The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the capacities on the existing arcs, or by adding new arcs to the network. Both operations are coming with an expansion cost. In this paper, the problem of finding the minimum network expansion cost so that the modified network can transport a given amount of flow from the source node to the sink node is studied. A strongly polynomial algorithm is deduced to solve the problem.

中文翻译：

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通过网络扩展流量增加

当需要增加通过现有交通、电力、水、气等网络的流量时，网络扩展问题是一个非常重要的实际优化问题。在这个问题中，流量增加可以通过增加容量来实现在现有弧上，或通过向网络添加新弧。这两项操作都伴随着扩张成本。本文研究了寻找最小网络扩展成本的问题，以便修改后的网络可以将给定的流量从源节点传输到汇节点。推导出强多项式算法来解决该问题。