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 − 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 log 2 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]. 2009 24th Annual IEEE Conference on Computational Complexity 978-0-7695-3717-7/09 $25.00
This matches the inapproximability result known, up to doubly-logarithmic factors, that holds assuming the Unique Games Conjecture REF .
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
2009 24th Annual IEEE Conference on Computational Complexity
2009 24th Annual IEEE Conference on Computational Complexity
Mathematics Computer Science