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oai:drops-oai.dagstuhl.de:13382 2024-03-06T10:51:50Z ddc:004 open_access

Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems Georgiadis, Loukas Kosinas, Evangelos 2-connectivity cut pairs strongly connected components 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Loukas Georgiadis and Evangelos Kosinas 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.38 urn:nbn:de:0030-drops-133820 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.38 eng https://creativecommons.org/licenses/by/3.0/legalcode