From restricted path consistency to max-restricted path consistency

Debruyne, Romuald; Bessière, Christian

doi:10.1007/bfb0017448

Cited by 51 publications

(55 citation statements)

References 7 publications

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“…Berlandier proposed an algorithm in O(end 3 ). The optimal complexity of achieving RPC on a binary normalized network is in O(en + ed 2 + td 2 ), where t is the number of triples of variables (x , , x j , x k ) with c ij , c jk and c ik all in C. An algorithm with this optimal time complexity was presented by Debruyne and Bessiere [42].…”

Section: Definition 59 (Restricted Path Consistency)mentioning

confidence: 99%

Constraint Propagation

Bessière¹

2006

Handbook of Constraint Programming

178

182

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Section: Definition 59 (Restricted Path Consistency)mentioning

confidence: 99%

Constraint Propagation

Bessière¹

2006

Handbook of Constraint Programming

178

182

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“…Indeed, experiments showed that MAC can solve without backtracking certain instances belonging to 3-BTP even when they do not verify the corresponding level of consistency. From a practical point of view, an interesting challenge is to find the minimum (generally) required level of consistency among different kinds of local consistencies such as PIC [18], maxRPC [19] or SAC [20]. Note that, from a theoretical point of view, we can easily deduce from Theorem 3 that any local consistency that only performs domain filtering (e.g.…”

Section: Resultsmentioning

confidence: 99%

A Microstructure-Based Family of Tractable Classes for CSPs

Cooper

Jégou²,

Terrioux³

2015

Lecture Notes in Computer Science

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15358The contribution was presented at CP 2015 :http://booleconferences.ucc.ie/cp2015 Abstract. The study of tractable classes is an important issue in Artificial Intelligence, especially in Constraint Satisfaction Problems. In this context, the Broken Triangle Property (BTP) is a state-of-the-art microstructure-based tractable class which generalizes well-known and previously-defined tractable classes, notably the set of instances whose constraint graph is a tree. In this paper, we propose to extend and to generalize this class using a more general approach based on a parameter k which is a given constant. To this end, we introduce the k-BTP property (and the class of instances satisfying this property) such that we have 2-BTP = BTP, and for k > 2, k-BTP is a relaxation of BTP in the sense that k-BTP (k + 1)-BTP. Moreover, we show that if k-TW is the class of instances having tree-width bounded by a constant k, then k-TW (k + 1)-BTP. Concerning tractability, we show that instances satisfying k-BTP and which are strong k-consistent are tractable, that is, can be recognized and solved in polynomial time. We also study the relationship between k-BTP and the approach of Naanaa who proposed a set-theoretical tool, known as the directional rank, to extend tractable classes in a parameterized way. Finally we propose an experimental study of 3-BTP which shows the practical interest of this class, particularly w.r.t. the practical solving of instances satisfying 3-BTP and for other instances, w.r.t. to backdoors based on this tractable class.

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“…One avenue to make solvers more robust is to enforce strong consistencies, i.e., consistencies stronger than GAC. Whereas GAC corresponds to the strongest form of local reasoning when constraints are treated separately, strong consistencies necessarily involve several constraints (e.g., path inverse consistency [12], max-restricted path consistency [8] and their adaptations [20] to non-binary constraints) or even the entire constraint network (e.g., singleton arc consistency [9]). …”

Section: Introductionmentioning

confidence: 99%

A Framework for Decision-Based Consistencies

Condotta

Lecoutre

2011

Principles and Practice of Constraint Programming – CP 2011

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Abstract. Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S φ ∆ , E φ ∆ , B φ ∆ and D φ ∆ , study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this general framework provides us with a better insight into decision-based consistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones.

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From restricted path consistency to max-restricted path consistency

Cited by 51 publications

References 7 publications

Constraint Propagation

Constraint Propagation

A Microstructure-Based Family of Tractable Classes for CSPs

A Framework for Decision-Based Consistencies

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