  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.
