# Towards a Characterization of Constant-Factor Approximable Finite-Valued CSPs

@article{Dalmau2016TowardsAC,
title={Towards a Characterization of Constant-Factor Approximable Finite-Valued CSPs},
author={V{\'i}ctor Dalmau and Andrei A. Krokhin and Rajsekar Manokaran},
journal={ArXiv},
year={2016},
volume={abs/1610.01019}
}
• Published 4 October 2016
• Computer Science
• ArXiv
10 Citations
• Computer Science
ESA
• 2020
It is shown that obtaining a running time of the form $O(2^{(1-\epsilon)n})$ for particular classes of Max CSPs is as hard as breaching this barrier for Max $d$-SAT for some $d$.
• Computer Science
STOC
• 2019
A new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem are introduced, and it is shown that every PCSP with a fixed constraint language is equivalent to a problem of this form.
• Mathematics
MFCS
• 2021
A combinatorial characterization of the Sherali-Adams hierarchy applied to the homomorphism problem in terms of fractional isomorphism is given and a description of the families of CSPs that are closed under Weisfeiler-Leman invariance in Terms of their polymorphisms as well as decidability by the first level of theSherali- Adams hierarchy is obtained.
• Mathematics
ICALP
• 2019
Given two (di)graphs G, H and a cost function $c:V(G)\times V(H) \to \mathbb{Q}_{\geq 0}\cup\{+\infty\}$, in the minimum cost homomorphism problem, MinHOM(H), goal is finding a homomorphism
• Mathematics
• 2019
Given two (di)graphs G, H and a cost function c : V (G)×V (H)→ Q≥0∪{+∞}, in the minimum cost homomorphism problem, MinHOM(H), we are interested in finding a homomorphism f : V (G)→ V (H) (a.k.a
• Mathematics
ArXiv
• 2022
We study the Sherali-Adams linear programming hierarchy in the context of promise constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy accepts an instance in terms
It is shown that minimal boundedwidth algebras can be arranged into a pseudovariety with one basic ternary operation, and a structure theorem is proved for minimal bounded width algeBRas which have no majority subalgebra, which form a Pseudovarieties with a commutative binary operation.
• Computer Science, Mathematics
ArXiv
• 2022
It is shown that the hierarchies of minion tests obtained in this way are general enough to capture the (combinatorial) bounded width and also the Sherali-Adams LP, Sum-of-Squares SDP, and affine IP hierarchies.
• Computer Science, Mathematics
SODA
• 2022
The main technical finding is that the template of every PCSP that is solvable in bounded width satisfies a certain structural condition implying that its algebraic closure-properties include weak near unanimity polymorphisms of all large arities.
The theory of algebraic structures with few subpowers, the theory of absorbing subalgebras and its applications to studying CSP templates which can be solved by local consistency methods, and the dichotomy theorem for conservative C SP templates are covered.

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It is proved that if a constraint language satisfies this algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language, then the VCSP is tractable.
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