The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks [Wang, SODA 2019] runs in $O(k^5n\text{ polylog}(nU))$ where $k$ is the number of sources and sinks, and $U$ is the largest capacity of a single vertex. In this work we give a faster implementation for a procedure used by Wang's algorithm, improving the overall running time of his algorithm to $O(k^4n\text{ polylog}(nU))$

翻译：目前最高效的算法用于计算具有顶峰容量和多种源和汇的平面图中的最大整数流[Wang, SODA 2019],以$O(k ⁇ 5n\text{ polog}(nU) 美元运行,其中美元是源和汇的数量,美元是单一顶点的最大容量。在这项工作中,我们加快了王算法所用程序的实施速度,将他的算法总运行时间提高到$O(k ⁇ 4n\text{ polog}(nU))