@techreport{TR-IC-00-14,
number = {IC-00-14},
author = {F. K. Miyazawa and Y. Wakabayashi},
title = {Parametric On-Line Algorithms for Packing Rectangles and Boxes},
month = {August},
year = {2000},
institution = {Institute of Computing, University of Campinas},
note = {In English, 16 pages.
\par\selectlanguage{english}\textbf{Abstract}
We present approximation algorithms for the following problems: the
two-dimensional bin packing, the three-dimensional packing problem and
the container packing problem. We consider the special case in which
the items to be packed are small and must be packed on-line. We say
an item is small if each of its dimension is at most $1/m$ of the
respective dimension of the recipient, where $m$ is an integer greater
than 1. To our knowledge, the asymptotic performance bound of these
algorithms are the best so far obtained for this special case
(parametric on-line). For the above problems, (in the respective
order) the algorithms we describe have bounds 2.112, 2.112, and 3.112,
for $m = 2$; and bounds 1.73, 1.73 and 2.285, for $m = 3$.
}
}