Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles   In this paper we study two geometric data structure problems in the special
case when input objects or queries are fat rectangles. We show that in this
case a significant improvement compared to the general case can be achieved.
  We describe data structures that answer two- and three-dimensional orthogonal
range reporting queries in the case when the query range is a \emph{fat}
rectangle. Our two-dimensional data structure uses $O(n)$ words and supports
queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the
data structure, $U$ is the size of the universe and $k$ is the number of points
in the query range. Our three-dimensional data structure needs
$O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U
+ k)$ time. We also consider the rectangle stabbing problem on a set of
three-dimensional fat rectangles. Our data structure uses $O(n)$ space and
answers stabbing queries in $O(\log U\log\log U +k)$ time.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg