The problem I try to solve is as follows. I have two sets of points $A$ and $B$ ($n(A) > n(B)$).
In set $A$ there is a subset $A^{cor} \subset A$ that corresponds roughly with set $B$ only by a scale transformation, so for two elements in $B$, $b_i$ and $b_j$, there are two corresponding elements in $A^{cor}$, $a_k$ and $a_l$ for which $D(b_i, b_j) - \alpha D(a_k, a_l) < \epsilon$. In which $\alpha$ is constant across all combinations.
The question is whether there is an algorithm that can extract the subset $A^{cor}$ from $A$ given $B$ that scales a bit gracefully. Doing this in brute-force will probably not be fast enough ($n(A)$ can be up to 5000). Is there such an algorithm?