Minimum area rectangle that enclose a set of rectangles
I was asked the following question by a friend who seeks an algorithm to the problem. I’m sure it is well studied but I can’t find any relevant information:
Given a set of axis-aligned rectangles, one want to arrange them on the plane by translations, such that the smallest rectangle covering them is minimized. What is the minimum area of such a covering rectangle?
The problem have this NP-Hard feel to it. Indeed I am able to reduce it to set partition.
Consider the set of blocks are of the size , . It is easy to show there is a set partition of iff the minimum area of the covering rectangle is . (As long as the sum is larger than 3.)
I particularly liked this reduction so I posted it here.