Fully Dynamic Min-Cut of Superconstant Size in Subpolynomial Time

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 $\tilde{O}(\sqrt{n})$ for any $c>2$ and $c=O(\log n)$ [Thorup, Combinatorica’07].