Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully dynamic hierarchical diameter k-clustering and k-center   We develop dynamic data structures for maintaining a hierarchical k-center
clustering when the points come from a discrete space $\{1,\ldots,\Delta\}^d$.
Our first data structure is for the low dimensional setting, i.e., d is a
constant, and processes insertions, deletions and cluster representative
queries in $\log^{O(1)} (\Delta n)$ time, where $n$ is the current size of the
point set. For the high dimensional case and an integer parameter $\ell > 1$,
we provide a randomized data structure that maintains an $O(d
\ell)$-approximation. The amortized expected insertion time is $O(d^2 \ell \log
n \log \Delta)$. The amortized expected deletion time is $O(d^2 n^{1/\ell}
\log^2 n \log \Delta)$. At any point of time, with probability at least
$1-1/n$, the data structure can correctly answer all queries for cluster
representatives in $O(d \ell \log n \log \Delta)$ time per query.

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin