Computing persistent homology of directed flag complexes

Daniel Luetgehetmann, Dejan Govc, Jason Smith, Ran Levi*

*Corresponding author for this work

Research output: Contribution to journalArticle

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 [Bau18a], but is optimized specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelization 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.
Original languageEnglish
JournalAlgorithms
Publication statusAccepted/In press - 3 Jan 2020

Fingerprint

Brain
Directed graphs
Computer hardware
Data storage equipment

Keywords

  • math.AT
  • q-bio.NC
  • 55-04

Cite this

Computing persistent homology of directed flag complexes. / Luetgehetmann, Daniel; Govc, Dejan; Smith, Jason; Levi, Ran.

In: Algorithms, 03.01.2020.

Research output: Contribution to journalArticle

@article{c7388d7081e949feb770202267044fa6,
title = "Computing persistent homology of directed flag complexes",
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 [Bau18a], but is optimized specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelization 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.",
keywords = "math.AT, q-bio.NC, 55-04",
author = "Daniel Luetgehetmann and Dejan Govc and Jason Smith and Ran Levi",
year = "2020",
month = "1",
day = "3",
language = "English",
journal = "Algorithms",
issn = "1999-4893",
publisher = "MDPI",

}

TY - JOUR

T1 - Computing persistent homology of directed flag complexes

AU - Luetgehetmann, Daniel

AU - Govc, Dejan

AU - Smith, Jason

AU - Levi, Ran

PY - 2020/1/3

Y1 - 2020/1/3

N2 - 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 [Bau18a], but is optimized specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelization 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.

AB - 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 [Bau18a], but is optimized specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelization 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.

KW - math.AT

KW - q-bio.NC

KW - 55-04

M3 - Article

JO - Algorithms

JF - Algorithms

SN - 1999-4893

ER -