A Faster Directed Single-Source Shortest Path Algorithm

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 $O(m{\log }^{2\mathrm{/}3}n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].