How to take short cuts
type: Item
instance of: scholarly article
title: How to take short cuts
zbMATH Open document ID: 0760.52002
DOI: 10.1007/BF02293048
published in: Discrete \& Computational Geometry
publication date: 1993-01-16T00:00:00Z
review text: Let \(S\) be a rectifiable curve in Euclidean plane. The authors describe a geometric construction for adding short cuts so that every two points of \(S\) can be linked by a path along the union of \(S\) and the added short cuts. The construction guarantees that the length of the path is always at most the Euclidean distance of the linked points times a constant depending only on \(S\). The construction is provided for a polygon \(P\) approximating \(S\) and is based on the Voronoi polygons of the edges of \(P\). This approach supplies the not necessarily computable construction given by \textit{P. Jones} [Invent. Math. 102, No. 1, 1-15 (1990; Zbl 0731.30018)].
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 93447
zbMATH Keywords: path
zbMATH Keywords: polygon
zbMATH Keywords: rectifiable curve
zbMATH Keywords: short cut
zbMATH Keywords: Voronoi polygon
author: Claire Kenyon
author: Richard Kenyon
MaRDI profile type: Publication
cites work: Rectifiable sets and the traveling salesman problem
description: scientific article; zbMATH DE number 93447