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arXiv · 2010.07976

Sampling and homology via bottlenecks

Sandra Di Rocco·David Eklund·Oliver Gäfvert
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Abstract

In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing $\textit{bottlenecks}$ of the variety. Using geometric information such as the bottlenecks and the $\textit{local reach}$ we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et. al.

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Sandra Di Rocco, David Eklund, Oliver Gäfvert. 2020-10-15. Sampling and homology via bottlenecks. https://arxiv.org/abs/2010.07976

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