Approximating the smallest spanning subgraph for 2-edge-connectivity in directed graphs

Let G be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of G that maintains respectively: the 2-edge-connected blocks of G (2EC-B); the 2-edge-connected components of G (2EC-C); both the 2-edge-connected blocks and the 2-edge-connected components of G (2EC-B-C). All three problems are NP-hard, and thus we are interested in efficient approximation algorithms. For 2EC-C we can obtain a 3/2-approximation by combining previously known results. For 2EC-B and 2EC-B-C, we present new 4- approximation algorithms that run in linear time. We also propose various heuristics to improve the size of the computed subgraphs in practice, and conduct a thorough experimental study to assess their merits in practical scenarios