Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs

Oded Goldreich

doi:10.1007/978-3-642-22670-0_11

Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs

Oded Goldreich

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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. 2. Approximating the size of the minimum vertex cover in 4-regular hypergraphs to within a factor of 1.49999 is NP-hard. Both results are inferior to known results (by Trevisan (2001) and Holmerin (2001)), but they are derived using much simpler proofs. Furthermore, these proofs demonstrate the applicability of the FGLSS-reduction in the context of reductions among combinatorial optimization problems.

Original language	English GB
Title of host publication	Studies in Complexity and Cryptography
Subtitle of host publication	Miscellanea on the Interplay between Randomness and Computation
Editors	Oded Goldreich
Chapter	11
Pages	88-97
Number of pages	10
DOIs	https://doi.org/10.1007/978-3-642-22670-0_11
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6650 LNCS

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-22670-0_11

Cite this

Goldreich, O. (2011). Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. In O. Goldreich (Ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation (pp. 88-97). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS). https://doi.org/10.1007/978-3-642-22670-0_11

Goldreich, Oded. / Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. editor / Oded Goldreich. 2011. pp. 88-97 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs",

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. 2. Approximating the size of the minimum vertex cover in 4-regular hypergraphs to within a factor of 1.49999 is NP-hard. Both results are inferior to known results (by Trevisan (2001) and Holmerin (2001)), but they are derived using much simpler proofs. Furthermore, these proofs demonstrate the applicability of the FGLSS-reduction in the context of reductions among combinatorial optimization problems.",

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Goldreich, O 2011, Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. in O Goldreich (ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6650 LNCS, pp. 88-97. https://doi.org/10.1007/978-3-642-22670-0_11

Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. / Goldreich, Oded.
Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. ed. / Oded Goldreich. 2011. p. 88-97 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AB - 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. 2. Approximating the size of the minimum vertex cover in 4-regular hypergraphs to within a factor of 1.49999 is NP-hard. Both results are inferior to known results (by Trevisan (2001) and Holmerin (2001)), but they are derived using much simpler proofs. Furthermore, these proofs demonstrate the applicability of the FGLSS-reduction in the context of reductions among combinatorial optimization problems.

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Goldreich O. Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs. In Goldreich O, editor, Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. 2011. p. 88-97. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22670-0_11

Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs

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