Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Glisse, Marc; Pritam, Siddharth https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-160525
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Swap, Shift and Trim to Edge Collapse a Filtration

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Abstract

Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method required only the 1-skeleton of the filtration. In this paper we revisit the use of edge collapse for efficient computation of persistent homology. We first give a simple and intuitive explanation of the principles underlying that algorithm. This in turn allows us to propose various extensions including a zigzag filtration simplification algorithm. We finally show some experiments to better understand how it behaves.

BibTeX - Entry

@InProceedings{glisse_et_al:LIPIcs.SoCG.2022.44,
  author =	{Glisse, Marc and Pritam, Siddharth},
  title =	{{Swap, Shift and Trim to Edge Collapse a Filtration}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16052},
  URN =		{urn:nbn:de:0030-drops-160525},
  doi =		{10.4230/LIPIcs.SoCG.2022.44},
  annote =	{Keywords: edge collapse, flag complex, graph, persistent homology}
}

Keywords: edge collapse, flag complex, graph, persistent homology
Seminar: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue date: 2022
Date of publication: 01.06.2022
Supplementary Material: Software (Source Code): https://github.com/GUDHI/gudhi-devel archived at: https://archive.softwareheritage.org/swh:1:cnt:c823901feab91f79f85da1717314127803fe18fd


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