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Geometric conditions for Euclidean Steiner trees in R-d
Journal article   Open access   Peer reviewed

Geometric conditions for Euclidean Steiner trees in R-d

Jon W. Van Laarhoven and Kurt M. Anstreicher
Computational geometry : theory and applications, Vol.46(5), pp.520-531
07/01/2013
DOI: 10.1016/j.comgeo.2011.11.007
url
https://doi.org/10.1016/j.comgeo.2011.11.007View
Published (Version of record) Open Access

Abstract

We present geometric conditions that can be used to restrict or eliminate candidate topologies for Euclidean Steiner minimal trees in R-d, d >= 2. Our emphasis is on conditions that are not restricted to the planar case (d = 2). For trees with a Steiner topology we give restrictions on terminal-Steiner connections that are based on the Voronoi diagram associated with the set of terminal nodes. We then describe more restrictive conditions for trees with a full Steiner topology and show how these conditions can be used to improve implicit enumeration algorithms for finding Euclidean Steiner minimal trees with d > 2. (C) 2011 Elsevier B.V. All rights reserved.
Mathematics Mathematics, Applied Physical Sciences Science & Technology

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