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 multiplications. This algorithm transforms the shortest path problem into a matrix multiplication problem and takes advantage of its superior parallelism performance. To evaluate the effectiveness of our algorithm, we tested it using real network inputs from open source datasets. Our algorithm outperformed parallel single source shortest path algorithms on GPUs, achieving a speedup of 7.858 $\times$, and reducing latency to $13.5812\%$, on average.