Abstract
We present an O(m + n)-time algorithm that tests if a given directed graph is 2-vertex connected, where m is the number of arcs and n is the number of vertices. Based on this result we design an O(n)-space data structure that can compute in O(log2 n) time two internally vertex-disjoint paths from s to t, for any pair of query vertices s and t of a 2-vertex connected directed graph. The two paths can be reported in additional O(k) time, where k is their total length.
This research project has been funded by the John S. Latsis Public Benefit Foundation. The sole responsibility for the content of this paper lies with its author.
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Georgiadis, L. (2010). Testing 2-Vertex Connectivity and Computing Pairs of Vertex-Disjoint s-t Paths in Digraphs. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_62
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DOI: https://doi.org/10.1007/978-3-642-14165-2_62
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