2-Connectivity in Directed Graphs

We survey some recent results on 2-edge and 2-vertex connectivity problems in directed graphs. Despite being complete analogs of the corresponding notions on undirected graphs, in digraphs 2vertex and 2-edge connectivity have a much richer and more complicated structure. It is thus not surprising that 2-connectivity problems on directed graphs appear to be more difficult than on undirected graphs. For undirected graphs it has been known for over 40 years how to compute all bridges, articulation points, 2-edgeand 2-vertex-connected components in linear time, by simply using depth-first search. In the case of digraphs, however, the very same problems have been much more challenging and required the development of new tools and techniques. 1998 ACM Subject Classification E.1 [Graphs and Networks] Trees, F.2.2 [Nonnumerical Algorithms and Problems] Computations on Discrete Structures, G.2.2 [Graph Algorithms] Trees