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Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

Abstract : Guided by insights on the mapping class group of a surface, we give experimental evidence that the upper bound recently proven on the diameter of the flip graph of a surface by Despré, Schlenker, and Teillaud (SoCG'20) is largely overestimated. To obtain this result, we propose a set of techniques allowing us to actually perform experiments. We solve arithmetic issues by proving a density result on rationally described genus two hyperbolic surfaces, and we rely on a description of surfaces allowing us to propose a data structure on which flips can be efficiently implemented.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03462834
Contributor : Monique Teillaud Connect in order to contact the contributor
Submitted on : Wednesday, May 11, 2022 - 5:36:32 PM
Last modification on : Saturday, May 21, 2022 - 9:11:15 AM

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hyperbolic-flips_v2.pdf
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  • HAL Id : hal-03462834, version 2

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Vincent Despré, Loïc Dubois, Benedikt Kolbe, Monique Teillaud. Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces. 2022. ⟨hal-03462834v2⟩

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