2026-07-20T14:34:41Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8218 2024-03-06T10:41:53Z ddc:004 open_access

Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}} Sankowski, Piotr Wygocki, Piotr locality sensitive hashing approximate near neighbor search high- dimensional similarity search 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Piotr Sankowski and Piotr Wygocki 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.63 urn:nbn:de:0030-drops-82189 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.63 eng https://creativecommons.org/licenses/by/3.0/legalcode