Introduces SiRUP algorithm to update reduced boundary matrix, barcodes, and representative cycles for simplex removals in filtrations, claiming lower complexity than recomputing from scratch.
Matroid Filtrations and Computational Persistent Homology
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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.
fields
math.AT 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
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Pruning vineyards: updating barcodes and representative cycles by removing simplices
Introduces SiRUP algorithm to update reduced boundary matrix, barcodes, and representative cycles for simplex removals in filtrations, claiming lower complexity than recomputing from scratch.