EMBEDDING POINT SETS INTO PLANE GRAPHS OF SMALL DILATION-Reference-Cited by-同舟云学术

EMBEDDING POINT SETS INTO PLANE GRAPHS OF SMALL DILATION

Published:2007-06 Issue:03 Volume:17 Page:201-230
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

EBBERS-BAUMANN ANNETTE¹,GRÜNE ANSGAR¹,KLEIN ROLF¹,KARPINSKI MAREK²,KNAUER CHRISTIAN³,LINGAS ANDRZEJ⁴

Affiliation:

1. Institute of Computer Science I, University of Bonn, D-53117 Bonn, Germany

2. Institute of Computer Science V, University of Bonn, D-53117 Bonn, Germany

3. Institute of Computer Science, FU Berlin, D-14195 Berlin, Germany

4. Department of Computer Science, Lund University, 22100 Lund, Sweden

Abstract

Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the circle, this question seems hard to answer; it is not even clear if there exists a lower bound > 1. In this paper we provide the first upper and lower bounds for the embedding problem. 1. Each finite point set can be embedded into the vertex set of a finite triangulation of dilation ≤ 1.1247. 2. Each embedding of a closed convex curve has dilation ≥ 1.00157. 3. Let P be the plane graph that results from intersecting n infinite families of equidistant, parallel lines in general position. Then the vertex set of P has dilation [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195907002318

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