License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2021.20
URN: urn:nbn:de:0030-drops-137920
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Georgiadis, Loukas ; Giannis, Konstantinos ; Italiano, Giuseppe F. ; Kosinas, Evangelos

Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice

LIPIcs-SEA-2021-20.pdf (1.0 MB)


We consider two problems regarding the computation of connectivity cuts in undirected graphs, namely identifying vertex-edge cut-pairs and identifying 2-edge cuts, and present an experimental study of efficient algorithms for their computation. In the first problem, we are given a biconnected graph G and our goal is to find all vertices v such that G⧵v is not 2-edge-connected, while in the second problem, we are given a 2-edge-connected graph G and our goal is to find all edges e such that G⧵e is not 2-edge-connected. These problems are motivated by the notion of twinless strong connectivity in directed graphs but are also of independent interest. Moreover, the computation of 2-edge cuts is a main step in algorithms that compute the 3-edge-connected components of a graph. In this paper, we present streamlined versions of two recent linear-time algorithms of Georgiadis and Kosinas that compute all vertex-edge cut-pairs and all 2-edge cuts, respectively. We compare the empirical performance of our vertex-edge cut-pairs algorithm with an alternative linear-time method that exploits the structure of the triconnected components of G. Also, we compare the empirical performance of our 2-edge cuts algorithm with the algorithm of Tsin, which was reported to be the fastest one among the previously existing for this problem. To that end, we conduct a thorough experimental study to highlight the merits and weaknesses of each technique.

BibTeX - Entry

  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Italiano, Giuseppe F. and Kosinas, Evangelos},
  title =	{{Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-137920},
  doi =		{10.4230/LIPIcs.SEA.2021.20},
  annote =	{Keywords: 2-Connectivity, Graph Algorithms, Split Components}

Keywords: 2-Connectivity, Graph Algorithms, Split Components
Collection: 19th International Symposium on Experimental Algorithms (SEA 2021)
Issue Date: 2021
Date of publication: 31.05.2021
Supplementary Material: The source code, together with some sample input instances is available at
Software (Source Code): archived at:

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