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.APPROX/RANDOM.2020.43
URN: urn:nbn:de:0030-drops-126464
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12646/
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Agarwal, Ishan ; Regev, Oded ; Tang, Yi

Nearly Optimal Embeddings of Flat Tori

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LIPIcs-APPROX43.pdf (0.5 MB)

Abstract

We show that for any n-dimensional lattice ℒ ⊆ ℝⁿ, the torus ℝⁿ/ℒ can be embedded into Hilbert space with O(√{nlog n}) distortion. This improves the previously best known upper bound of O(n√{log n}) shown by Haviv and Regev (APPROX 2010, J. Topol. Anal. 2013) and approaches the lower bound of Ω(√n) due to Khot and Naor (FOCS 2005, Math. Ann. 2006).

BibTeX - Entry

@InProceedings{agarwal_et_al:LIPIcs:2020:12646,
  author =	{Ishan Agarwal and Oded Regev and Yi Tang},
  title =	{{Nearly Optimal Embeddings of Flat Tori}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12646},
  URN =		{urn:nbn:de:0030-drops-126464},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.43},
  annote =	{Keywords: Lattices, metric embeddings, flat torus}
}

Keywords: Lattices, metric embeddings, flat torus
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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