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2009
Springer

Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs

11 years 22 days ago
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: • 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 [7] up to the od(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O( d log2 d ). This improves the d logO(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [15]. Additionally, our result does not rely on the construction of a query efficient PCP as in [15]. ∗ Work done while at KTH – Royal Institute of Technology in Stockholm, funded by ERC Advanced investigator grant 226203 and a grant from the Mittag-Leffler Institute. † Research funded by NSF CAREER and NSF Expedition grants. ‡ Research partially supported by a bi-national US-Israeli BSF grant, and by an ISF grant. 1
Per Austrin, Subhash Khot, Muli Safra
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where COCO
Authors Per Austrin, Subhash Khot, Muli Safra
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