A Novel Shortest Paths Algorithm on Unweighted Graphs

The shortest paths problem is a common challenge in graph theory, with a broad range of potential applications. However, conventional serial algorithms often struggle to adapt to large-scale graphs. To address this issue, researchers have explored parallel computing as a solution. The state-of-the-art shortest paths algorithm is the Delta-stepping implementation method, which significantly improves the parallelism of Dijkstra's algorithm. We propose a novel shortest paths algorithm achieving higher parallelism and scalability, which requires $O(nm)$ and $O(S_{wcc} \cdot E_{wcc})$ times on the connected and unconnected graphs for APSP problems, respectively, where $S_{wcc}$ and $E_{wcc}$ denote the number of nodes and edges included in the largest weakly connected component in graph. To evaluate the effectiveness of our algorithm, we tested it using real network inputs from Stanford Network Analysis Platform and SuiteSparse Matrix Collection. Our algorithm outperformed the solution of BFS and Delta-stepping algorithm from Gunrock, achieving a speedup of 1,212.523$\times$ and 1,315.953$\times$, respectively.