphane; Debruyne, Romuald; Lecoutre, Christophe

doi:10.1007/s10601-009-9080-5

Cited by 30 publications

(21 citation statements)

References 17 publications

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“…SAC, which is stronger than maxRPC, has received considerable attention since, and significant progress has been made regarding new SAC algorithms [3,6,7,20]. However, there is no concrete evidence yet that SAC can be cost-effective when maintained during search.…”

Section: Maxrpcmentioning

confidence: 99%

New algorithms for max restricted path consistency

et al. 2011

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Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that enforces a higher order of consistency than arc consistency. Despite the strong pruning that can be achieved, maxRPC is rarely used because existing maxRPC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose and evaluate techniques that can boost the performance of maxRPC algorithms by eliminating many of these overheads and redundancies. These include the combined use of two data structures to avoid many redundant constraint checks, and the exploitation of residues to quickly verify the existence of supports. Based on these, we propose a number of closely related maxRPC algorithms. The first one, maxRPC3, has optimal O(end 3 ) time complexity, displays good performance when used stand-alone, but is expensive to apply during search.

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Section: Maxrpcmentioning

confidence: 99%

New algorithms for max restricted path consistency

et al. 2011

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“…Domain filtering removes values that cannot take part in any solution. Strong consistencies may be used to tighten the formulation of an instance [7,37]. Domains may be filtered by some form of propagation prior to (and potentially enabling) other reformulations.…”

Section: Variable Domain Filteringmentioning

confidence: 99%

“…We have previously [47,50] filtered the user-defined decision variables using a strong consistency related to Singleton Arc Consistency (SAC) [7]: SACBounds applies the SAC test to prune the upper and lower bound of each variable to exhaustion. The Minion solver [30] was used to establish SACBounds.…”

Section: Variable Domain Filteringmentioning

confidence: 99%

“…Domain filtering is an established preprocessing technique as described in Section 2.2. In Savile Row domain filtering is implemented by tailoring the problem instance for output to Minion and using Minion's standard propagation combined with singleton consistency [7] applied to the upper and lower bounds only (SACBounds). Subsequently the tailoring process is performed a second time, making use of the filtered variable domains.…”

Section: Experiments One: Variable Unification and Domain Filteringmentioning

confidence: 99%

“…We evaluated X-CSE on the 24 instances in Figure 1 of Puget [55] and also with (v, k, λ)= (7,3,20) and (8,4,12). When using the CP solver, we found that 3 instances time out with IdentCSE and 2 of those also time out with X-CSE.…”

Section: Case Study 1: Bibdmentioning

confidence: 99%

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Automatically improving constraint models in Savile Row

Nightingale

Akgün

Gent

et al. 2017

Artificial Intelligence

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When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and reformulation of constraint models. We study a range of automated reformulation techniques, finding combinations of techniques which perform particularly well together. We introduce and describe in detail a new algorithm, X-CSE, to perform Associative-Commutative Common Subexpression Elimination (AC-CSE) in constraint problems, significantly improving existing CSE techniques for associative and commutative operators such as +. We demonstrate that these reformulation techniques can be integrated in a single automated constraint modelling tool, called Savile Row, whose architecture we describe. We use Savile Row as an experimental testbed to evaluate each reformulation on a set of 50 problem classes, with 596 instances in total. Our recommended reformulations are well worthwhile even including overheads, especially on harder instances where solver time dominates. With a SAT solver we observed a geometric mean of 2.15 times speedup compared to a straightforward tailored model without recommended reformulations. Using a CP solver, we obtained a geometric mean of 5.96 times speedup for instances taking over 10 seconds to solve.

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Constraint Networks

Lecoutre¹

2009

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Constraint Programming (CP) is a useful technology for modeling and solving combinatorial constrained problems. On the one hand, on can use a library like PyCSP 3 for easily modeling problems arising in various application fields (e.g., scheduling, planning, data-mining, cryptography, bio-informatics, organic chemistry, etc.). Problem instances can then be directly generated from specific models and data. On the other hand, for solving instances (notably, represented in XCSP 3 format), one can use a constraint solver like ACE, which is presented in this paper.ACE is an open-source constraint solver, developed in Java, which focuses on integer variables (including 0/1-Boolean variables), state-of-the-art table constraints, popular global constraints, search heuristics and (mono-criterion) optimization. Constraints over Integer Variables Generic Constraints Constraint intension Constraint extension Language-based Constraints Constraint regular Constraint mdd Comparison-based Constraints Constraints allDifferent, allDifferentList, allEqual Constraints increasing, decreasing Constraints lexIncreasing, lexDecreasing Constraint precedence Counting Constraints Constraint sum Constraint count Constraint nValues Constraint cardinality Connection Constraints Constraints maximum and maximumArg Constraints minimum and minimumArg Constraint element and channel Packing and Scheduling Constraints

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Efficient algorithms for singleton arc consistency

Cited by 30 publications

References 17 publications

New algorithms for max restricted path consistency

New algorithms for max restricted path consistency

Automatically improving constraint models in Savile Row

Constraint Networks

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