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@Joseph O'Rourke If we replace the word disk by geodesic disk, then yes my problem is equivalent to your formulation. I guess your solution still works by just using a geodesic Voronoi diagram.
@Anton Petrunin I meant that maybe this optimization problem can be stated as a linear program (en.wikipedia.org/wiki/Linear_programming ) but I don't think that would be the right way to attack it.
@Igor Rivin I was just curious. Since packing problems received huge attention it amazed me that this version was not explicitly studied. But I guess Robert Israel's comment explains why.
