When Can Graph Hyperbolicity be Computed in Linear Time?

Till Fluschnik, Christian Komusiewicz, George B. Mertzios, André Nichterlein, Rolf Niedermeier, Nimrod Talmon

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Hyperbolicity is a distance-based measure of 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 algorithms used in practice for computing the hyperbolicity number of an n-vertex graph have running time O(n4). Exploiting the framework of parameterized complexity analysis, we explore possibilities for “linear-time FPT” algorithms to compute hyperbolicity. For example, we show that hyperbolicity can be computed in 2 O(k)+ O(n+ m) time (where m and k denote the number of edges and the size of a vertex cover in the input graph, respectively) while at the same time, unless the Strong Exponential Time Hypothesis (SETH) fails, there is no 2 o(k)· n2-ε-time algorithm for every ε> 0.

Original languageEnglish
Pages (from-to)2016-2045
Number of pages30
JournalAlgorithmica
Volume81
Issue number5
DOIs
StatePublished - 15 May 2019

Keywords

  • Cographs
  • FPT in P
  • Parameterized complexity
  • Polynomial-time algorithm
  • Strong Exponential Time Hypothesis
  • Vertex cover number

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