English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we show a construction of locality-sensitive hash functionswithout false negatives, i.e., which ensure collision for every pair of pointswithin a given radius $R$ in $d$ dimensional space equipped with $l_p$ normwhen $p \in [1,\infty]$. Furthermore, we show how to use these hash functionsto solve the $c$-approximate nearest neighbor search problem without falsenegatives. Namely, if there is a point at distance $R$, we will certainlyreport it and points at distance greater than $cR$ will not be reported for$c=\Omega(\sqrt{d},d^{1-\frac{1}{p}})$. The constructed algorithms work: - withpreprocessing time $\mathcal{O}(n \log(n))$ and sublinear expected query time,- with preprocessing time $\mathcal{O}(\mathrm{poly}(n))$ and expected querytime $\mathcal{O}(\log(n))$. Our paper reports progress on answering the openproblem presented by Pagh [8] who considered the nearest neighbor searchwithout false negatives for the Hamming distance.

Locality-Sensitive Hashing without False Negatives for l_p