Finding single-source shortest paths from unweighted directed graphs combining rough sets theory and marking strategy

As a classical concept of graph theory, single-source shortest paths (SSSPs) plays a crucial role in numerous practical applications. Presently, the time complexity of existing SSSPs algorithms is at least O(m+nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${O}(m + nlogn)$$\end{document}. Therefore, it is still significant to design SSSPs algorithms with higher computational efficiency. In our former works, the efficiency of computing strongly connected components (SCCs) has enhanced through utilizing rough sets theory (RST). Thus, this paper also attempts to compute SSSPs more efficiently based on RST. Firstly, the graph concept of SSSPs is analyzed in the framework of RST, to provide the theoretical basis of computing SSSPs through RST method. Secondly, k-step R-related set (one RST operator) is utilized for traversing those vertices which are reachable from the source vertex. Thirdly, a marking strategy is introduced to narrow the search scope of SSSPs, which can further promote the efficiency of computing SSSPs. Finally, based on RST and marking strategy, an algorithm named 3SP@RM is put forward for finding SSSPs of unweighted directed graphs. The comparative experiment is conducted over 14 datasets. Related results display that 3SP@RM algorithm can correctly compute SSSPs of unweighted directed graphs, and the efficiency of 3SP@RM algorithm exceeds that of two existing similar methods. Even the larger scale of dataset is, more efficiency advantage 3SP@RM algorithm has.