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The Gilbert arborescence problem

Volz, Marcus G., Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad ORCID: 0000-0002-1668-887X and Thomas, Doreen A. (2012) The Gilbert arborescence problem. Networks, 61 (3). pp. 238-247. ISSN 0028-3045

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Identification Number: 10.1002/net.21475


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.

Item Type: Article
Official URL:
Additional Information: © 2012 Wiley Periodicals, Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 02 Aug 2012 10:43
Last Modified: 16 May 2024 01:27

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