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Fast Algorithms for Diameter-Optimally Augmenting Paths

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9134))

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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.

The research on this topic has been initiated during the Korean Workshop on Computational Geometry 2014 (KW2014)

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Author information

Authors and Affiliations

  1. Institut für Angewandte Informatik, Universität Bayreuth, Bayreuth, Germany

    Ulrike Große, Christian Knauer & Fabian Stehn

  2. School of Information Technology, University of Sydney, Sydney, Australia

    Joachim Gudmundsson

  3. School of Computer Science, Carleton University, Ottawa, Canada

    Michiel Smid

Authors
  1. Ulrike Große
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  2. Joachim Gudmundsson
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  3. Christian Knauer
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  4. Michiel Smid
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  5. Fabian Stehn
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Corresponding author

Correspondence to Fabian Stehn .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Große, U., Gudmundsson, J., Knauer, C., Smid, M., Stehn, F. (2015). Fast Algorithms for Diameter-Optimally Augmenting Paths. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_55

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  • DOI: https://doi.org/10.1007/978-3-662-47672-7_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47671-0

  • Online ISBN: 978-3-662-47672-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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