Sparse subgraphs for 2-connectivity in directed graphs

Let G be a strongly connected directed graph. We consider the problem of computing the smallest strongly connected spanning subgraph of G that maintains the pairwise 2-vertex-connectivity of G, i.e., the 2-vertex-connected blocks of G (2VC-B). We provide linear-time approximation algorithms for this problem that achieve an approximation ratio of 6. Based on these algorithms, we show how to approximate, in linear time, within a factor of 6 the smallest strongly connected spanning subgraph of G that maintains respectively: both the 2-vertexconnected blocks and the 2-vertex-connected components of G (2VC-BC); all the 2-connectivity relations of G (2C), i.e., both the 2-vertexand the 2-edge-connected components and blocks. Moreover, we provide heuristics that improve the size of the computed subgraphs in practice, and conduct a thorough experimental study to assess their merits in practical scenarios.