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Vertex cover might be hard to approximate to within 2-ε

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TLDR
In this paper, it was shown that vertex cover is hard to approximate within any constant factor better than 2 on k-uniform hypergraphs, which is the same conjecture as in this paper.
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This article is published in Journal of Computer and System Sciences.The article was published on 2008-05-01 and is currently open access. It has received 810 citations till now. The article focuses on the topics: Unique games conjecture & Vertex cover.

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Book

Analysis of Boolean Functions

TL;DR: This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.
Book

The Design of Approximation Algorithms

TL;DR: In this paper, the authors present a survey of the central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization.
Journal ArticleDOI

On the hardness of approximating minimum vertex cover

TL;DR: The Minimum Vertex Cover problem is proved to be NP-hard to approximate to within a factor of 1.3606, extending on previous PCP and hardness of approximation technique.
Proceedings ArticleDOI

Optimal algorithms and inapproximability results for every CSP

TL;DR: A generic conversion from SDP integrality gaps to UGC hardness results for every CSP is shown, which achieves at least as good an approximation ratio as the best known algorithms for several problems like MaxCut, Max2Sat, MaxDiCut and Unique Games.
References
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Journal ArticleDOI

Some optimal inapproximability results

TL;DR: It is proved optimal, up to an arbitrary ε > 0, inapproximability results for Max-E k-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting.
Journal ArticleDOI

Proof verification and the hardness of approximation problems

TL;DR: It is proved that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP = P, and there exists a positive ε such that approximating the maximum clique size in an N-vertex graph to within a factor of Nε is NP-hard.
Journal ArticleDOI

Probabilistic checking of proofs: a new characterization of NP

TL;DR: It is shown that approximating Clique and Independent Set, even in a very weak sense, is NP-hard, and the class NP contains exactly those languages for which membership proofs can be verified probabilistically in polynomial time.
Proceedings ArticleDOI

On the power of unique 2-prover 1-round games

TL;DR: The main idea is to use the 2-prover game given by the Unique Games Conjecture as an "outer verifier" and build new probabilistically checkable proof systems (PCPs) on top of it.