Deterministic and Exact Fully-dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time
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| Format: | Preprint |
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2025
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| _version_ | 1866917146867531776 |
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| author | El-Hayek, Antoine Henzinger, Monika Li, Jason |
| author_facet | El-Hayek, Antoine Henzinger, Monika Li, Jason |
| contents | 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 $c>0$, 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 $(1+ε)$-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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deterministic and Exact Fully-dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time El-Hayek, Antoine Henzinger, Monika Li, Jason Data Structures and Algorithms 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 $c>0$, 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 $(1+ε)$-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). |
| title | Deterministic and Exact Fully-dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2512.13105 |