We give a randomized (Las-Vegas) parallel algorithm for computing strongly connected components of a graph with n vertices andm edges. The runtime is dominated byO(log n) multi-source parallel reachability queries; i.e. O(log n) calls to a subroutine that computes the union of the descendants of a given set of vertices in a given digraph. Our algorithm also topologically sorts the strongly conn...

We present randomized algorithms with a total update time of Õ(m √ n) for the problems of decremental singlesource reachability and decremental strongly connected components on directed graphs. This improves recent breakthrough results of Henzinger, Krinninger and Nanongkai [STOC 14, ICALP 15]. In addition, our algorithms are arguably simpler. Keywords-dynamic algorithm; single-source reachabil...

In a seminal paper Eswaran and Tarjan [1] introduced several augmentation problems and presented linear time algorithms for them. This paper points out an error in Eswaran and Tarjan's algorithm for the strong connectivity augmentation problem. Consequently, the application of their algorithm can result in a network that is not strongly connected. Luckily, the error can be fixed fairly easily, ...

A Bluetooth ad-hoc network consists of Bluetooth devices interconnected into piconets and piconets interconnected into scatternets. The specification has not yet addressed the issue of algorithms for scatternet formation. Some algorithms have been proposed, but they are either synchronous, they work only with strongly connected topologies, or they are master-slave based and hierarchical of natu...

Structure-based approaches to diagnosis provide useful computational guarantees based on a device structure. In particular, these approaches can identify device structures for which the complexity of model-based diagnosis is guaranteed to be linear. Structure-based approaches, however, can fail to answer even the simplest diagnostic queries if the device structure is not well behaved (strongly ...

In this paper we consider the steiner multicut problem. This is a generalization of the minimum multicut problem where instead of separating node pairs, the goal is to find a minimum weight set of edges that separates all given sets of nodes. A set is considered separated if it is not contained in a single connected component. We show an O(log3(kt)) approximation algorithm for the steiner multi...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

In this paper we study the problem of maintaining the strongly connected components of a graph in the presence of failures. In particular, we show that given a directed graph G = (V,E) with n = |V | and m = |E|, and an integer value k ≥ 1, there is an algorithm that computes in O(2n log2 n) time for any set F of size at most k the strongly connected components of the graph G \ F . The running t...

We propose a novel method for Web page grouping based only on hyperlink information. Because of the explosive growth of the World Wide Web, page grouping is expected to provide a general grasp of the Web for effective information search and netsurfing. The Web can be regarded as a gigantic digraph where pages are vertices and links are arcs. Our grouping method is a generalization of decomposit...