Distance calculation in metric space - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T11:03:06Z http://mathoverflow.net/feeds/question/106356 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106356/distance-calculation-in-metric-space Distance calculation in metric space Gokhan 2012-09-04T15:34:21Z 2012-09-04T19:17:43Z <p>Dear All,</p> <p>I want to calculate the distance between two sets in which the maximum distance between the sets are minimized. Formally problem defined as,</p> <p>$\displaystyle \min_{a \in A} \max_{b \in B}$ d(a,b)</p> <p>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. </p> <ul> <li>Is there any specific name of my problem that I missed? </li> <li>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. </li> </ul> <p>Best Regards</p> http://mathoverflow.net/questions/106356/distance-calculation-in-metric-space/106377#106377 Answer by Robert Israel for Distance calculation in metric space Robert Israel 2012-09-04T19:17:43Z 2012-09-04T19:17:43Z <p>This sort of thing is considered under the name "minimax facility location problem". See <a href="http://en.wikipedia.org/wiki/Facilities_location" rel="nofollow">http://en.wikipedia.org/wiki/Facilities_location</a>. </p>