论文标题
公平的整体下管流
Fair Integral Submodular Flows
论文作者
论文摘要
研究了整数元素流多面体$ Q $的整数值元素，从而减少了最小（DEC-MIN）的意义，因为它们的最大成分尽可能小，在此内，第二大组成部分尽可能小，等等。作为主要结果，我们证明了$ Q $的DEC-MIN积分元素集是另一组积分次数多面体多面体的组成元素，该元素是由$ Q $与盒子相交的$ q $产生的。基于此描述，我们开发了一种强烈的多项式算法，用于计算DEC-MIN数字值的下管流，甚至相对于线性成本功能最便宜。一个特殊情况是找到混合图的混合图的牢固连接（或$ k $连接的）方向的问题，该图的内在矢量降低了最小。
Integer-valued elements of an integral submodular flow polyhedron $Q$ are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. As a main result, we prove that the set of dec-min integral elements of $Q$ is the set of integral elements of another integral submodular flow polyhedron arising from $Q$ by intersecting a face of $Q$ with a box. Based on this description, we develop a strongly polynomial algorithm for computing not only a dec-min integer-valued submodular flow but even a cheapest one with respect to a linear cost-function. A special case is the problem of finding a strongly connected (or $k$-edge-connected) orientation of a mixed graph whose in-degree vector is decreasingly minimal.
