{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/matroid-filtrations-and-computational","title":"Matroid Filtrations and Computational Persistent Homology","arxiv_id":"1606.00199","date":"2016-06-01","proceeding":null,"authors":["Gregory Henselman","Robert Ghrist"],"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.","url_abs":"https://arxiv.org/abs/1606.00199v2","url_pdf":"https://arxiv.org/pdf/1606.00199v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"matroid-filtrations-and-computational","repo_url":"https://github.com/Eetion/Eirene.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"matroid-filtrations-and-computational","repo_url":"https://github.com/UnofficialJuliaMirror/Eirene.jl-9c0f25c4-2ca1-5870-89f6-52640788da1d","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"matroid-filtrations-and-computational","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/Eirene.jl-9c0f25c4-2ca1-5870-89f6-52640788da1d","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}