On-Line Potato-Sack Algorithm Efficient for Packing Into Small Boxes

Abstract

The aim of this paper is to show an on-line algorithm for packing sequences of d-dimensional boxes of edge lengths at most 1 in a box of edge lengths at least 1. It is more efficient than a previously known algorithm in the case when packing into a box with short edges. In particular, our method permits packing every sequence of boxes of edge lengths at most 1 and of total volume at most \((1 - \frac{1} {2}\sqrt 3 )^{d - 1} \) in the unit cube. For packing sequences of convex bodies of diameters at most 1 the result is d! times smaller.