Matroid Filtrations and Computational Persistent Homology

1 Jun 2016  ·  Gregory Henselman, Robert Ghrist ·

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.

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