A Novel All-Pairs Shortest Path Algorithm

The shortest path problem is a common challenge in graph theory and network science, 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 path algorithm is the Delta-stepping implementation method, which significantly improves the parallelism of Dijkstra's algorithm. We propose a novel all-pairs shortest path algorithm based on matrix operations, which requires $O(d\cdot n \cdot m)$ time and $O(m)$ space, achieving higher parallelism and scalability. 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 shortest path algorithm from Gunrock, achieving a speedup of 2.464$\times$, and reducing latency to $66.975\%$, on average.