On the minimum local-vertex-connectivity augmentation in graphs

  • Authors:

  • Hiroshi Nagamochi;Toshimasa Ishii

  • Affiliations:

  • Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2003

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Abstract

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 for some constant k ≥ 2 G is (k - 1 )-vertex-connected and r(u,v) ∈ {0,k} holds for u,v ∈ V. 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.