An approximation algorithm for the minimum weight vertex-connectivity problem in complete graphs with sharpened triangle inequality

Consider a complete graph G with the edge weights satisfying the beta-sharpened triangle inequality: weight(u, v) less than or equal to beta(weight(u, x) + weight (x,v)), for 1/2 less than or equal to beta < 1. We study the NP-hard problem of finding a minimum weight spanning subgraph of G which is k-vertex-connected, k greater than or equal to 2, and give a detailed analysis of an approximation quadratic-time algorithm whose performance ratio is beta/1-beta. The algorithm is derived from the one presented by Bockenhauer et al. in [3] for the k-edge connectivity problem on graphs satisfying the beta-sharpened triangle inequality.