Finding k-Connected Subgraphs with Minimum Average Weight

We consider the problems of finding k-connected spanning subgraphs with minimum average weight. We show that the problems are NP-hard for k>1. Approximation algorithms are given for four versions of the minimum average edge weight problem: 3-approximation for k-edge-connectivity,O(logk) approximation for k-node-connectivity2+ ε approximation for k-node-connectivity in Euclidian graphs, for any constant ε> 0,5.8-approximation for k-node-connectivity in graphs satisfying the triangle inequality.