Ripser: efficient computation of Vietoris–Rips persistence barcodes

We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage...

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Bibliographic Details
Published in:	Journal of applied and computational topology Vol. 5; no. 3; pp. 391 - 423
Main Author:	Bauer, Ulrich
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.09.2021
Subjects:	Algebraic Topology Computational Science and Engineering Mathematical and Computational Biology Mathematics Mathematics and Statistics 55N31 . 55-04 Persistent homology . Vietoris-Rips complexes . Topological data analysis . Discrete Morse theory
ISSN:	2367-1726, 2367-1734
Online Access:	Get full text
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Summary:	We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.
ISSN:	2367-1726 2367-1734
DOI:	10.1007/s41468-021-00071-5