The Gilbert Arborescence Problem

Details The Gilbert Arborescence Problem The Gilbert Arborescence Problem

2009-09-23

arxiv.org/abs/0909.4270v2

Mathematics

Optimization and Control

19 pages, 7 figures. arXiv admin note: text overlap with arXiv:0903.2124

Scientific paper

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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