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.2020.32
URN: urn:nbn:de:0030-drops-121908
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12190/
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Cohen-Steiner, David ; Lieutier, André ; Vuillamy, Julien

Lexicographic Optimal Homologous Chains and Applications to Point Cloud Triangulations

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LIPIcs-SoCG-2020-32.pdf (3 MB)


Abstract

This paper considers a particular case of the Optimal Homologous Chain Problem (OHCP) for integer modulo 2 coefficients, where optimality is meant as a minimal lexicographic order on chains induced by a total order on simplices. The matrix reduction algorithm used for persistent homology is used to derive polynomial algorithms solving this problem instance, whereas OHCP is NP-hard in the general case. The complexity is further improved to a quasilinear algorithm by leveraging a dual graph minimum cut formulation when the simplicial complex is a pseudomanifold. We then show how this particular instance of the problem is relevant, by providing an application in the context of point cloud triangulation.

BibTeX - Entry

@InProceedings{cohensteiner_et_al:LIPIcs:2020:12190,
  author =	{David Cohen-Steiner and Andr{\'e} Lieutier and Julien Vuillamy},
  title =	{{Lexicographic Optimal Homologous Chains and Applications to Point Cloud Triangulations}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12190},
  URN =		{urn:nbn:de:0030-drops-121908},
  doi =		{10.4230/LIPIcs.SoCG.2020.32},
  annote =	{Keywords: OHCP, simplicial homology, triangulation, Delaunay}
}

Keywords: OHCP, simplicial homology, triangulation, Delaunay
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020


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