Cookies?
Library Header Image
LSE Research Online LSE Library Services

Shortest directed networks in the plane

Maxwell, Alastair and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2020) Shortest directed networks in the plane. Graphs and Combinatorics. ISSN 0911-0119

[img] Text (Shortest directed networks in the place) - Published Version
Available under License Creative Commons Attribution.

Download (737kB)

Identification Number: 10.1007/s00373-020-02183-8

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 Our results build on unpublished work of Alfaro, Camp- bell, Sher, and Soto from 1989 and 1990.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
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: 30 Jun 2020 13:06
URI: http://eprints.lse.ac.uk/id/eprint/104368

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics