Document Open Access Logo

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

Authors Loukas Georgiadis , Konstantinos Giannis, Giuseppe F. Italiano , Evangelos Kosinas

PDF
Thumbnail PDF

File

LIPIcs.SEA.2021.20.pdf
  • Filesize: 0.99 MB
  • 19 pages

Document Identifiers

Author Details

Loukas Georgiadis
  • Department of Computer Science & Engineering, University of Ioannina, Greece
Konstantinos Giannis
  • Gran Sasso Science Institute, L'Aquila, Italy
Giuseppe F. Italiano
  • LUISS University, Rome, Italy
Evangelos Kosinas
  • Department of Computer Science & Engineering, University of Ioannina, Greece

Funding

Research at the University of Ioannina supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the "First Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant", Project FANTA (eFficient Algorithms for NeTwork Analysis), number HFRI-FM17-431. G. F. Italiano is partially supported by MIUR, the Italian Ministry for Education, University and Research, under PRIN Project AHeAD (Efficient Algorithms for HArnessing Networked Data)

Cite AsGet BibTex

Loukas Georgiadis, Konstantinos Giannis, Giuseppe F. Italiano, and Evangelos Kosinas. Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.SEA.2021.20

Abstract

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • 2-Connectivity
  • Graph Algorithms
  • Split Components

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Supplementary Materials

References

  1. G. Di Battista and R. Tamassia. On-line maintenance of triconnected components with SPQR-trees. Algorithmica, 15(4):302–318, April 1996. Google Scholar
  2. G. Di Battista and R. Tamassia. On-line planarity testing. SIAM Journal on Computing, 25(5):956–997, 1996. Google Scholar
  3. M. Chimani, C. Gutwenger, M. Junger, G. W. Klau, K. Klein, and P. Mutzel. The open graph drawing framework. In Handbook of Graph Drawing and Visualization, pages 543-570. CRC Press, 2013. Google Scholar
  4. D. Fussell, V. Ramachandran, and R. Thurimella. Finding triconnected components by local replacement. SIAM J. Comput., 22(3):587–616, June 1993. URL: https://doi.org/10.1137/0222040.
  5. Z. Galil and G. F. Italiano. Reducing edge connectivity to vertex connectivity. SIGACT News, 22(1):57–61, 1991. URL: https://doi.org/10.1145/122413.122416.
  6. L. Georgiadis and E. Kosinas. Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems. In Yixin Cao, Siu-Wing Cheng, and Minming Li, editors, 31st International Symposium on Algorithms and Computation (ISAAC 2020), volume 181 of Leibniz International Proceedings in Informatics (LIPIcs), pages 38:1-38:16, Dagstuhl, Germany, 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2020.38.
  7. C. Gutwenger and P. Mutzel. A linear time implementation of spqr-trees. In Joe Marks, editor, Graph Drawing, pages 77-90, Berlin, Heidelberg, 2001. Springer Berlin Heidelberg. Google Scholar
  8. J. E. Hopcroft and R. E. Tarjan. Dividing a graph into triconnected components. SIAM Journal on Computing, 2(3):135-158, 1973. Google Scholar
  9. R. Jaberi. Twinless articulation points and some related problems, 2019. URL: http://arxiv.org/abs/1912.11799.
  10. Z. Jiang. An empirical study of 3-vertex connectivity algorithms. Master’s thesis, University of Windsor, 2013. Electronic Theses and Dissertations, paper 4980. Google Scholar
  11. J. Leskovec and A. Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, June 2014.
  12. K. Mehlhorn, A. Neumann, and J. M. Schmidt. Certifying 3-edge-connectivity. Algorithmica, 77(2):309–335, February 2017. URL: https://doi.org/10.1007/s00453-015-0075-x.
  13. H. Nagamochi and T. Ibaraki. A linear time algorithm for computing 3-edge-connected components in a multigraph. Japan J. Indust. Appl. Math, 9(163), 1992. URL: https://doi.org/10.1007/BF03167564.
  14. S. Raghavan. Twinless strongly connected components. In F. B. Alt, M. C. Fu, and B. L. Golden, editors, Perspectives in Operations Research: Papers in Honor of Saul Gass' 80th Birthday, pages 285-304. Springer US, Boston, MA, 2006. URL: https://doi.org/10.1007/978-0-387-39934-8_17.
  15. R. A. Rossi and N. K. Ahmed. The network data repository with interactive graph analytics and visualization. In AAAI, 2015. URL: http://networkrepository.com.
  16. R. E. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2):146-160, 1972. Google Scholar
  17. Y. H. Tsin. Yet another optimal algorithm for 3-edge-connectivity. Journal of Discrete Algorithms, 7(1):130-146, 2009. Selected papers from the 1st International Workshop on Similarity Search and Applications (SISAP). URL: https://doi.org/10.1016/j.jda.2008.04.003.
  18. Wikipedia contributors. SPQR tree - Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=SPQR_tree&oldid=951256273, 2020.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact