This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log \log n})$ for sparse graphs. This improves the recent breakthrough result of $O(m\log^{2/3} n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].

翻译：本文针对具有非负边权重的定向图，提出了一种新的确定性单源最短路径算法，其运行时间为 $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$，对于稀疏图而言为 $O(m\sqrt{\log n\log \log n})$。该结果改进了近期定向单源最短路径算法 $O(m\log^{2/3} n)$ 时间的突破性成果 [Duan, Mao, Mao, Shu, Yin 2025]。