When can graph hyperbolicity be computed in linear time?

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

doi:https://doi.org/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

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	American 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

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

https://doi.org/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",

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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