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与网络科学中的一个常见挑战，具有广泛的应用前景。然而，传统的串行算法往往难以适应大规模图结构。为解决此问题，研究人员探索了并行计算方案。当前最先进的最短路径算法是Delta-stepping实现方法，该方法显著提升了Dijkstra算法的并行性。本文提出一种基于矩阵乘法的全源最短路径算法。该算法将最短路径问题转化为矩阵乘法问题，并利用了其卓越的并行性能。为评估算法有效性，我们使用开源数据集的真实网络输入进行测试。实验表明，相较于GPU上的并行单源最短路径算法，本算法实现了7.858倍的加速比，并将平均延迟降低至13.5812%。