A strong local consistency for constraint satisfaction

Debruyne, Romuald

doi:10.1109/tai.1999.809787

Cited by 7 publications

(6 citation statements)

References 13 publications

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“…To con rm these results, an algorithm called Quick that maintains an adaptation of Max-RPC has been compared to MAC. The results of these experiments (Debruyne, 1999) show that Quick has better cpu time performances than MAC on large and hard randomly generated CNs that are relatively sparse. More interestingly, Quick has a more impor-tant stability than MAC (the cpu time performances of Quick have a very low standard deviation).…”

Section: Discussionmentioning

confidence: 98%

Domain Filtering Consistencies

Debruyne¹,

Bessière²

2001

jair

Self Cite

104

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Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.

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Section: Discussionmentioning

confidence: 98%

Domain Filtering Consistencies

Debruyne¹,

Bessière²

2001

jair

Self Cite

104

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“…This algorithm has a higher time complexity than the other two, but it has some advantages compared to them because of its lighter use of data structures during search (this is explained below and in Section 3.2). Finally, maxRPCEn1 is a fine-grained algorithm closely related to maxRPC1 [13]. This algorithm is based on AC-7 [8] and achieves maxRPCEn, a local consistency stronger than maxRPC.…”

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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“…Two different relation-filtering consistencies related to path consistency have been defined in terms of closed graph-paths. The first is partial path consistency (partial PC or PPC, Bliek & Sam-Haroud, 1999) and the second is conservative path consistency (conservative PC or CPC, Debruyne, 1999).…”

Section: Deep In Path Consistencymentioning

confidence: 99%

“…The main apparent drawback of path consistency can be avoided by adopting a conservative approach, in which the search for inconsistent pairs of values is restricted to existing constraints. This is called conservative path consistency (CPC, Debruyne, 1999) when restricted to paths of length 2 in the constraint graph, and partial path consistency (PPC, Bliek & Sam-Haroud, 1999) when restricted to paths of arbitrary length in the constraint graph; CPC and PPC are equivalent when the constraint graph is triangulated.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Consistencies

Lecoutre¹,

Cardon²,

Vion³

2011

jair

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In this paper, we propose a comprehensive study of second-order consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic second-order consistencies, namely path consistency (PC), 3-consistency (3C), dual consistency (DC) and 2-singleton arc consistency (2SAC), as well as their conservative and strong variants. Interestingly, dual consistency is an original property that can be established by using the outcome of the enforcement of generalized arc consistency (GAC), which makes it rather easy to obtain since constraint solvers typically maintain GAC during search. On binary constraint networks, DC is equivalent to PC, but its restriction to existing constraints, called conservative dual consistency (CDC), is strictly stronger than traditional conservative consistencies derived from path consistency, namely partial path consistency (PPC) and conservative path consistency (CPC). After introducing a general algorithm to enforce strong (C)DC, we present the results of an experimentation over a wide range of benchmarks that demonstrate the interest of (conservative) dual consistency. In particular, we show that enforcing (C)DC before search clearly improves the performance of MAC (the algorithm that maintains GAC during search) on several binary and non-binary structured problems

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A strong local consistency for constraint satisfaction

Cited by 7 publications

References 13 publications

Domain Filtering Consistencies

Domain Filtering Consistencies

New algorithms for max restricted path consistency

Second-Order Consistencies

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