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Communication Dans Un Congrès Année : 2012

The Stretch Factor of ${L}_1$- and ${L}_\infty$-{D}elaunay Triangulations

Résumé

In this paper we determine the stretch factor of L1-Delaunay and L∞-Delaunay triangulations, and we show that it is equal to √(4 + 2√2) ≈ 2.61. Between any two points x, y of such triangulations, we construct a path whose length is no more than √(4 + 2√2) times the Euclidean distance between x and y, and this bound is the best possible. This definitively improves the 25-year old bound of triangulations of √10 by Chew (SoCG '86). This is the first time the stretch factor of the Lp-Delaunay for any real p ≥ 1, is determined exactly.

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Dates et versions

hal-00725844 , version 1 (28-08-2012)

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  • HAL Id : hal-00725844 , version 1

Citer

Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse, Ljubomir Perkovic. The Stretch Factor of ${L}_1$- and ${L}_\infty$-{D}elaunay Triangulations. 20th Annual European Symposium on Algorithms (ESA), Sep 2012, Ljubljana, Slovenia. pp.205-216. ⟨hal-00725844⟩
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