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arXiv · 2211.11987

The Tight Spanning Ratio of the Rectangle Delaunay Triangulation

Andrè van Renssen·Yuan Sha·Yucheng Sun·Sampson Wong
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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 $\sqrt{2} \sqrt{1+A^2 + A \sqrt{A^2 + 1}}$, which matches the known lower bound.

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Andrè van Renssen, Yuan Sha, Yucheng Sun, Sampson Wong. 2022-11-22. The Tight Spanning Ratio of the Rectangle Delaunay Triangulation. https://arxiv.org/abs/2211.11987

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