We present a faster algorithm for low-diameter decompositions on directed graphs, matching the $O(\log n\log\log n)$ loss factor from Bringmann, Fischer, Haeupler, and Latypov (ICALP 2025) and improving the running time to $O((m+n\log\log n)\log n\log\log n)$ in expectation. We then apply our faster low-diameter decomposition to obtain an algorithm for negative-weight single source shortest paths on integer-weighted graphs in $O((m+n\log\log n)\log(nW)\log n\log\log n)$ time, a nearly log-factor improvement over the algorithm of Bringmann, Cassis, and Fischer (FOCS 2023).

翻译：我们提出了一种用于有向图上低直径分解的更快算法，其损失因子与Bringmann、Fischer、Haeupler和Latypov（ICALP 2025）的$O(\log n\log\log n)$结果相匹配，并将期望运行时间改进为$O((m+n\log\log n)\log n\log\log n)$。随后，我们应用这一更快的低直径分解算法，在整数加权图上得到了一个求解负权单源最短路径的算法，其时间复杂度为$O((m+n\log\log n)\log(nW)\log n\log\log n)$，这相较于Bringmann、Cassis和Fischer（FOCS 2023）的算法实现了近对数因子的改进。