Computing persistent homology of directed flag complexes

Lütgehetmann, D, Govc, D, Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604 and Levi, R, 2020. Computing persistent homology of directed flag complexes. Algorithms, 13 (1): 19.

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Abstract

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser by U. Bauer, but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.

Item Type:	Journal article
Publication Title:	Algorithms
Creators:	Lütgehetmann, D., Govc, D., Smith, J.P. and Levi, R.
Publisher:	MDPI
Date:	2020
Volume:	13
Number:	1
Identifiers:	Number Type 10.3390/a13010019 DOI 1390734 Other
Rights:	© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	22 Apr 2021 15:22
Last Modified:	14 Jan 2022 11:19
URI:	https://irep.ntu.ac.uk/id/eprint/42749

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