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 within a factor 2−(2+od(1))loglogdlogd
. This exactly matches the algorithmic result of Halperin (SICOMP 2002) up to the od(1)
term.
Independent Set is Unique Games-hard to approximate within a factor O(d/log2d)
. This improves the d/logO(1)(d)
Unique Games hardness result of Samorodnitsky and Trevisan (STOC'06). Additionally, our proof does not rely on the construction of a query-efficient PCP.
Vertex Cover is Unique Games-hard to approximate within a factor 2−(2+od(1))loglogdlogd
. This exactly matches the algorithmic result of Halperin (SICOMP 2002) up to the od(1)
term.
Independent Set is Unique Games-hard to approximate within a factor O(d/log2d)
. This improves the d/logO(1)(d)
Unique Games hardness result of Samorodnitsky and Trevisan (STOC'06). Additionally, our proof does not rely on the construction of a query-efficient PCP.
| Original language | English |
|---|---|
| Article number | 3 |
| Pages (from-to) | 27-43 |
| Number of pages | 17 |
| Journal | Theory of Computing |
| Volume | 7 |
| DOIs | |
| State | Published - 2011 |