On the Minimum Local-Vertex-Connectivity Augmentation in Graphs

• Authors: Hiroshi Nagamochi;Toshimasa Ishii
• Venue: ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
• Year: 2001

Given a graph G and target values r(u, v) prescribed for each pair of vertices u and v, we consider the problem of augmenting G by a smallest set F of new edges such that the resulting graph G + F has at least r(u, v) internally disjoint paths between each pair of vertices u and v. We show that the problem is NP-hard even if G is (k-1)-vertex-connected and r(u, v) ∈ {0, k}, u, v ∈ V holds for a constant k ≤ 2. We then give a linear time algorithm which delivers a 3/2 -approximation solution to the problem with a connected graph G and r(u, v) ∈ {0, 2}, u, v ∈ V.