License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.43
URN: urn:nbn:de:0030-drops-169813
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16981/
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Dey, Tamal K. ; Hou, Tao

Fast Computation of Zigzag Persistence

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LIPIcs-ESA-2022-43.pdf (0.8 MB)

Abstract

Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We propose an algorithm called FastZigzag which narrows this efficiency gap. Our main result is that an input simplex-wise zigzag filtration can be converted to a cell-wise non-zigzag filtration of a Δ-complex with the same length, where the cells are copies of the input simplices. This conversion step in FastZigzag incurs very little cost. Furthermore, the barcode of the original filtration can be easily read from the barcode of the new cell-wise filtration because the conversion embodies a series of diamond switches known in topological data analysis. This seemingly simple observation opens up the vast possibilities for improving the computation of zigzag persistence because any efficient algorithm/software for standard persistence can now be applied to computing zigzag persistence. Our experiment shows that this indeed achieves substantial performance gain over the existing state-of-the-art softwares.

BibTeX - Entry

@InProceedings{dey_et_al:LIPIcs.ESA.2022.43,
  author =	{Dey, Tamal K. and Hou, Tao},
  title =	{{Fast Computation of Zigzag Persistence}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16981},
  URN =		{urn:nbn:de:0030-drops-169813},
  doi =		{10.4230/LIPIcs.ESA.2022.43},
  annote =	{Keywords: zigzag persistence, persistent homology, fast computation}
}

Keywords: zigzag persistence, persistent homology, fast computation
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022
Supplementary Material: Software (Source Code): https://github.com/taohou01/fzz

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