We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same running time, thereby improving on the recent bound of $\tilde{O}(n^{2.5})$ by Abboud et al. (FOCS 2021). Our running time is nearly optimal as a function of $n$.

翻译：我们给出了美元2+1美元(美元)的时值算法,用于在一纸简单的、无方向的图表中找到所有顶点的美元和美元。我们这样做的方式是在同一时间建造一棵高木树(或剪切等效树),从而改进了Abboud等人(FOCS 2021)最近对$2+1美元(美元2.5美元)的约束。我们的运行时间几乎以美元为单位,是最佳的。