This paper examines the Balanced Submodular Flow Problem, that is the problem of finding a feasible submodular flow minimizing the difference between the flow values along the edges. A min-max formula is given to the problem and an algorithm is presented to solve it using $O(m^2)$ submodular function minimizations. Then, these result are extended to the weighted version of the problem. Finally, the Balanced Integer Submodular Flow Problem is discussed.

翻译：本文研究平衡子模流问题，即寻找一条可行子模流，使得各边流量值之差最小化。针对该问题给出了一个极小极大公式，并提出了一种利用$O(m^2)$次子模函数最小化来求解的算法。随后，将这些结果推广到问题的加权版本。最后，讨论了平衡整数子模流问题。