When can graph hyperbolicity be computed in linear time?

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

doi:10.1007/978-3-319-62127-2_34

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 proceeding › Conference contribution › peer-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 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)n²-time algorithm.

Original language	English
Title of host publication	Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
Editors	Faith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
Publisher	Springer Verlag
Pages	397-408
Number of pages	12
ISBN (Print)	9783319621265
DOIs	https://doi.org/10.1007/978-3-319-62127-2_34
State	Published - 1 Jan 2017
Externally published	Yes
Event	15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada Duration: 31 Jul 2017 → 2 Aug 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10389 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th International Symposium on Algorithms and Data Structures, WADS 2017
Country/Territory	Canada
City	St. John’s
Period	31/07/17 → 2/08/17

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-319-62127-2_34

Cite this

Fluschnik, T., Komusiewicz, C., Mertzios, G. B., Nichterlein, A., Niedermeier, R., & Talmon, N. (2017). When can graph hyperbolicity be computed in linear time? In F. Ellen, A. Kolokolova, & J-R. Sack (Eds.), Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings (pp. 397-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10389 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-62127-2_34

Fluschnik, Till ; Komusiewicz, Christian ; Mertzios, George B. et al. / When can graph hyperbolicity be computed in linear time?. Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. editor / Faith Ellen ; Antonina Kolokolova ; Jorg-Rudiger Sack. Springer Verlag, 2017. pp. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "When can graph hyperbolicity be computed in linear time?",

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.",

author = "Till Fluschnik and Christian Komusiewicz and Mertzios, {George B.} and Andr{\'e} Nichterlein and Rolf Niedermeier and Nimrod Talmon",

note = "Funding Information: C. Komusiewicz — Supported by the DFG, project MAGZ (KO 3669/4-1). Funding Information: A. Nichterlein — Supported by a postdoctoral fellowship of the DAAD while at Durham University. Funding Information: T. Fluschnik — Supported by the DFG, project DAMM (NI 369/13-2). Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 15th International Symposium on Algorithms and Data Structures, WADS 2017 ; Conference date: 31-07-2017 Through 02-08-2017",

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doi = "10.1007/978-3-319-62127-2_34",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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editor = "Faith Ellen and Antonina Kolokolova and Jorg-Rudiger Sack",

booktitle = "Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings",

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Fluschnik, T, Komusiewicz, C, Mertzios, GB, Nichterlein, A, Niedermeier, R & Talmon, N 2017, When can graph hyperbolicity be computed in linear time? in F Ellen, A Kolokolova & J-R Sack (eds), Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10389 LNCS, Springer Verlag, pp. 397-408, 15th International Symposium on Algorithms and Data Structures, WADS 2017, St. John’s, Canada, 31/07/17. https://doi.org/10.1007/978-3-319-62127-2_34

When can graph hyperbolicity be computed in linear time? / Fluschnik, Till; Komusiewicz, Christian; Mertzios, George B. et al.
Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. ed. / Faith Ellen; Antonina Kolokolova; Jorg-Rudiger Sack. Springer Verlag, 2017. p. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10389 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review