**The Maximum Resource Bin Packing Problem***Joan Boyar, Leah Epstein, Lene M. Favrholdt, Jens S. Kohrt, Kim S. Larsen, Morten M. Pedersen, Sanne Wøhlk*

Theoretical Computer Science, in press.

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems.

For the offline variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing.

For the online variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no online algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms.

We study the general versions of the problems as well as the
parameterized
versions where there is an upper bound of *1/k* on the item
sizes, for
some integer *k*.

Last modified: Sat Aug 19 15:03:19 CEST 2006 Joan Boyar (joan@imada.sdu.dk)