A 4/3-approximation for the minimum 2-local-vertex-connectivity augmentation in a connected graph

  • Authors:

  • Hiroshi Nagamochi

  • Affiliations:

  • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto, Japan

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2005

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Abstract

Given a simple connected graph G = (V, E) and a set R of pairs of vertices, we consider the problem of augmenting G by a smallest set F of new edges such that the resulting graph G + F remains simple and has at least two internally disjoint paths between u and v for each pair (u, v) ∈ R. The problem is known to be NP-hard, and a 3/2-approximation algorithm has been obtained so far. In this paper, we introduce new stronger lower bounds on the optimal value, and propose an O(|E| + |R|) time 4/3-approximation algorithm to the problem.