Approximating node connectivity problems via set covers

Given a graph (directed or undirected) with costs on the edges, and an integer k, we consider the problem of nding a k-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple 2k-approximation algorithm. Better algorithms are known for various ranges of n; k. For undirected graphs with metric costs Khuller and Raghavachari gave