On computing the 2-vertex-connected components of directed graphs

In this paper we consider the problem of computing the 2-vertex-connected components of directed graphs. We present a new algorithm for solving this problem in O(nm) time. Furthermore, we show that the old algorithm of Erusalimskii and Svetlov runs in O(nm2) time. In this paper, we investigate the relationship between 2-vertex-connected components and dominator trees. We also consider three applications of our new algorithm, which are approximation algorithms for problems that are generalization of the problem of approximating the smallest 2-vertex-connected spanning subgraph of 2-vertex-connected directed graph.