We devise a deterministic algorithm for minimum Steiner cut which uses polylogarithmic maximum flow calls and near-linear time outside of these maximum flow calls. This improves on Li and Panigrahi's (FOCS 2020) algorithm which takes $O(m^{1+\epsilon})$ time outside of maximum flow calls. 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 which generalizes all existing $s$-strong partitioning methods and may have future applications.

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