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On the Minimum Augmentation of an ℓ-Connected Graph to a k-Connected Graph

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Algorithm Theory - SWAT 2000 (SWAT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

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Abstract

Given an undirected graph G = (V, E) and a positive integer k, we consider the problem of augmenting G by the smallest number of new edges to obtain a k-vertex-connected graph. In this paper, we show that, for k = 4 and k = a+2, an I- vertex-connected graph G can be made k-vertex-connected by adding at most a(k - 1)+max{0, (a - l)(a - 3) - 1} surplus edges over the optimum in O(a(k2n2 + k3n3/2)) time, where S = k-a andn= |V|.

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Authors and Affiliations

  1. Department of Information and Computer Science, Toyohashi University of Technology, Aichi, 441-8580, Japan

    Toshimasa Ishii & Hiroshi Nagamochi

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  1. Toshimasa Ishii
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  2. Hiroshi Nagamochi
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© 2000 Springer-Verlag Berlin Heidelberg

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Ishii, T., Nagamochi, H. (2000). On the Minimum Augmentation of an ℓ-Connected Graph to a k-Connected Graph. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_26

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  • DOI: https://doi.org/10.1007/3-540-44985-X_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

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