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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 article, 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)

—The computation of dominators is a central tool in program optimization and code generation, and it has applications in other diverse areas including constraint programming, circuit testing, and biology. In this paper we survey recent results, applications, and open problems related to the notion of dominators in directed graphs, including dominator… (More)

Link recommendations are critical for both improving the utility and expediting the growth of social networks. Most previous approaches focus on suggesting links that are highly likely to be adopted. In this paper, we add a different perspective to the problem by aiming at recommending links that also improve specific properties of the network. In… (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)

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)