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.2017.50
URN: urn:nbn:de:0030-drops-71822
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7182/
Naor, Assaf
A Spectral Gap Precludes Low-Dimensional Embeddings
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.}
}
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Keywords: |
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Metric embeddings, dimensionality reduction, expander graphs, nonlinear spectral gaps, nearest neighbor search, complex interpolation, Markov type. |
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Collection: |
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33rd International Symposium on Computational Geometry (SoCG 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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20.06.2017 |
