Erratum: An Approximation Algorithm for Minimum-Cost Vertex-Connectivity Problems

There is an error in our paper ``An Approximation Algorithm for Minimum-Cost Vertex- Connectivity Problems'' (Algorithmica (1997), 18:21—43). In that paper we considered the following problem: given an undirected graph and values rij for each pair of vertices i and j , find a minimum-cost set of edges such that there are rij vertex-disjoint paths between vertices i and j . We gave approximation algorithms for two special cases of this problem. Our algorithms rely on a primal—dual approach which has led to approximation algorithms for many edge-connectivity problems. The algorithms work in a series of stages; in each stage an augmentation subroutine augments the connectivity of the current solution. The error is in a lemma for the proof of the performance guarantee of the augmentation subroutine.