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The Gilbert arborescence problem

Volz, Marcus G. and Brazil, Marcus and Ras, Charl J. and Swanepoel, Konrad 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

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 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: http://onlinelibrary.wiley.com/journal/10.1002/%28...
Additional Information: © 2012 Wiley Periodicals, Inc.
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 02 Aug 2012 10:43
Last Modified: 09 May 2013 10:51
URI: http://eprints.lse.ac.uk/id/eprint/45051

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