Ripser: efficient computation of Vietoris-Rips persistence barcodes
Algebraic Topology
2021-06-28 v2 Computational Geometry
Mathematical Software
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.
Cite
@article{arxiv.1908.02518,
title = {Ripser: efficient computation of Vietoris-Rips persistence barcodes},
author = {Ulrich Bauer},
journal= {arXiv preprint arXiv:1908.02518},
year = {2021}
}
Comments
26 pages. Software available at http://ripser.org