Distributed Persistent Homology for 2D Alpha Complexes
Algebraic Topology
2024-03-04 v1
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.
Cite
@article{arxiv.2403.00445,
title = {Distributed Persistent Homology for 2D Alpha Complexes},
author = {Freya Jensen and Álvaro Torras-Casas},
journal= {arXiv preprint arXiv:2403.00445},
year = {2024}
}
Comments
32 pages, 15 figures