License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.38
URN: urn:nbn:de:0030-drops-133820
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13382/
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Georgiadis, Loukas ; Kosinas, Evangelos

Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems

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LIPIcs-ISAAC-2020-38.pdf (0.6 MB)

Abstract

A directed graph G = (V,E) is twinless strongly connected if it contains a strongly connected spanning subgraph without any pair of antiparallel (or twin) edges. The twinless strongly connected components (TSCCs) of a directed graph G are its maximal twinless strongly connected subgraphs. These concepts have several diverse applications, such as the design of telecommunication networks and the structural stability of buildings. A vertex v ∈ V is a twinless strong articulation point of G, if the deletion of v increases the number of TSCCs of G. Here, we present the first linear-time algorithm that finds all the twinless strong articulation points of a directed graph. We show that the computation of twinless strong articulation points reduces to the following problem in undirected graphs, which may be of independent interest: Given a 2-vertex-connected undirected graph H, find all vertices v for which there exists an edge e such that H⧵{v,e} is not connected. We develop a linear-time algorithm that not only finds all such vertices v, but also computes the number of edges e such that H⧵{v,e} is not connected. This also implies that for each twinless strong articulation point v which is not a strong articulation point in a strongly connected digraph G, we can compute the number of TSCCs in G⧵v.

BibTeX - Entry

@InProceedings{georgiadis_et_al:LIPIcs:2020:13382,
  author =	{Loukas Georgiadis and Evangelos Kosinas},
  title =	{{Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13382},
  URN =		{urn:nbn:de:0030-drops-133820},
  doi =		{10.4230/LIPIcs.ISAAC.2020.38},
  annote =	{Keywords: 2-connectivity, cut pairs, strongly connected components}
}

Keywords: 2-connectivity, cut pairs, strongly connected components
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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