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

Antoine El-Hayek; Monika Henzinger; Jason Li

Paper

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

deterministic update time when the minimum cut size is at most

for any

, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is

. Combined with graph sparsification, we obtain the first

-approximate fully-dynamic minimum cut algorithm on weighted graphs, for any

, in

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).