Online algorithms for 1space bounded multi dimensional bin packing and hypercube packing
 Yong Zhang,
 Francis Y. L. Chin,
 HingFung Ting,
 Xin Han
 … show all 4 hide
Abstract
In this paper, we study 1space bounded multidimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a ddimensional 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 ddimensional hypercubes with unit length on each side. In ddimensional 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 1space 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 ddimensional bin packing, an online algorithm with competitive ratio 4^{ d } is given. Moreover, we consider ddimensional hypercube packing, and give a 2^{ d+1}competitive algorithm. These two results are the first study on 1space bounded multi dimensional bin packing and hypercube packing.
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 Title
 Online algorithms for 1space bounded multi dimensional bin packing and hypercube packing
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of Combinatorial Optimization
Volume 26, Issue 2 , pp 223236
 Cover Date
 20130801
 DOI
 10.1007/s108780129457z
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Online algorithms
 Bin packing
 1space bounded
 Multi dimensional
 Industry Sectors
 Authors

 Yong Zhang ^{(1)} ^{(2)}
 Francis Y. L. Chin ^{(1)}
 HingFung Ting ^{(1)}
 Xin Han ^{(3)}
 Author Affiliations

 1. Department of Computer Science, The University of Hong Kong, Hong Kong, China
 2. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
 3. School of Software, Dalian University of Technology, Dalian, China