License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.32
URN: urn:nbn:de:0030-drops-87453
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8745/
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Dey, Tamal K. ; Xin, Cheng

Computing Bottleneck Distance for 2-D Interval Decomposable Modules

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LIPIcs-SoCG-2018-32.pdf (0.8 MB)

Abstract

Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-D persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-D persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called 2-D interval decomposable modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called dimension distance that bounds it from below.

BibTeX - Entry

@InProceedings{dey_et_al:LIPIcs:2018:8745,
  author =	{Tamal K. Dey and Cheng Xin},
  title =	{{Computing Bottleneck Distance for 2-D Interval Decomposable Modules}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8745},
  URN =		{urn:nbn:de:0030-drops-87453},
  doi =		{10.4230/LIPIcs.SoCG.2018.32},
  annote =	{Keywords: Persistence modules, bottleneck distance, interleaving distance}
}

Keywords: Persistence modules, bottleneck distance, interleaving distance
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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