Vertex cover might be hard to approximate to within 2-ε
Subhash Khot,Oded Regev +1 more
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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.About:
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.read more
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Analysis of Boolean Functions
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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.
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On the hardness of approximating minimum vertex cover
Irit Dinur,Samuel Safra +1 more
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.
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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.
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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.
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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.
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Probabilistic checking of proofs: a new characterization of NP
Sanjeev Arora,Shmuel Safra +1 more
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.
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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.