minimizing overlap in random rectangles

Question

I have a number of possibly overlapping rectangles, of random size and position within a fixed plane. Since these rectangles are random, some may not overlap:

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Answer 1

Very interesting question - I think it's best to solve the problem a pair of rectangles at a time rather than looking at 3 or more at one time. Start by discarding those within other rectangles. Now you only have 3 kinds of intersections - corner overlap and pass through overlap and partial overlap (where the rectangle doesn't pass all the way through). These each create a new set of rectangles, right?

Number your starting rectangles from 1 to N. Starting with rectangle 1 cycle through until you find an intersecting rectangle. Create new rectangles. Delete the two intersecting rectangles and add the 3 or more newly created rectangles to your set and start again.

The result will be a whole bunch of non-overlapping rectangles. Does this create the fewest rectangles? Probably not, but you didn't specify that minimizing the number of rectangles was important. Does it take over o(n^2) time? Probably.