Abstract
Given a directed graph, two vertices v and w are 2-vertex-connected if there are two internally vertex-disjoint paths from v to w and two internally vertex-disjoint paths from w to v. In this paper, we show how to compute this relation in \(O(m+n)\) time, where n is the number of vertices and m is the number of edges of the graph. As a side result, we show how to build in linear time an O(n)-space data structure, which can answer in constant time queries on whether any two vertices are 2-vertex-connected. Additionally, when two query vertices v and w are not 2-vertex-connected, our data structure can produce in constant time a “witness” of this property, by exhibiting a vertex or an edge that is contained in all paths from v to w or in all paths from w to v. We are also able to compute in linear time a sparse certificate for 2-vertex connectivity, i.e., a subgraph of the input graph that has O(n) edges and maintains the same 2-vertex connectivity properties as the input graph.
Giuseppe F. Italiano—Partially supported by the Italian Ministry of Education, University and Research (MIUR) under Project AMANDA (Algorithmics for MAssive and Networked DAta).
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Georgiadis, L., Italiano, G.F., Laura, L., Parotsidis, N. (2015). 2-Vertex Connectivity in Directed Graphs. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_49
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DOI: https://doi.org/10.1007/978-3-662-47672-7_49
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