\] into $P^{v}_{\text{in}}$ and $P^{v}_{\text{out}}$ where $\textbf{v}$ is the parent node. Store only the single point $\text{rep}_v = m \in P$ in node $\textbf{v}$, the center of the ball $B(m,r_0)$. We continue this partitioning until we have nodes with only a single point contained in them. Since each child contains at least $\frac{n}{c}$ points