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DOI: 10.4230/LIPIcs.SoCG.2020.53

Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Authors: Michael Kerber and Arnur Nigmetov

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract

In topological data analysis, the matching distance is a computationally tractable metric on multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision ε>0. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.

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Michael Kerber and Arnur Nigmetov. Efficient Approximation of the Matching Distance for 2-Parameter Persistence. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 53:1-53:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kerber_et_al:LIPIcs.SoCG.2020.53,
  author =	{Kerber, Michael and Nigmetov, Arnur},
  title =	{{Efficient Approximation of the Matching Distance for 2-Parameter Persistence}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{53:1--53:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.53},
  URN =		{urn:nbn:de:0030-drops-122116},
  doi =		{10.4230/LIPIcs.SoCG.2020.53},
  annote =	{Keywords: multi-parameter persistence, matching distance, approximation algorithm}
}

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Efficient Approximation of the Matching Distance for 2-Parameter Persistence

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