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arXiv · 2412.15069

Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation

Antoine El-Hayek·Monika Henzinger·Jason Li
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Abstract

Dynamically maintaining the minimum cut in a graph $G$ under edge insertions and deletions is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an $n$-node graph the best known $(1+o(1))$-approximate algorithm takes $\tilde O(\sqrt{n})$ update time [Thorup 2007]. If the minimum cut is guaranteed to be $(\log n)^{o(1)}$, a deterministic exact algorithm with $n^{o(1)}$ update time exists [Jin, Sun, Thorup 2024]. We present the first fully dynamic algorithm for $(1+o(1))$-approximate minimum cut with $n^{o(1)}$ update time. Our main technical contribution is to show that it suffices to consider small-volume cuts in suitably contracted graphs.

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Antoine El-Hayek, Monika Henzinger, Jason Li. 2024-12-19. Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation. https://arxiv.org/abs/2412.15069

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