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Minimum augmentation to k-edge-connect specified vertices of a graph

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ \(\subseteq \) V, find a minimum set E′ of edges,each connecting distinct vertices of V, such that G′=(V, E ∪ E′) has at least k edge-disjoint paths between any pair of vertices in Γ”. We propose an O(λ 2¦V¦(¦V¦+¦Γ¦log λ)+¦E¦) algorithm for (λ + 1)ECA-SV with Γ(V), where λ is the edge-connectivity of Γ (the cardinality of a minimum cut separating two vertices of Γ). Also mentioned is an O(¦V¦ log ¦V¦+¦E¦) algorithm for a special case where λ is equal to the edge-connectivity of G.

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Authors and Affiliations

  1. Department of Circuits and Systems, Faculty of Engineering, Hiroshima University, 4-1 Kagamiyama, 1 Chome, 724, Higashi-Hiroshima, Japan

    Satoshi Taoka & Toshimasa Watanabe

Authors
  1. Satoshi Taoka
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  2. Toshimasa Watanabe
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Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Taoka, S., Watanabe, T. (1994). Minimum augmentation to k-edge-connect specified vertices of a graph. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_184

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  • DOI: https://doi.org/10.1007/3-540-58325-4_184

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

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