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.ISAAC.2017.63
URN: urn:nbn:de:0030-drops-82189
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8218/
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Sankowski, Piotr ; Wygocki, Piotr

Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}

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LIPIcs-ISAAC-2017-63.pdf (0.6 MB)

Abstract

In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the near neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate near neighbors problem without false negatives for Euclidean high dimensional space
\mathcal{R}^d. These data structures work for any c = \omega(\sqrt{\log{\log{n}}}), where n is the number of points in the input set, with poly-logarithmic query time and polynomial
pre-processing time. This improves over the known algorithms, which require c to be \Omega(\sqrt{d}).

This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate near neighbor search without false negatives instances in \big(\Rspace^k\big)^L space equipped with metric m(x,y) = \max_{1 \le i \leL}(\dist{x_i - y_i}_2).

BibTeX - Entry

@InProceedings{sankowski_et_al:LIPIcs:2017:8218,
  author =	{Piotr Sankowski and Piotr Wygocki},
  title =	{{Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{63:1--63:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8218},
  URN =		{urn:nbn:de:0030-drops-82189},
  doi =		{10.4230/LIPIcs.ISAAC.2017.63},
  annote =	{Keywords: locality sensitive hashing, approximate near neighbor search, high- dimensional, similarity search}
}

Keywords: locality sensitive hashing, approximate near neighbor search, high- dimensional, similarity search
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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