Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameterized Convexity Testing   In this work, we develop new insights into the fundamental problem of
convexity testing of real-valued functions over the domain $[n]$. Specifically,
we present a nonadaptive algorithm that, given inputs $\eps \in (0,1), s \in
\mathbb{N}$, and oracle access to a function, $\eps$-tests convexity in $O(\log
(s)/\eps)$, where $s$ is an upper bound on the number of distinct discrete
derivatives of the function. We also show that this bound is tight. Since $s
\leq n$, our query complexity bound is at least as good as that of the optimal
convexity tester (Ben Eliezer; ITCS 2019) with complexity $O(\frac{\log \eps
n}{\eps})$; our bound is strictly better when $s = o(n)$. The main contribution
of our work is to appropriately parameterize the complexity of convexity
testing to circumvent the worst-case lower bound (Belovs et al.; SODA 2020) of
$\Omega(\frac{\log (\eps n)}{\eps})$ expressed in terms of the input size and
obtain a more efficient algorithm.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat