Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs

We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: (1) 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 up to the o d (1) term. (2) Indepen...

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Bibliographic Details
Published in2009 24th Annual IEEE Conference on Computational Complexity pp. 74 - 80
Main Authors Austrin, P., Khot, S., Safra, M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2009
SeriesAnnual IEEE Conference on Computational Complexity
Subjects
ALGORITHMS
APPROXIMATE
Approximation algorithms
CLIQUE
Computational complexity
Computer science
Datavetenskap
Information technology
Informationsteknik
MIGHT
NP-complete problem
TECHNOLOGY
TEKNIKVETENSKAP
Yield estimation
HARD
CUT
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ISBN9780769537177
0769537170
ISSN1093-0159
DOI10.1109/CCC.2009.38

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Summary:We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: (1) 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 up to the o d (1) term. (2) Independent Set is Unique Games-hard to approximate to within a factor O(d/log 2 d). This improves the d/log O(1) (d)) Unique Games hardness result of Samorodnitsky and Trevisan. Additionally, our result does not rely on the construction of a query efficient PCP as in.
ISBN:9780769537177
0769537170
ISSN:1093-0159
DOI:10.1109/CCC.2009.38