Theoretical analysis of singleton arc consistency and its extensions

Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). One way to solve a CSP instance is to encode it into SAT and use a SAT-solver. However, important information about the problem can get lost during the translation stage. For example, although the general constraint satisfaction problem is known to be NP-complete, there are some classes of CSP instances that have been shown to be tractable. These include the classes of CSP instances that contain only max-closed or connected-row-convex constraints. In this paper we show that translating such instances using some common standard encodings results in SAT instances which do not fall into known tractable classes. However, translating such instances using the order encoding results in SAT instances that do fall into known tractable classes. Moreover, modern clause learning SAT-solvers can then solve them efficiently. Hence, we give a theory-based argument to prefer the order encoding for certain families of constraint satisfaction problems.

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“…Recently this result has been strengthened by considering another type of consistency known as singleton arc consistency [5].…”

Section: Connected Row-convex Constraintsmentioning

confidence: 99%

The Order Encoding: From Tractable CSP to Tractable SAT

Petke

Jeavons

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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“…Note that there exist consistencies φ and decision mappings ∆ such that B φ ∆ is strictly stronger (⊲) than S φ ∆ and E φ ∆ (and also S φ ∆ +E φ ∆ ). For example, when φ = AC and ∆ = ∆ = , we have B φ ∆ = BiSAC, S φ ∆ = SAC and S φ ∆ + E φ ∆ = 1-AC, and we know that BiSAC ⊲ 1-AC [4], and 1-AC ⊲ SAC [2].…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…A value (x, a) of P is 1-AC-consistent iff (x, a) is SAC-consistent and ∀y ∈ vars(P ) \ {x}, ∃b ∈ dom(y) | (x, a) ∈ GAC (P | y=b ) [2]. A value (x, a) of P is BiSAC-consistent iff GAC (P ia | x=a ) = ⊥ where P ia is the CN obtained after removing every value (y, b) of P such that y = x and (x, a) / ∈ GAC(P | y=b ) [4]. P is SAC-consistent (resp., 1-AC-consistent, BiSAC-consistent) iff every value of P is SAC-consistent (resp., 1-AC-consistent, BiSAC-consistent).…”

Section: Consistenciesmentioning

confidence: 99%

“…Among such decision-based consistencies, we find SAC (singleton arc consistency), partition-k-AC [2], weak-k-SAC [22], BiSAC [4], and DC (dual consistency) [15]. Besides, a partial form of SAC, better known as shaving, has been introduced for a long time [6,18] and is still an active subject of research [17,21]; when shaving systematically concerns the bounds of each variable domain, it is called BoundSAC [16].…”

Section: Introductionmentioning

confidence: 99%

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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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“…The extensions of AC that we study are look-ahead arc consistency (LAAC) [12]; peek arc consistency (PAC) [8], and singleton arc consistency (SAC) [16,7]. Each of these algorithms is natural, conceptually simple, readily understandable, and easily implementable using arc consistency as a black box.…”

Section: Contributionsmentioning

confidence: 99%

Arc consistency and friends

Chen

Dalmau

Grußien

2011

Journal of Logic and Computation

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A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc consistency, a heavily investigated inference method, and three extensions thereof from the perspective of constraint languages. We conduct a comparison of the studied methods on the basis of which constraint languages they solve, and we present new polynomial-time tractability results for singleton arc consistency, the most powerful method studied.

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Theoretical analysis of singleton arc consistency and its extensions

Cited by 42 publications

References 13 publications

The Order Encoding: From Tractable CSP to Tractable SAT

The Order Encoding: From Tractable CSP to Tractable SAT

A Framework for Decision-Based Consistencies

Arc consistency and friends

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