Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Illuminating Algorithm for the Light Bulb Problem   The Light Bulb Problem is one of the most basic problems in data analysis.
One is given as input $n$ vectors in $\{-1,1\}^d$, which are all independently
and uniformly random, except for a planted pair of vectors with inner product
at least $\rho \cdot d$ for some constant $\rho > 0$. The task is to find the
planted pair. The most straightforward algorithm leads to a runtime of
$\Omega(n^2)$. Algorithms based on techniques like Locality-Sensitive Hashing
achieve runtimes of $n^{2 - O(\rho)}$; as $\rho$ gets small, these approach
quadratic.
  Building on prior work, we give a new algorithm for this problem which runs
in time $O(n^{1.582} + nd),$ regardless of how small $\rho$ is. This matches
the best known runtime due to Karppa et al. Our algorithm combines techniques
from previous work on the Light Bulb Problem with the so-called `polynomial
method in algorithm design,' and has a simpler analysis than previous work. Our
algorithm is also easily derandomized, leading to a deterministic algorithm for
the Light Bulb Problem with the same runtime of $O(n^{1.582} + nd),$ improving
previous results.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con