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When Can Graph Hyperbolicity Be Computed in Linear Time?

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

  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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