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.

翻译：最短路径问题是图论和网络科学中常见的挑战，具有广泛的潜在应用。然而，传统的串行算法往往难以适应大规模图形。为了解决这个问题，研究人员探索了并行计算作为解决方案。目前最先进的最短路径算法是Delta-stepping实现方法，它显着提高了Dijkstra算法的并行性。我们提出了一种基于矩阵乘法的新型全对最短路径算法。该算法将最短路径问题转化为矩阵乘法问题，并利用其优越的并行性能。为评估我们算法的有效性，我们使用开源数据集中的真实网络输入进行了测试。我们的算法在GPU上优于并行单源最短路径算法，平均加速比为7.858倍，同时将延迟降低了13.5812%。