AI 中文总结
该研究提出首个有向全局最小割增量算法，为Gabow静态算法的严格增量扩展，在总更新时间O(km log n)内可维护全局最小割或证明其值至少为k，突破了现有研究对k≤2或图为无向的限制。
AI 中文摘要
我们提出了首个有向全局最小割的增量算法。给定含n个顶点的有向图，经历m条边插入操作时，该确定性算法在总更新时间O(km log n)内，可显式维护全局最小割，或证明其值至少为k。现有研究要求k≤2或图为无向，而本算法是Gabow于1995年提出的最优静态算法（发表于JCSS）的严格增量扩展，在整个插入序列上的运行时间无渐近损失。
英文摘要
We give the first incremental algorithm for directed global minimum cut. Given a directed graph with $n$ vertices undergoing $m$ edge insertions, our deterministic algorithm explicitly maintains a global minimum cut or certifies that its value is at least $k$ in $O(km\log n)$ total update time. Prior work required either that $k\le2$ or that the graph is undirected. Our algorithm is a strict incremental extension of Gabow's state-of-the-art static algorithm (JCSS 1995), with no asymptotic loss in running time over the entire insertion sequence.
