Geometric conditions for Euclidean Steiner trees in \(\mathbb R^d\)
type: Item
instance of: scholarly article
title: Geometric conditions for Euclidean Steiner trees in \(\mathbb R^d\)
zbMATH Open document ID: 1277.65014
author: Jon W. Van Laarhoven
author: Kurt M. Anstreicher
published in: Computational Geometry
publication date: 2013-03-12T00:00:00Z
review text: The authors present some important results in the study of the topologies for Euclidean Steiner minimal trees in \(\mathbb R^d\). Also, some conditions for trees with a full Steiner topologies are described. The paper consists of five sections. In the first section, some important notions concerning the Steiner Euclidean tree problem are re-called. In the second section, called geometric conditions for Euclidean Steiner minimal trees, the authors use in the proofs of some lemmas and theorems, the link between Voronoi diagrams, Delaunay triangulations and Euclidean Steiner trees. In the third section, some conditions for a Steiner minimal tree with a full Steiner topology are presented. In Section 4, some implementations of Smith's algorithm are presented for solving the Euclidean tree problem in \(\mathbb R^d\). In the last section, there are presented some conclusions and future works. The bibliography contains 12 titles, some of them very recent. In conclusion, the paper is well written and presents some important results at the border of computational geometry, graph theory and topology.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 6143378
zbMATH Keywords: Voronoi diagram
zbMATH Keywords: Delaunay triangulation
zbMATH Keywords: Euclidean Steiner minimal trees
zbMATH Keywords: Steiner topology
zbMATH Keywords: Smith's algorithm
reviewed by: Laurian Ioan Piscoran
MaRDI profile type: Publication
full work available at URL: j.comgeo.2011.11.007
OpenAlex ID: W1990179360
DOI: 10.1016/J.COMGEO.2011.11.007
description: scientific article; zbMATH DE number 6143378