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- Ebbers-Baumann, Annette (author)
Embedding point sets into plane graphs of small dilation
- Article/chapterEnglish2007
Publisher, publication year, extent ...
- 2007
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- LIBRIS-ID:oai:lup.lub.lu.se:7f6b3f7d-3a40-4334-9540-dd3c476f1c48
- https://lup.lub.lu.se/record/969071URI
- https://doi.org/10.1142/S0218195907002318DOI
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- Language:English
- Summary in:English
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- 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 in to 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 >= 2/root 3 approximate to 1.1547.
Subject headings and genre
- NATURVETENSKAP Data- och informationsvetenskap Datavetenskap hsv//swe
- NATURAL SCIENCES Computer and Information Sciences Computer Sciences hsv//eng
- geometric network
- spanning ratio
- plane graph
- lower bound
- stretch factor
- dilation
Added entries (persons, corporate bodies, meetings, titles ...)
- Gruene, Ansgar (author)
- Klein, Rolf (author)
- Karpinski, Marek (author)
- Knauer, Christian (author)
- Lingas, AndrzejLund University,Lunds universitet,Data Vetenskap,Naturvetenskapliga fakulteten,Computer Science,Faculty of Science(Swepub:lu)cs-ali (author)
- Data VetenskapNaturvetenskapliga fakulteten (creator_code:org_t)
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- In:International Journal of Computational Geometry and Applications17:3, s. 201-2300218-1959
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