On variable-sized multidimensional packing

Abstract

The main contribution of this paper is an optimal bounded space online algorithm for variable-sized multidimensional packing. In this problem, hyperboxes must be packed in d-dimensional bins of various sizes, and the goal is to minimize the total volume of the used bins. We show that the method used can also be extended to deal with the problem of resource augmented multidimensional packing, where the online algorithm has larger bins than the offline algorithm that it is compared to. Finally, we give new lower bounds for unbounded space multidimensional bin packing of hypercubes. © Springer-Verlag 2004.