Finding strongly connected components of simple digraphs based on granulation strategy

Abstract

Strongly connected components (SCCs) are an important kind of subgraphs in digraphs. It can be viewed as a kind of knowledge in the viewpoint of knowledge discovery. In our previous work, a knowledge discovery algorithm called RSCC was proposed for finding SCCs of simple digraphs based on two operators, k-step R-related set and k-step upper approximation, of rough set theory (RST). RSCC algorithm can find SCCs more efficiently than Tarjan algorithm of linear complexity. However, on the one hand, as the theoretical basis of RST applied to SCCs discovery of digraphs, the theoretical relationships between RST and graph theory investigated in previous work only include four equivalences between fundamental RST and graph concepts relating to SCCs. The reasonability of using the two RST operators to find SCCs still need to be investigated. On the other hand, it is found that there are three SCCs correlations between vertices after we use three RST concepts, R-related set, lower and upper approximation sets, to analyze SCCs. RSCC algorithm ignores these SCCs correlations so that the efficiency of RSCC is affected negatively. For the above two issues, firstly, we explore the equivalence between the two RST operators and Breadth-First Search (BFS) which is one of the most basic graph search algorithms and the most direct way to find SCCs. These equivalences explain the reasonability of using the two RST operators to find SCCs, and enrich the content of the theoretical relationships between RST and graph theory. Secondly, we design a granulation strategy according to these three SCCs correlations. Then an algorithm called GRSCC for finding SCCs of simple digraphs based on granulation strategy is proposed. Experimental results show that GRSCC provides better performance to RSCC.