DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2018.32

Computing Bottleneck Distance for 2-D Interval Decomposable Modules

Authors: Tamal K. Dey and Cheng Xin

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

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.

Cite as

Tamal K. Dey and Cheng Xin. Computing Bottleneck Distance for 2-D Interval Decomposable Modules. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{dey_et_al:LIPIcs.SoCG.2018.32,
  author =	{Dey, Tamal K. and Xin, Cheng},
  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 =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.32},
  URN =		{urn:nbn:de:0030-drops-87453},
  doi =		{10.4230/LIPIcs.SoCG.2018.32},
  annote =	{Keywords: Persistence modules, bottleneck distance, interleaving distance}
}

Search Results

Documents authored by Xin, Cheng

Computing Bottleneck Distance for 2-D Interval Decomposable Modules

Abstract

Cite as

Thanks for your feedback!

Could not send message