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Facility location studies optimal placement of a certain number $n$ of points (facilities) in some region $R$. (https://en.wikipedia.org/wiki/Facility_location_problem) The minimax facility location ...

If I had to partition the unit square $[0,1]\times[0,1]$ into $k^2$ rectangles such that the sum of their diagonals is minimum possible, I would simply choose the $k \times k$ grid of squares. Now ...