Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Point Location in Dynamic Planar Subdivisions   We study the point location problem on dynamic planar subdivisions that
allows insertions and deletions of edges. In our problem, the underlying graph
of a subdivision is not necessarily connected. We present a data structure of
linear size for such a dynamic planar subdivision that supports sublinear-time
update and polylogarithmic-time query. Precisely, the amortized update time is
$O(\sqrt{n}\log n(\log\log n)^{3/2})$ and the query time is $O(\log n(\log\log
n)^2)$, where $n$ is the number of edges in the subdivision. This answers a
question posed by Snoeyink in the Handbook of Computational Geometry. When only
deletions of edges are allowed, the update time and query time are just
$O(\alpha(n))$ and $O(\log n)$, respectively.

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con