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.

翻译：我们设计了一种用于最小斯坦纳割的确定性算法，该算法在最大流调用中仅使用多对数级别的次数，且在最大流调用之外的时间复杂度接近线性。这改进了Li与Panigrahi（FOCS 2020）算法中最大流调用外需要$O(m^{1+\epsilon})$时间的局限。因此，我们的算法表明，在任意黑盒确定性最大流算法的基础上，最小斯坦纳割可以在最大流时间（仅差多对数因子）内解决。本文的主要技术贡献是一种新颖的确定性图分解方法，该方法针对终端顶点设计，统一了所有现有的$s$-强划分方法，并可能在未来具有广泛应用。