The Tight Spanning Ratio of the Rectangle Delaunay Triangulation
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Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed using an equilateral triangle, a square, or a regular hexagon. However, all other shapes have remained elusive. In this paper we extend the restricted class of spanners for which tight bounds are known. We prove that Delaunay triangulations constructed using rectangles with aspect ratio A have spanning ratio at most √2p1 + A2 + A√A2 + 1, which matches the known lower bound.
Originalsprog | Engelsk |
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Titel | 31st Annual European Symposium on Algorithms, ESA 2023 |
Redaktører | Inge Li Gortz, Martin Farach-Colton, Simon J. Puglisi, Grzegorz Herman |
Forlag | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publikationsdato | 2023 |
Sider | 1-15 |
Artikelnummer | 99 |
ISBN (Elektronisk) | 9783959772952 |
DOI | |
Status | Udgivet - 2023 |
Begivenhed | 31st Annual European Symposium on Algorithms, ESA 2023 - Amsterdam, Holland Varighed: 4 sep. 2023 → 6 sep. 2023 |
Konference
Konference | 31st Annual European Symposium on Algorithms, ESA 2023 |
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Land | Holland |
By | Amsterdam |
Periode | 04/09/2023 → 06/09/2023 |
Navn | Leibniz International Proceedings in Informatics, LIPIcs |
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Vol/bind | 274 |
ISSN | 1868-8969 |
Bibliografisk note
Publisher Copyright:
© André van Renssen, Yuan Sha, Yucheng Sun, and Sampson Wong;
ID: 382560215