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Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study 2-edge connectivity problems in directed graphs and, in particular, we consider the computation of the following natural… (More)

We complement our study of 2-connectivity in directed graphs [7], by considering the computation of the following 2-vertex-connectivity relations: We say that two vertices v and w are 2-vertex-connected if there are two internally vertex-disjoint paths from v to w and two internally vertex-disjoint paths from w to v. We also say that v and w are… (More)

In this paper, we investigate some basic problems related to the strong connectivity and to the 2-connectivity of a directed graph, by considering the effect of edge and vertex deletions on its strongly connected components. Let G be a directed graph with m edges and n vertices. We present a collection of O(n)-space data structures that, after O(m + n)-time… (More)

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… (More)

A new discipline at the intersection of the development and operation of software systems known as DevOps has seen significant growth recently. Among the wide range of tasks of DevOps professionals, we focus on that of selecting appropriate cloud deployments for distributed applications. Despite the advent of automated software deployment and management… (More)

In this paper, we initiate the study of the dynamic maintenance of 2-edge-connectivity relationships in directed graphs. We present an algorithm that can update the 2-edge-connected blocks of a directed graph with n vertices through a sequence of m edge insertions in a total of O(mn) time. After each insertion, we can answer the following queries in… (More)