Dear All,

I want to calculate the distance between two sets in which the maximum distance between the sets are minimized. Formally problem defined as,

$\displaystyle \min_{a \in A} \max_{b \in B}$ d(a,b)

This problem looks similar to Hausdorff distance, but the order of $min$ and $max$ are swapped. While a lot of studies can be found about Hausdorff distance, I could not find any study about my problem.

- Is there any specific name of my problem that I missed?
- Do you have any solution advises for the problem except for the complete enumeration? Since the complexity of the complete enumeration is $O(|A| \cdot |B|)$, in my case it is not acceptable as a solution method.

Best Regards