Inapproximability of vertex cover and independent set in bounded degree graphs

Per Austrin; Subhash Khot; Muli Safra

doi:10.1109/CCC.2009.38

Inapproximability of vertex cover and independent set in bounded degree graphs

Per Austrin^*, Subhash Khot, Muli Safra

^*Corresponding author for this work

School of Computer Science

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

45 Scopus citations

Abstract

We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+o_d(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o _d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log² d ). This improves the d/log ^O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].

Original language	English
Title of host publication	Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
Pages	74-80
Number of pages	7
DOIs	https://doi.org/10.1109/CCC.2009.38
State	Published - 2009
Event	2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009 - Paris, France Duration: 15 Jul 2009 → 18 Jul 2009

Publication series

Name	Proceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)	1093-0159

Conference

Conference	2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
Country/Territory	France
City	Paris
Period	15/07/09 → 18/07/09

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10.1109/CCC.2009.38

Cite this

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title = "Inapproximability of vertex cover and independent set in bounded degree graphs",

abstract = "We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+od(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log2 d ). This improves the d/log O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].",

author = "Per Austrin and Subhash Khot and Muli Safra",

note = "Funding Information: We thank an anonymous referee for helpful suggestions that helped improve the Letter. We appreciate useful discussions with Gregory Sivakoff, Jeffrey Crane, and Allyson Polak. We gratefully acknowledge support by NSF grant AST 03-07851, NASA/JPL contract 1228235, the Virginia Space Grant Consortium, and Frank Levinson through the Celerity Foundation. D. L. N. is also supported by the ARCS Foundation and the Green Bank Telescope Student Support Program. P. M. F. is supported by NASA GSRP and UVa dissertation fellowships.; 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009 ; Conference date: 15-07-2009 Through 18-07-2009",

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doi = "10.1109/CCC.2009.38",

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Austrin, P, Khot, S & Safra, M 2009, Inapproximability of vertex cover and independent set in bounded degree graphs. in Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009., 5231231, Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 74-80, 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009, Paris, France, 15/07/09. https://doi.org/10.1109/CCC.2009.38

Inapproximability of vertex cover and independent set in bounded degree graphs. / Austrin, Per; Khot, Subhash; Safra, Muli.
Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009. 2009. p. 74-80 5231231 (Proceedings of the Annual IEEE Conference on Computational Complexity).

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

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Inapproximability of vertex cover and independent set in bounded degree graphs

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