Existence of shortest directed networks in \(\mathbb{R}^ 2\)
type: Item
instance of: scholarly article
title: Existence of shortest directed networks in \(\mathbb{R}^ 2\)
zbMATH Open document ID: 0821.05030
published in: Pacific Journal of Mathematics
publication date: 1995-07-03T00:00:00Z
review text: This paper establishes the existence of a shortest directed network in \(\mathbb{R}^ 2\) connecting all of a given set of starting points to all of a given set of ending points. In such networks, up to six segments sometimes meet at a point. The main difficulty is bounding the number of nodes, since shortest directed networks may contain cycles. It is an open question whether existence holds in \(\mathbb{R}^ n\).
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 769657
zbMATH Keywords: minimal networks
zbMATH Keywords: shortest directed network
zbMATH Keywords: starting points
zbMATH Keywords: ending points
zbMATH Keywords: bounding
zbMATH Keywords: number of nodes
zbMATH Keywords: cycles
author: M. Alfaro
MaRDI profile type: Publication
full work available at URL: pjm.1995.167.201
OpenAlex ID: W2069592661
DOI: 10.2140/PJM.1995.167.201
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description: scientific article; zbMATH DE number 769657