Finding strongly connected components of simple digraphs based on generalized rough sets theory

Rough sets theory is not good at discovering knowledge from digraphs which is a kind of relational data. In order to solve this problem, we introduce binary relations derived from simple digraphs and propose a new concept of k-step R-related set in the framework of generalized rough sets theory. In addition, we first investigate the relationships between generalized rough sets theory and graph theory on the basis of mutual representation between binary relations and digraphs. The relationships established in this work make it possible to use generalized rough sets theory to find strongly connected components of simple directed graphs, which previously can be solved only by graph algorithms. An algorithm is correspondingly developed based on the above works, especially k-step R-related set. A series of experiments are carried out to test the proposed algorithm. The results show that our algorithm provides comparable performance to the classical Tarjan algorithm. In addition, the proposed algorithm can be implemented in parallel. And its parallel performance is comparable to existing state-of-the-art parallel algorithms.