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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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
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Abstract	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.
AbstractList	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.
Author	Bauer, Ulrich
Author_xml	– sequence: 1 givenname: Ulrich surname: Bauer fullname: Bauer, Ulrich email: mail@ulrich-bauer.org organization: Technical University of Munich (TUM)
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Snippet	We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on...
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Title	Ripser: efficient computation of Vietoris–Rips persistence barcodes
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