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Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

Vincent Despré 1 Loïc Dubois 1 Benedikt Kolbe 1 Monique Teillaud 1
1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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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https://hal.inria.fr/hal-03462834
Contributor : Monique Teillaud Connect in order to contact the contributor
Submitted on : Thursday, December 2, 2021 - 9:54:27 AM
Last modification on : Friday, May 13, 2022 - 3:36:49 AM
Long-term archiving on: : Thursday, March 3, 2022 - 6:51:37 PM

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  • HAL Id : hal-03462834, version 1

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Vincent Despré, Loïc Dubois, Benedikt Kolbe, Monique Teillaud. Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces. 2021. ⟨hal-03462834v1⟩

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