My problem is: Given N points in a plane and a number R, list/enumerate all subsets of points, where points in each subset are enclosed by a circle with radius of R. Two subsets $S_i$ and $S_j$ should be different and not covered each other, i.e. $S_i/S_j \neq \emptyset$ and $S_j/S_i \neq \emptyset$.
Efficiency may not be much important, but the algorithm should not be too slow.
In a special case, can we find K subsets with most points? Approximation algorithm can be accepted.