Distributed Persistent Homology for 2D Alpha Complexes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916143714795520 |
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| author | Jensen, Freya Torras-Casas, Álvaro |
| author_facet | Jensen, Freya Torras-Casas, Álvaro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Persistent Homology for 2D Alpha Complexes Jensen, Freya Torras-Casas, Álvaro Algebraic Topology 55N31, 55T99, 55-04 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. |
| title | Distributed Persistent Homology for 2D Alpha Complexes |
| topic | Algebraic Topology 55N31, 55T99, 55-04 |
| url | https://arxiv.org/abs/2403.00445 |