Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Las Vegas Locality Sensitive Data Structures   We show that approximate similarity (near neighbour) search can be solved in
high dimensions with performance matching state of the art (data independent)
Locality Sensitive Hashing, but with a guarantee of no false negatives.
  Specifically, we give two data structures for common problems.
  For $c$-approximate near neighbour in Hamming space we get query time
$dn^{1/c+o(1)}$ and space $dn^{1+1/c+o(1)}$ matching that of
\cite{indyk1998approximate} and answering a long standing open question
from~\cite{indyk2000dimensionality} and~\cite{pagh2016locality} in the
affirmative.
  By means of a new deterministic reduction from $\ell_1$ to Hamming we also
solve $\ell_1$ and $\ell_2$ with query time $d^2n^{1/c+o(1)}$ and space $d^2
n^{1+1/c+o(1)}$.
  For $(s_1,s_2)$-approximate Jaccard similarity we get query time
$dn^{\rho+o(1)}$ and space $dn^{1+\rho+o(1)}$,
$\rho=\log\frac{1+s_1}{2s_1}\big/\log\frac{1+s_2}{2s_2}$, when sets have equal
size, matching the performance of~\cite{tobias2016}.
  The algorithms are based on space partitions, as with classic LSH, but we
construct these using a combination of brute force, tensoring, perfect hashing
and splitter functions \`a la~\cite{naor1995splitters}. We also show a new
dimensionality reduction lemma with 1-sided error.

14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn