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

Connected components.

Alternatively, because you only have rectangles you may be able to design an very efficient sweep line algorithm.

I would expect the best algorithm to take at least O( n^2 ) time because given n rectangles there are O( n^2 ) possible intersections, and any algorithm to compute what you want would need to consider all intersections at some point.