The Gilbert arborescence problem

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...

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Veröffentlicht in:Networks 2013-05, Vol.61 (3), p.238-247
Hauptverfasser: Volz, M. G., Brazil, M., Ras, C. J., Swanepoel, K. J., Thomas, D. A.
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Sprache:eng
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Zusammenfassung: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 characterize 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. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013
ISSN:0028-3045
1097-0037
DOI:10.1002/net.21475