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arXiv · 2202.09591

Persistent homology of semi-algebraic sets

Saugata Basu·Negin Karisani
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Abstract

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.

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Saugata Basu, Negin Karisani. 2022-02-19. Persistent homology of semi-algebraic sets. https://arxiv.org/abs/2202.09591

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