Testing 2-vertex connectivity and computing pairs of vertex-disjoint s-t paths in digraphs

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. The two paths can be reported in additional O(k) time, where k is their total length.