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arXiv · 0909.4270

The Gilbert Arborescence Problem

M. G. Volz·M. Brazil·C. J. Ras·K. J. Swanepoel·D. A. Thomas
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Abstract

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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M. G. Volz, M. Brazil, C. J. Ras, K. J. Swanepoel, D. A. Thomas. 2009-09-23. The Gilbert Arborescence Problem. https://doi.org/10.1002/net.21475

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