Fast Algorithms for Diameter-Optimally Augmenting Paths

  • Ulrike Große
  • Joachim Gudmundsson
  • Christian Knauer
  • Michiel Smid
  • Fabian Stehn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)

Abstract

We consider the problem of augmenting a graph with \(n\) vertices embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present an exact algorithm for the cases when the input graph is a path that runs in \(O(n \log ^3 n)\) time. We also present an algorithm that computes a \((1+\varepsilon )\)-approximation in \(O(n + 1/\varepsilon ^3)\) time for paths in \({\mathbb {R}}^{d}\), where \(d\) is a constant.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ulrike Große
    • 1
  • Joachim Gudmundsson
    • 2
  • Christian Knauer
    • 1
  • Michiel Smid
    • 3
  • Fabian Stehn
    • 1
  1. 1.Institut für Angewandte InformatikUniversität BayreuthBayreuthGermany
  2. 2.School of Information TechnologyUniversity of SydneySydneyAustralia
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada

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