There are many papers on the "Circle Placement Problem" in 2D Euclidean space, but I haven't been able to find any papers discussing this problem on the sphere. The problem is: given a set of points on a sphere and a fixed radius for a circle, find the location to place the circle that will cover the maximum number of points.
An example of a paper that discusses this problem in 2D is "On a Circle Placement Problem" by Chazelle and Lee. As discussed in this paper, this problem could be used to find the best location for a radio transmission tower with a fixed range given the locations of nearby cities.
Any thoughts you may have would be welcome. Thanks!
