Closing the gap for pseudo-polynomial strip packing

We study pseudo-polynomial Strip Packing. Given a set of rectangular axis parallel items and a strip with bounded width and infinite height the objective is to find a packing of the items into the strip which minimizes the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial algorithm for Strip Packing with a ratio better than 5/4 unless P = NP . The best algorithm so far has a ratio of 4/3 + ε. In this paper, we close this gap: We present an algorithm with approximation ratio 5/4 + ε. This algorithm uses a structural result which is the main accomplishment of this paper. This structural result applies to other problem settings as well, which enabled us to present algorithms with approximation ratio 5/4 + ε for Strip Packing with rotations (90 degrees) and Contiguous Moldable Task Scheduling.