The survivable network design problem (SNDP) is to construct a minimum-cost subgraph satisfying certain given edge-connectivity requirements. The first polynomial-time approximation algorithm was given by Williamson et al. (Combinatorica 15 (1995) 435454). This paper gives an improved version that is more efficient. Consider a graph of n vertices and connectivity requirements that are at most k. Both algorithms find a solution that is within a factor 2k - 1
Harold N. Gabow, Michel X. Goemans, David P. Willi