There is an $\text{N} \times \text{N}$ grid of squares. Some arbitrary subset of those squares must be covered by some number of rectangles (a given square must be covered entirely by one rectangle, rectangles can only cover these ares, not anything else). How can I find the set of rectangles that covers all of a given set of squares with the smallest possible number of rectangles?
What is the maximum number of rectangles needed to fill in any subset of an $\text{N} \times \text{N}$ square?
