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arXiv · 2312.16415

Deterministic Minimum Steiner Cut in Maximum Flow Time

Matthew Ding·Jason Li
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Abstract

We devise a deterministic algorithm for minimum Steiner cut, which uses $(\log n)^{O(1)}$ maximum flow calls and additional near-linear time. This algorithm improves on Li and Panigrahi's (FOCS 2020) algorithm, which uses $(\log n)^{O(1/\epsilon^4)}$ maximum flow calls and additional $O(m^{1+\epsilon})$ time, for $\epsilon > 0$. Our algorithm thus shows that deterministic minimum Steiner cut can be solved in maximum flow time up to polylogarithmic factors, given any black-box deterministic maximum flow algorithm. Our main technical contribution is a novel deterministic graph decomposition method for terminal vertices that generalizes all existing $s$-strong partitioning methods, which we believe may have future applications.

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Matthew Ding, Jason Li. 2023-12-27. Deterministic Minimum Steiner Cut in Maximum Flow Time. https://arxiv.org/abs/2312.16415

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