# List all sets of points in a plane that are enclosed by circles with given radius

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.

Thanks,

• @mvw: I rewrite the question for more clarification. – Arnold Jun 27 '15 at 10:28
• What operation is $S_i/S_j$? – mvw Jun 27 '15 at 10:38
• @mvw: difference operation: items in $S_i$ but not in $S_j$ – Arnold Jun 27 '15 at 11:30