Pseudo-deterministic algorithms are randomized algorithms that, with high constant probability, output a fixed canonical solution. The study of pseudo-deterministic algorithms for the global minimum cut problem was recently initiated by Agarwala and Varma [ITCS'26], who gave a black-box reduction incurring an $O(\log n \log \log n)$ overhead. We introduce a natural graph-theoretic tie-breaking mechanism that uniquely selects a canonical minimum cut. Using this mechanism, we obtain: (i) A pseudo-deterministic minimum cut algorithm for weighted graphs running in $O(m\log^2 n)$ time, eliminating the $O(\log n \log \log n)$ overhead of prior work and matching existing randomized algorithms. (ii) The first pseudo-deterministic algorithm for maintaining a canonical minimum cut in a fully-dynamic unweighted graph, with $\mathrm{polylog}(n)$ update time and $\tilde{O}(n)$ query time. (iii) Improved pseudo-deterministic algorithms for unweighted graphs in the dynamic streaming and cut-query models of computation, matching the best randomized algorithms.

翻译：伪确定性算法是指以高常数概率输出固定规范解的随机化算法。Agarwala与Varma [ITCS'26] 近期开创了针对全局最小割问题的伪确定性算法研究，他们提出的黑盒归约方法会产生$O(\log n \log \log n)$的开销。本文引入了一种自然的图论决胜机制，能够唯一地选择规范最小割。基于该机制，我们实现了：（一）针对加权图的伪确定性最小割算法，其运行时间为$O(m\log^2 n)$，消除了先前工作中$O(\log n \log \log n)$的开销，并与现有随机化算法性能相当；（二）首个在完全动态无权图中维护规范最小割的伪确定性算法，具有$\mathrm{polylog}(n)$的更新时间和$\tilde{O}(n)$的查询时间；（三）在动态流计算与割查询计算模型中，针对无权图的改进型伪确定性算法，其性能与最佳随机化算法持平。