On Finding the Strongly Connected Components in a Directed Graph
نویسندگان
چکیده
We present two improved versions of Tarjan's algorithm for the detection of strongly connected components in a directed graph. Our new algorithms handle sparse graphs and graphs with many trivial components (containing only one node) more economically than Tarjan's original algorithm. As an application we present an eecient transitive closure algorithm.
منابع مشابه
Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
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...
متن کاملGraph partitioning and a componentwise PageRank algorithm
In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known ‘strongly connected components’ as well as another type of components we call ‘connected acyclic component’. We will give an algorithm based on Tarjan’s algorithm for finding strongly connected components used to find such a partitioning. We will also sh...
متن کاملA space-efficient algorithm for finding strongly connected components
Tarjan’s algorihm for finding the strongly connected components of a directed graph is widely used and acclaimed. His original algorithm required at most v(2 + 5w) bits of storage, where w is the machine’s word size, whilst Nuutila and Soisalon-Soininen reduced this to v(1 + 4w). Many real world applications routinely operate on very large graphs where the storage requirements of such algorithm...
متن کاملStrongly connected components-Algorithm for finding the strongly connected components of a graph
A directed graph G (V, E) is strongly connected if and only if, for any pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is represented by the partition of all vertices from the graph, so that for any two vertices, X and Y, from the same partition, there exists a path from X to...
متن کاملTwinless Strongly Connected Components
Tarjan [9], describes how depth first search can be used to identify Strongly Connected Components (SCC) of a directed graph in linear time. It is standard to study Tarjan’s SCC algorithm in most senior undergraduate or introductory graduate computer science algorithms courses. In this paper we introduce the concept of a twinless strongly connected component (TSCC) of a directed graph. Loosely ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 49 شماره
صفحات -
تاریخ انتشار 1994