Resource augmentation in two-dimensional packing with orthogonal rotations

We consider the problem of packing two-dimensional rectangles into the minimum number of unit squares, when 90∘ rotations are allowed. Our main contribution is a polynomial-time algorithm for packing rectangles into at most OPT bins whose sides have length (1+ε), for any positive ε. Additionally, we show near-optimal packing results for a number of related packing problems.