Computing connected components of simple undirected graphs based on generalized rough sets

A novel approach for calculating single-source shortest paths of weighted digraphs based on rough sets theory

Calculating single-source shortest paths (SSSPs) rapidly and precisely from weighted digraphs is a crucial problem in graph theory. As a mathematical model of processing uncertain tasks, rough sets theory (RST) has been proven to possess the ability of investigating graph theory problems. Recently, some efficient RST approaches for discovering different subgraphs (e.g. strongly connected components) have been presented. This work was devoted to discovering SSSPs of weighted digraphs by aid of RST. First, SSSPs problem was probed by RST, which aimed at supporting the fundamental theory for taking RST approach to calculate SSSPs from weighted digraphs. Second, a heuristic search strategy was designed. The weights of edges can be served as heuristic information to optimize the search way of $ k $-step $ R $-related set, which is an RST operator. By using heuristic search strategy, some invalid searches can be avoided, thereby the efficiency of discovering SSSPs was promoted. Finally, the W3SP@R algorithm based on RST was presented to calculate SSSPs of weighted digraphs. Related experiments were implemented to verify the W3SP@R algorithm. The result exhibited that W3SP@R can precisely calculate SSSPs with competitive efficiency.