Consider the single-source shortest paths problem on a directed graph with real-valued edge weights. We solve this problem in $O(n^{2.5}\log^{4.5}n)$ time, improving on prior work of Fineman (STOC 2024) and Huang-Jin-Quanrud (SODA 2025, 2026) on dense graphs. Our main technique is an shortcutting procedure that iteratively reduces the number of negative-weight edges along shortest paths by a constant factor.

翻译：考虑在具有实值边权重的有向图上的单源最短路径问题。我们在$O(n^{2.5}\log^{4.5}n)$时间内解决了该问题，改进了Fineman（STOC 2024）与Huang-Jin-Quanrud（SODA 2025，2026）在稠密图上的先前工作。我们的核心技术是一种捷径化过程，通过迭代地将最短路径上的负权边数量以常数因子减少。