Online Algorithm for 1-Space Bounded Multi-dimensional Bin Packing

摘要

In this paper, we study 1-space bounded multi-dimensional bin packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox and the length of each side is no more than 1. These items must be packed Without overlapping into d-dimensional hy-percubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P_(ij). When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90°-rotation on any plane P_(ij) is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For this problem, we give an online algorithm with competitive ratio 4~d, which is the first study on 1-space bounded d-dimensional bin packing.