Maxwell, Alastair and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2020) Shortest directed networks in the plane. Graphs and Combinatorics, 36 (5). 1457 - 1475. ISSN 0911-0119
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Abstract
Given a set of sources and a set of sinks as points in the Euclidean plane, a directed network is a directed graph drawn in the plane with a directed path from each source to each sink. Such a network may contain nodes other than the given sources and sinks, called Steiner points. We characterize the local structure of the Steiner points in all shortest-length directed networks in the Euclidean plane. This charac- terization implies that these networks are constructible by straightedge and compass. Our results build on unpublished work of Alfaro, Camp- bell, Sher, and Soto from 1989 and 1990. Part of the proof is based on a new method that uses other norms in the plane. This approach gives more conceptual proofs of some of their results, and as a consequence, we also obtain results on shortest directed networks for these norms.
Item Type: | Article |
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Official URL: | https://www.springer.com/journal/373 |
Additional Information: | © 2020 The Authors |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 13 May 2020 10:33 |
Last Modified: | 14 Sep 2024 08:16 |
URI: | http://eprints.lse.ac.uk/id/eprint/104368 |
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