Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Query Shortest Paths Amidst Growing Discs   The determination of collision-free shortest paths among growing discs has
previously been studied for discs with fixed growing rates. Here, we study a
more general case of this problem, where: (1) the speeds at which the discs are
growing are polynomial functions of degree $\dd$, and (2) the source and
destination points are given as query points. We show how to preprocess the $n$
growing discs so that, for two given query points $s$ and $d$, a shortest path
from $s$ to $d$ can be found in $O(n^2 \log (\dd n))$ time. The preprocessing
time of our algorithm is $O(n^2 \log n + k \log k)$ where $k$ is the number of
intersections between the growing discs and the tangent paths (straight line
paths which touch the boundaries of two growing discs). We also prove that $k
\in O(n^3\dd)$.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom