Characterizations of several Maltsev conditions

Kozik, Marcin; Krokhin, Andrei; Valeriote, Matthew; Willard, Ross

doi:10.1007/s00012-015-0327-2

Cited by 52 publications

(42 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 2.8 in [29] states that this property implies that Pol(Γ) contains WNU polymorphisms g 3 , g 4 of arity 3 and 4, respectively, such that g 3 (y, x, x) = g 4 (y, x, x, x) holds for for every x, y ∈ A. The proof of Theorem 2.8 in [29] shows how to obtain g n for n = 3, 4, but the proof generalizes immediately to show that, for each n ≥ 3, Γ has an nary WNU polymorphism g n , of arity n, and the identity g n (y, x, . .…”

Section: Np-hardness Resultsmentioning

confidence: 99%

Towards a Characterization of Constant-Factor Approximable Min CSPs

Dalmau¹,

Krokhin²,

Manokaran³

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

Self Cite

View full text Add to dashboard Cite

Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe study the approximability of Minimum Constraint Satisfaction Problems (Min CSPs) with a fixed finite constraint language Γ on an arbitrary finite domain. The goal in such a problem is to minimize the number of unsatisfied constraints in a given instance of CSP(Γ). A recent result of Ene et al. says that, under the mild technical condition that Γ contains the equality relation, the basic LP relaxation is optimal for constant-factor approximation for Min CSP(Γ) unless the Unique Games Conjecture fails. Using the algebraic approach to the CSP, we introduce a new natural algebraic condition, stable probability distributions on symmetric polymorphisms of a constraint language, and show that the presence of such distributions on polymorphisms of each arity is necessary and sufficient for the finiteness of the integrality gap for the basic LP relaxation of Min CSP(Γ). We also show how stable distributions on symmetric polymorphisms can in principle be used to round solutions of the basic LP relaxation, and how, for several examples that cover all previously known cases, this leads to efficient constant-factor approximation algorithms for Min CSP(Γ). Finally, we show that the absence of another condition, which is implied by stable distributions, leads to NP-hardness of constant-factor approximation.

show abstract

Section: Np-hardness Resultsmentioning

confidence: 99%

Towards a Characterization of Constant-Factor Approximable Min CSPs

Dalmau¹,

Krokhin²,

Manokaran³

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

Self Cite

View full text Add to dashboard Cite

show abstract

“…We only state a nice characterization of such clones from [19]. (Using Corollary 6.5 this characterization was improved in [17] For the proof of the main result, we will only use two properties of SD(∧) clones stated in Theorems 7.2 and 7.3.…”

Section: Characterization Of Bounded Widthmentioning

confidence: 99%

The collapse of the bounded width hierarchy

Barto

2014

J Logic Computation

147

View full text Add to dashboard Cite

show abstract

“…In the case of rigid cores, the class of languages with WNU polymorphisms of all arities greater than or equal to 3 can be recognized in polynomial time [8] by combining an alternative characterization involving only two WNU polymorphisms of fixed arity [124] and a variant of the recognition algorithm used for near-unanimity polymorphisms. However, deciding whether an arbitrary language has bounded width is NP-hard [34].…”

Section: Recognition Of Different Families Of Polymorphismsmentioning

confidence: 99%

Tractability in constraint satisfaction problems: a survey

Carbonnel

Cooper

2015

Constraints

View full text Add to dashboard Cite

Even though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP. What is tractability?The idea that an algorithm is efficient if its time complexity is a polynomial function of the size of its input can be traced back to pioneering work of Cobham [45] and Edmonds [83], but the foundations of complexity theory are based on the seminal work of Cook [52] and Karp [118]. A computational decision problem (such as the constraint satisfaction problem or CSP) consists of a generic instance (in the case of the CSP, a set of variables, their

show abstract

Characterizations of several Maltsev conditions

Cited by 52 publications

References 21 publications

Towards a Characterization of Constant-Factor Approximable Min CSPs

Towards a Characterization of Constant-Factor Approximable Min CSPs

The collapse of the bounded width hierarchy

Tractability in constraint satisfaction problems: a survey

Contact Info

Product

Resources

About