Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Maximum Exposure Problem   Given a set of points $P$ and axis-aligned rectangles $\mathcal{R}$ in the
plane, a point $p \in P$ is called \emph{exposed} if it lies outside all
rectangles in $\mathcal{R}$. In the \emph{max-exposure problem}, given an
integer parameter $k$, we want to delete $k$ rectangles from $\mathcal{R}$ so
as to maximize the number of exposed points. We show that the problem is
NP-hard and assuming plausible complexity conjectures is also hard to
approximate even when rectangles in $\mathcal{R}$ are translates of two fixed
rectangles. However, if $\mathcal{R}$ only consists of translates of a single
rectangle, we present a polynomial-time approximation scheme. For range space
defined by general rectangles, we present a simple $O(k)$ bicriteria
approximation algorithm; that is by deleting $O(k^2)$ rectangles, we can expose
at least $\Omega(1/k)$ of the optimal number of points.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys