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arXiv · 2403.00445

Distributed Persistent Homology for 2D Alpha Complexes

Freya Jensen·Álvaro Torras-Casas
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Abstract

We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to compute the persistence Mayer-Vietoris spectral sequence from these covers and how to obtain persistent homology from it. For this, we introduce second-page collapse conditions and explain how to solve the extension problem. Finally, we give an overview of an implementation in C++ using Open MPI and discuss some experimental results.

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Freya Jensen, Álvaro Torras-Casas. 2024-03-01. Distributed Persistent Homology for 2D Alpha Complexes. https://arxiv.org/abs/2403.00445

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