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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.50
URN: urn:nbn:de:0030-drops-71822
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7182/
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Naor, Assaf

A Spectral Gap Precludes Low-Dimensional Embeddings

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LIPIcs-SoCG-2017-50.pdf (0.5 MB)


Abstract

We prove that if an n-vertex O(1)-expander embeds with average distortion D into a finite dimensional normed space X, then necessarily the dimension of X is at least n^{c/D} for some universal constant c>0. This is sharp up to the value of the constant c, and it improves over the previously best-known estimate dim(X)> c(log n)^2/D^2 of Linial, London and Rabinovich, strengthens a theorem of Matousek, and answers a question of Andoni, Nikolov, Razenshteyn and Waingarten.

BibTeX - Entry

@InProceedings{naor:LIPIcs:2017:7182,
  author =	{Assaf Naor},
  title =	{{A Spectral Gap Precludes Low-Dimensional Embeddings}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{50:1--50:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7182},
  URN =		{urn:nbn:de:0030-drops-71822},
  doi =		{10.4230/LIPIcs.SoCG.2017.50},
  annote =	{Keywords: Metric embeddings, dimensionality reduction, expander graphs, nonlinear spectral gaps, nearest neighbor search, complex interpolation, Markov type.}
}

Keywords: Metric embeddings, dimensionality reduction, expander graphs, nonlinear spectral gaps, nearest neighbor search, complex interpolation, Markov type.
Seminar: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 08.06.2017


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