I am given a finite set $S\subset\mathbb{R}^n$ and a natural number $m$. Both $n,m$ are supposed to be small compared to $|S|$. Now I want to find the decomposition $S=\cup_{i=1}^m S_i$ such that $\max_{i=1}^m \max_{a,b\in S_i}||a-b||$ is minimal.
Here are my questions:
-Does this problem have a name?
-Are there methods to solve it efficiently, at least approximately?
-Where are these methods implemented?
This is known as minmax diameter clustering. You can find an example algorithm and background information in this paper.