Inapproximability Results for Orthogonal Rectangle Packing Problems with Rotations

摘要

Recently Bansal and Sviridenko proved that there is no asymptotic PTAS for 2-DIMENSIONAL ORTHOGONAL RECTANGLE BIN PACKING without rotations allowed, unless P = NP. We show that similar approximation hardness results hold for several rectangle packing problems even if rotations by ninety degrees around the axes are allowed. Moreover, for some of these problems we provide explicit lower bounds on asymptotic approximation ratio of any polynomial time approximation algorithm.