How can I group an array of rectangles into “Islands” of connected regions?

Question

The problem

I have an array of java.awt.Rectangles. For those who are not familiar with this class, the important piece of information is that they provid

Answer 1

If you desire an O(n log n) algorithm, one was shown by Imai and Asano in Finding the connected components and a maximum clique of an intersection graph of rectangles in the plane.

Note: I'm still working on my own plane sweep algorithm to find the set in O(n log n) time.