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

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

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Subject Classification

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

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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.

Cite As Get 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

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)

Supplementary Materials

References

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