Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum Volume Subset Selection for Anchored Boxes   Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each
box has a corner at the origin and the other corner in the positive quadrant of
$\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of
selecting $k$ boxes in $B$ that maximize the volume of the union of the
selected boxes. This research is motivated by applications in skyline queries
for databases and in multicriteria optimization, where the problem is known as
the hypervolume subset selection problem. It is known that the problem can be
solved in polynomial time in the plane, while the best known running time in
any dimension $d \ge 3$ is $\Omega\big(\binom{n}{k}\big)$. We show that:
  - The problem is NP-hard already in 3 dimensions.
  - In 3 dimensions, we break the bound $\Omega\big(\binom{n}{k}\big)$, by
providing an $n^{O(\sqrt{k})}$ algorithm.
  - For any constant dimension $d$, we present an efficient polynomial-time
approximation scheme.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg