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.

翻译：最短路径问题是图论与网络科学中的常见挑战，具有广泛的潜在应用。然而，传统的串行算法难以适应大规模图结构。为解决该问题，研究者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，它显著提升了Dijkstra算法的并行性。本文提出一种基于矩阵运算的新型全对最短路径算法，该算法需要$O(d\cdot n \cdot m)$时间和$O(m)$空间，可实现更高的并行性与可扩展性。为评估算法有效性，我们使用Stanford Network Analysis Platform和SuiteSparse Matrix Collection的真实网络输入进行测试。实验表明，与Gunrock库中的最短路径算法相比，本算法平均加速比达2.464倍，延迟降低至66.975%。