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://drops.dagstuhl.de/opus/volltexte/2017/8218/
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### Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}

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### 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},