Persistent homology of semi-algebraic sets
| Autor: | Basu, Saugata, Karisani, Negin |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $\ell$ (for any fixed $\ell \geq 0$) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding results for computing the Betti numbers up to dimension $\ell$ of semi-algebraic sets with no filtration present. Comment: 33 pages, 3 figures. New references added. arXiv admin note: substantial text overlap with arXiv:2009.13365 |
| Databáze: | arXiv |
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