Finding k-connected subgraphs with minimum average weight

Abstract

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: 1. 3-approximation for k-edge-connectivity, 2. O(logk) approximation for k-node-connectivity 3. 2 + ε approximation for k-node-connectivity in Euclidian graphs, for any constant ε > 0, 4. 5.8-approximation for k-node-connectivity in graphs satisfying the triangle inequality. © Springer-Verlag 2004.