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



Distance calculation in metric space
This sort of thing is considered under the name "minimax facility location problem". See <http://en.wikipedia.org/wiki/Facilities_location>. 


