Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Simple Analysis of Graph Tests for Linearity and PCP
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Query Efficient PCPs with Perfect Completeness
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs
Studies in complexity and cryptography
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On LP-based approximability for strict CSPs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximating vertex cover in dense hypergraphs
Journal of Discrete Algorithms
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We prove that Minimum Vertex Cover on k-uniform hypergraphs is NP-hard to approximate within 驴(k1-驴). The result follows by a new reduction and a PCP characterization of NP by H氓stad and Khot [11]. We also give an alternate construction of a PCP with the required properties. We also show that Minimum Vertex Cover on 3- uniform hypergraphs is NP-hard to approximate within 3/2 - 驴. Of independent interest may be a 3 query PCP for NP with perfect completeness where answers are from a domain of size d and where the soundness is 2/d.