When Can Graph Hyperbolicity Be Computed in Linear Time?

  • Till Fluschnik
  • Christian Komusiewicz
  • George B. Mertzios
  • André Nichterlein
  • Rolf Niedermeier
  • Nimrod Talmon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

Abstract

Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known practical algorithms for computing the hyperbolicity number of a n-vertex graph have running time \(O(n^4)\). Exploiting the framework of parameterized complexity analysis, we explore possibilities for “linear-time FPT” algorithms to compute hyperbolicity. For instance, we show that hyperbolicity can be computed in time \(2^{O(k)} + O(n +m)\) (m being the number of graph edges, k being the size of a vertex cover) while at the same time, unless the SETH fails, there is no \(2^{o(k)}n^2\)-time algorithm.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Till Fluschnik
    • 1
  • Christian Komusiewicz
    • 2
  • George B. Mertzios
    • 3
  • André Nichterlein
    • 1
    • 3
  • Rolf Niedermeier
    • 1
  • Nimrod Talmon
    • 4
  1. 1.Institut Für Softwaretechnik Und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Institut Für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  3. 3.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  4. 4.Weizmann Institute of ScienceRehovotIsrael

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