Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tree Structure For Dynamic Facility Location   We study the metric facility location problem with client insertions and
deletions. This setting differs from the classic dynamic facility location
problem, where the set of clients remains the same, but the metric space can
change over time. We show a deterministic algorithm that maintains a constant
factor approximation to the optimal solution in worst-case time $\tilde
O(2^{O(\kappa^2)})$ per client insertion or deletion in metric spaces while
answering queries about the cost in $O(1)$ time, where $\kappa$ denotes the
doubling dimension of the metric. For metric spaces with bounded doubling
dimension, the update time is polylogarithmic in the parameters of the problem.

10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ