Constraints, consistency and closure

Jeavons, Peter; Cohen, David A.; Cooper, Martin

doi:10.1016/s0004-3702(98)00022-8

Cited by 192 publications

(196 citation statements)

References 20 publications

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“…(Near-Unanimity Operations) An operation ϕ : A k → A with k ≥ 3 is near-unanimity (NU) if for all x, y ∈ A, we have that ϕ(x, y, .., y) = ϕ(y, x, .., y) = · · · = ϕ(y, y, .., x) = y Tractability of CSP(Inv(ϕ)) for any arbitrary near-unanimity operation ϕ was proved in [19] (See also [22]). …”

Section: Dalmaumentioning

confidence: 99%

Generalized Majority-Minority Operations are Tractable

Dalmau¹

2006

Logical Methods in Computer Science

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Abstract. Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint relations are invariant under a (fixed) GMM operation, is solvable in polynomial time. This constitutes one of the largest tractable cases of the CSP.

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Section: Dalmaumentioning

confidence: 99%

Generalized Majority-Minority Operations are Tractable

Dalmau¹

2006

Logical Methods in Computer Science

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“…This is one of the two most general properties of relational structures B that are known to guarantee that the problem CSP(B) solvable in polynomial time, and the vast majority of such structures have bounded treewidth duality. The notion of bounded treewidth duality has strong links with methods of solving constraint satisfaction problems based on establishing local consistency (see, e.g., [12,18,37,28]). …”

Section: Bounded Treewidth Dualitymentioning

confidence: 99%

Dualities for Constraint Satisfaction Problems

Bulatov

Krokhin

Larose

2008

Lecture Notes in Computer Science

110

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“…From [30] we know that if a relational structure H has a near-unanimity polymorphism then CSP(H) is tractable. The following variation of this notion was developed by E. Kiss and Valeriote while investigating the Bounded Width Conjecture.…”

Section: Weak Near-unanimity Operationsmentioning

confidence: 99%

“…An early tractability result of Jeavons, Cohen and Cooper [30] establishes that algebras having near unanimity terms are tractable, and it is no coincidence that this tractability result can be proved using the Baker-Pixley theorem.…”

Section: Definition 5 ([2])mentioning

confidence: 99%