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The Tight Spanning Ratio of the Rectangle Delaunay Triangulation

Authors André van Renssen , Yuan Sha, Yucheng Sun, Sampson Wong



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Author Details

André van Renssen
  • University of Sydney, Australia
Yuan Sha
  • University of Sydney, Australia
Yucheng Sun
  • University of Sydney, Australia
Sampson Wong
  • BARC, University of Copenhagen, Denmark

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André van Renssen, Yuan Sha, Yucheng Sun, and Sampson Wong. The Tight Spanning Ratio of the Rectangle Delaunay Triangulation. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 99:1-99:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ESA.2023.99

Abstract

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 √2 √{1+A² + A √{A²+1}}, which matches the known lower bound.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Spanners
  • Delaunay Triangulation
  • Spanning Ratio

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References

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