# 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} }

## 10 Citations

### Optimal polynomial-time compression for Boolean Max CSP

- Computer ScienceESA
- 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 $d$.

### Algebraic approach to promise constraint satisfaction

- Computer ScienceSTOC
- 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.

### Fractional homomorphism, Weisfeiler-Leman invariance, and the Sherali-Adams hierarchy for the Constraint Satisfaction Problem

- MathematicsMFCS
- 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.

### Toward a Dichotomy for Approximation of $H$-coloring

- MathematicsICALP
- 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…

### 91 : 2 Toward a Dichotomy for Approximation of H-Coloring 1

- 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…

### The Sherali-Adams Hierarchy for Promise CSPs through Tensors

- MathematicsArXiv
- 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…

### Examples, counterexamples, and structure in bounded width algebras

- MathematicsArXiv
- 2019

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.

### Hierarchies of Minion Tests for PCSPs through Tensors

- Computer Science, MathematicsArXiv
- 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.

### Promise Constraint Satisfaction and Width

- Computer Science, MathematicsSODA
- 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.

### Notes on CSPs and Polymorphisms

- Computer ScienceArXiv
- 2022

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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