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.ESA.2017.28
URN: urn:nbn:de:0030-drops-78259
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7825/
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Choudhary, Aruni ; Kerber, Michael ; Raghvendra, Sharath

Improved Approximate Rips Filtrations with Shifted Integer Lattices

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LIPIcs-ESA-2017-28.pdf (0.8 MB)

Abstract

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R^d, we present a scheme to construct a 4.24-approximation of the multi-scale filtration of the Rips complex in the L-infinity metric, which extends to a O(d^{0.25})-approximation of the Rips filtration for the Euclidean case. The k-skeleton of the resulting approximation has a total size of n2^{O(d log k)}. The scheme is based on the integer lattice and on the barycentric subdivision of the d-cube.

BibTeX - Entry

@InProceedings{choudhary_et_al:LIPIcs:2017:7825,
  author =	{Aruni Choudhary and Michael Kerber and Sharath Raghvendra},
  title =	{{Improved Approximate Rips Filtrations with Shifted Integer Lattices}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7825},
  URN =		{urn:nbn:de:0030-drops-78259},
  doi =		{10.4230/LIPIcs.ESA.2017.28},
  annote =	{Keywords: Persistent homology, Rips filtrations, Approximation algorithms, Topological Data Analysis}
}

Keywords: Persistent homology, Rips filtrations, Approximation algorithms, Topological Data Analysis
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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