Select dispersed diffusers from points distributed in the plane

Question

I have N=200 points (known x and y coordinates) distributed in the plane.

I want to select M=10 of them, and then it will have M*(M-1)/2 = 10 * 9 / 2 = 45 edges.

I need these points 10 be sufficiently dispersed, which means that I want to select those points 10 in such a way as to give the maximum length of the minimum edges.

In other words, I would like to solve the optimization problem (find the maximum) of the function

F = min (lengths_of_all_45_edges) by changing the selected points 10 .

Any fast algorithm to implement it?

Answer 1

You can get a minimal spanning tree, and then look for any 10 edges that make the shortest path.