  In this paper, we study the $r$-gather problem, a natural formulation of
minimum-size clustering in metric spaces. The goal of $r$-gather is to
partition $n$ points into clusters such that each cluster has size at least
$r$, and the maximum radius of the clusters is minimized. This additional
constraint completely changes the algorithmic nature of the problem, and many
clustering techniques fail. Also previous dynamic and parallel algorithms do
not achieve desirable complexity. We propose algorithms both in the Massively
Parallel Computation (MPC) model and in the dynamic setting. Our MPC algorithm
handles input points from the Euclidean space $\mathbb{R}^d$. It computes an
$O(1)$-approximate solution of $r$-gather in $O(\log^{\varepsilon} n)$ rounds
using total space $O(n^{1+\gamma}\cdot d)$ for arbitrarily small constants
$\varepsilon,\gamma > 0$. In addition our algorithm is fully scalable, i.e.,
there is no lower bound on the memory per machine. Our dynamic algorithm
maintains an $O(1)$-approximate $r$-gather solution under insertions/deletions
of points in a metric space with doubling dimension $d$. The update time is $r
\cdot 2^{O(d)}\cdot \log^{O(1)}\Delta$ and the query time is $2^{O(d)}\cdot
\log^{O(1)}\Delta$, where $\Delta$ is the ratio between the largest and the
smallest distance.
