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.ESA.2020.43
URN: urn:nbn:de:0030-drops-129097
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12909/
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Eisenbrand, Friedrich ; Venzin, Moritz

Approximate CVP_p in Time 2^{0.802 n}

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Abstract

We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any ?_p-norm can be computed in time 2^{(0.802 +ε) n}. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. ?₂. To obtain our result, we combine the latter algorithm w.r.t. ?₂ with geometric insights related to coverings.

BibTeX - Entry

@InProceedings{eisenbrand_et_al:LIPIcs:2020:12909,
  author =	{Friedrich Eisenbrand and Moritz Venzin},
  title =	{{Approximate CVP_p in Time 2^{0.802 n}}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12909},
  URN =		{urn:nbn:de:0030-drops-129097},
  doi =		{10.4230/LIPIcs.ESA.2020.43},
  annote =	{Keywords: Shortest and closest vector problem, approximation algorithm, sieving, covering convex bodies}
}

Keywords: Shortest and closest vector problem, approximation algorithm, sieving, covering convex bodies
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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