Deterministic and Exact Fully-dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time

Abstract

We present an exact fully-dynamic minimum cut algorithm that runs in $n^{o(1)}$ deterministic update time when the minimum cut size is at most $2^{\hat{I}˜({\log }^{3/4-c}n)}$ for any $c>0$, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is $(\log n{)}^{o(1)}$. Combined with graph sparsification, we obtain the first $(1+\hat{I}\mu )$-approximate fully-dynamic minimum cut algorithm on weighted graphs, for any $\hat{I}\mu \ge 2^{-\hat{I}˜({\log }^{3/4-c}n)}$, in $n^{o(1)}$ randomized update time. Our main technical contribution is a deterministic local minimum cut algorithm, which replaces the randomized LocalKCut procedure from El-Hayek, Henzinger, and Li (SODA 2025).

To appear at SODA 2026