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Abstract: Using known results regarding PCP, we present simple proofs of the inapproximability of vertex cover for hypergraphs. Specifically, we show that 1. Approximating the size of the minimum vertex cover in O(1)-regular hypergraphs to within a factor of 1.99999 is NP-hard. (Update)
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.... hard to approximate within a factor of k , and also that it is NP hard to approximate E3 Vertex Cover within factor (3=2 ) Goldreich [10] showed a direct FGLSS type [9] reduction (involving no use of the long code, a crucial component in most recent PCP constructions)...
.... Cover is NP hard to approximate within k 1 , and also that it is NP hard to approximate E3 VertexCover within factor (3=2 ) Goldreich [8] showed a direct FGLSS type [6] reduction (involving no use of the long code, a crucial component in most recent PCP constructions)...
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On Probabilistic Proof Systems and Hardness of Approximation - Holmerin (2002) (Correct)
Vertex Cover Might be Hard to Approximate to within 2-epsilon - Khot, Regev (2003) (Correct)
A New Multilayered PCP and the Hardness of Hypergraph.. - Dinur, Guruswami, Khot, .. (2002) (Correct)
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3: The Importance of Being Biased - Dinur, Safra - 2001
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BibTeX entry: (Update)
O. Goldreich. Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. ECCC Technical Report TR01-102, December 2001. http://citeseer.ist.psu.edu/goldreich01using.html More
@article{ goldreich01using,
author = "Oded Goldreich",
title = "Using the {FGLSS}-reduction to Prove Inapproximability Results for Minimum Vertex Cover in Hypergraphs",
journal = "Electronic Colloquium on Computational Complexity (ECCC)",
number = "102",
year = "2001",
url = "citeseer.ist.psu.edu/goldreich01using.html" }
Citations (may not include all citations):203 Approximating Clique is almost NP-complete (context) - Feige, Goldwasser et al.
173 Proof Verification and Intractability of Approximation Probl.. (context) - Arora, Lund et al.
115 PCPs and Non-Approximability -- Towards Tight Results (context) - Bellare, Goldreich et al. - 1998
53 The Hardness of Approximations: Gap Location - Petrank - 1994
47 Clique is hard to approximate within n 1\Gammaffl (context) - Hastad
39 Probabilistic Checkable Proofs: A New Characterization of NP (context) - Arora, Safra
29 The Importance of Being Biased - Dinur, Safra - 2001
22 Non-approximability Results for Optimization Problems on Bou.. - Trevisan - 2001
9 Algorithms and Combinatorics series (context) - Goldreich, Probabilistic et al. - 1999
8 Vertex Cover on 4-regular Hypergraphs is Hard to Approximate.. - Holmerin - 2001
5 Improved Inapproximability Results for Vertex Cover on k-reg.. (context) - Holmerin - 2001
5 Some optimal in-approximability results (context) - Hastad - 1997
1 Query efficient PCPs with Perfect Completeness - Hastad, Khot - 2001
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Candidate One-Way Functions Based on Expander Graphs - Oded Goldreich Department (2000) (Correct)
On the Security of Modular Exponentiation with Application.. - Goldreich, Rosen (2000) (Correct)
On Testing Expansion in Bounded-Degree Graphs - Oded Goldreich Dept (2000) (Correct)
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