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

## 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 |
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Official URL: | http://onlinelibrary.wiley.com/journal/10.1002/%28... |

Additional Information: | © 2012 Wiley Periodicals, Inc. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 02 Aug 2012 10:43 |

Last Modified: | 20 Oct 2021 01:57 |

URI: | http://eprints.lse.ac.uk/id/eprint/45051 |

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