@techreport{TR-IC-04-07, number = {IC-04-07}, author = {F. K. Miyazawa and Y. Wakabayashi}, title = {Two- and three-dimensional packings with orthogonal rotations}, month = {July}, year = {2004}, institution = {Institute of Computing, University of Campinas}, note = {In English, 42 pages. \par\selectlanguage{english}\textbf{Abstract} We present approximation algorithms for the following packing problems: the two-dimensional strip packing problem, the two-dimensional bin packing problem, the three-dimensional strip packing problem, and the three-dimensional bin packing problem. For all these problems, we consider orthogonal packings where ninety-degree rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 1.613, 2.64, 2.76 and 4.89, respectively. We also present an algorithm for the z-oriented three-dimensional strip packing problem with asymptotic performance bound 2.64. To our knowledge, these are the best bounds known for each problem. } }