Efficient parallel algorithm for finding strongly connected components based on granulation strategy

Strongly connected components (SCCs) are a significant subgraph structure in digraphs. In the previous work, an algorithm based on rough set theory (RST) called KGRSCC was proposed, which can compute SCCs with high efficiency. Notably, KGRSCC utilized a granulation strategy, which was designed based on SCC correlations between vertices. These SCC correlations are confined to the situations that R-related set or upper approximation set only contains one vertex. However, the situations of ’only one’ cannot fully deduce SCCs correlations, which may limit the computation efficiency of SCCs. In this paper, firstly, the graph concept of SCCs is further analyzed in the framework of RST, and then, four ’not only one’ SCC correlations between vertices can be concluded. Secondly, the four SCC correlations can be divided two classes: trivial and nontrivial. Then, two new granulation strategies are proposed based on the two classes of SCC correlations. They can granulate the vertex set to construct two types of vertex granules. Thirdly, with combination of two types of vertex granules, a parallel algorithm named P@KGS is proposed based on KGRSCC. Finally, experimental results show that the P@KGS algorithm performs higher computational efficiency than compared algorithms.