Sciweavers

Share
STOC
2003
ACM

A new multilayered PCP and the hardness of hypergraph vertex cover

8 years 8 months ago
A new multilayered PCP and the hardness of hypergraph vertex cover
Given a k-uniform hypergraph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyperedge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within a factor of (k − 1 − ε) for arbitrary constants ε > 0 and k ≥ 3. The result is nearly tight as this problem can be easily approximated within factor k. Our construction makes use of the biased Long-Code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets. We also give a different proof that shows an inapproximability factor of ⌊k 2 ⌋ − ε. In addition to being simpler, this proof also works for super-constant values of k up to (log N)1/c where c > 1 is a fixed constant and N is the number of hyperedges.
Irit Dinur, Venkatesan Guruswami, Subhash Khot, Od
Added 05 Jul 2010
Updated 05 Jul 2010
Type Conference
Year 2003
Where STOC
Authors Irit Dinur, Venkatesan Guruswami, Subhash Khot, Oded Regev
Comments (0)
books