Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Clustering via Preprocessing   We examine the efficiency of clustering a set of points, when the
encompassing metric space may be preprocessed in advance. In computational
problems of this genre, there is a first stage of preprocessing, whose input is
a collection of points $M$; the next stage receives as input a query set
$Q\subset M$, and should report a clustering of $Q$ according to some
objective, such as 1-median, in which case the answer is a point $a\in M$
minimizing $\sum_{q\in Q} d_M(a,q)$.
  We design fast algorithms that approximately solve such problems under
standard clustering objectives like $p$-center and $p$-median, when the metric
$M$ has low doubling dimension. By leveraging the preprocessing stage, our
algorithms achieve query time that is near-linear in the query size $n=|Q|$,
and is (almost) independent of the total number of points $m=|M|$.

20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin