When can graph hyperbolicity be computed in linear time?

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

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(n4). 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 2O(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 2o(k)n2-time algorithm.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
EditorsFaith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
PublisherSpringer Verlag
Pages397-408
Number of pages12
ISBN (Print)9783319621265
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
Duration: 31 Jul 20172 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10389 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Symposium on Algorithms and Data Structures, WADS 2017
Country/TerritoryCanada
CitySt. John’s
Period31/07/172/08/17

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