吉尔伯特树形问题
The Gilbert Arborescence Problem
摘要：
我们研究的问题，设计一个最小成本的流网络互连n个源和一个单一的汇，每个已知的位置在一个赋范空间和相关的流量需求。网络可以包含空间中任意有限数量的额外非指定节点;这些节点被称为斯坦纳点。对于凹递增费用函数，这种最小费用网络具有树拓扑，因此可以称为最小吉尔伯特树形（MGA）。我们将局部拓扑结构的施泰纳点的MGAs，显示，特别是，对于广泛的指标，并为一些典型的现实世界的成本函数，每个施泰纳点的程度是3。
英文摘要：
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics, and for some typical real-world cost-functions, the degree of each Steiner point is 3.
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