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论文类型：期刊论文

发表时间：2013-08-01

发表刊物：JOURNAL OF COMBINATORIAL OPTIMIZATION

收录刊物：EI、SCIE

卷号：26

期号：2,SI

页面范围：223-236

ISSN号：1382-6905

关键字：Online algorithms; Bin packing; 1-space bounded; Multi dimensional

摘要：In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes 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(a similar to)-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 d-dimensional bin packing, an online algorithm with competitive ratio 4 (d) is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 (d+1)-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing.