Matroid Filtrations and Computational Persistent Homology
Abstract
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here presented rely on a novel relationship between discrete Morse theory, matroid theory, and classical matrix factorizations. We provide background, detail the algorithms, and benchmark the software implementation in the Eirene package.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2016
- arXiv:
- arXiv:1606.00199
- Bibcode:
- 2016arXiv160600199H
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - Combinatorics
- E-Print:
- v2: 16 pages