Rectangle packing with one-dimensional resource augmentation

In the rectangle packing problem we are given a set R of rectangles with positive profits and the goal is to pack a subset of R into a unit size square bin 10, 11 x 10, 11 so that the total profit of the rectangles that are packed is maximized. We present algorithms that for any value is an element of > 0 find a subset R' subset of R of rectangles of total profit at least (1 - is an element of)OPT, where OPT is the profit of an optimum solution, and pack them (either without rotations or with 90 degrees rotations) into the augmented bin [0, 1] x [0, 1 + is an element of]. This algorithm can be used to design asymptotic polynomial time approximation schemes (AnAS) for the strip packing problem without and with 90 degrees rotations. The additive constant in the approximation ratios of both algorithms is 1, thus improving on the additive term in the approximation ratios of the algorithm by Kenyon and Remila (for the problem without rotations) and Jansen and van Stee (for the problem with rotations), both of which have a much larger additive constant O(1/epsilon(2)), epsilon > 0. (C) 2009 Elsevier B.V. All rights reserved.