{"ID":2828858,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13105","arxiv_id":"2512.13105","title":"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 $2^{Θ(\\log^{3/4-c}n)}$ for any $c\u003e0$, 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 $(1+ε)$-approximate fully-dynamic minimum cut algorithm on weighted graphs, for any $ε\\ge2^{-Θ(\\log^{3/4-c}n)}$, 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).","short_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 $2^{Θ(\\log^{3/4-c}n)}$ for any $c\u003e0$, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is $(\\log n)^{o(1)}$. Combined with gr...","url_abs":"https://arxiv.org/abs/2512.13105","url_pdf":"https://arxiv.org/pdf/2512.13105v1","authors":"[\"Antoine El-Hayek\",\"Monika Henzinger\",\"Jason Li\"]","published":"2025-12-15T09:03:31Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}