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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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

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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)


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
  • 2-Connectivity
  • Graph Algorithms
  • Split Components


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