We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs only rather simple O(mn)-time algorithms were known. We use a hierarchical sparsifi...

We consider the problem of maintaining the strongly connected components (SCCs) of an n-nodes and medges directed graph that undergoes a sequence of edge deletions. Recently, in SODA 2011, Łącki presented a deterministic algorithm that preprocess the graph in O(mn) time and creates a data structure that maintains the SCCs of a graph under edge deletions with a total update time of O(mn). The da...

The problem of decomposition of a directed graph into its strongly connected components is a fundamental graph problem inherently present in many scientific and commercial applications. In this paper we show how existing parallel algorithms can be reformulated in order to be accelerated by NVIDIA CUDA technology. In particular, we design a new CUDA-aware procedure for pivot selection and we red...

The traditional, serial, algorithm for finding the strongly connected components in a graph is based on depth first search and has complexity which is linear in the size of the graph. Depth first search is difficult to parallelize, which creates a need for a different parallel algorithm for this problem. We describe the implementation of a recently proposed parallel algorithm that finds strongl...

Frequently studied networks, such as social networks, are often massive, directed, and change over time. Thus studying network analysis algorithms in terms of data streaming is a practical model for understanding how companies and other organizations can process data in a useful, realistic way. One potentially interesting feature of a directed graph is strongly connected components. We design a...

The standard serial algorithm for strongly connected components is based on depth rst search, which is di cult to parallelize. We describe a divide-and-conquer algorithm for this problem which has signi cantly greater potential for parallelization. For a graph with n vertices in which degrees are bounded by a constant, we show the expected serial running time of our algorithm to be O(n log n).