Given a k-uniform hyper-graph, the Ek-Vertex-Cover problem is to find the
smallest subset of vertices that intersects every hyper-edge. 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 factor
(k−1−ϵ) for any k≥3 and any ϵ>0. The result is
essentially 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