We present a deterministic fully dynamic algorithm with subpolynomial worst-case time per graph update such that after processing each update of the graph, the algorithm outputs a minimum cut of the graph if the graph has a cut of size at most $c$ for some $c = (\log n)^{o(1)}$. Previously, the best update time was $\widetilde O(\sqrt{n})$ for any $c > 2$ and $c = O(\log n)$ [Thorup, Combinatorica'07].

翻译：我们提出了一种确定性完全动态算法，每次图更新后的最坏情况处理时间为次多项式级别。该算法在每次处理图更新后，若图存在大小至多为$c$的割（其中$c = (\log n)^{o(1)}$），则输出该最小割。此前，对于任意$c > 2$且$c = O(\log n)$的情况，最优更新时间为$\widetilde O(\sqrt{n})$ [Thorup, Combinatorica'07]。