@inproceedings{b74f7142bdf54fd390e2cb054c91f554,

title = "On-line algorithms for 2-space bounded cube and hypercube packing",

abstract = "We consider the problem of packing ddimensional cubes into the minimum number of unit cubes with 2-space bounded, as the generalization of the classic bin packing problem. Given a sequence of items, each of which is a d-dimensional (d ≥ 3) hypercube with side length not greater than 1 and an infinite number of d-dimensional (d ≥ 3) hypercube bins with unit length on each side, we want to pack all items in the sequence into a minimum number of bins. The constraint is that only two bins are active at anytime during the packing process. Each item should be orthogonally packed without overlapping with others. Items are given in an on-line manner which means each item comes without knowing any information about the subsequent items. We extend the technique of brick partitioning in paper [1] for square packing and obtain two results: a three dimensional box partitioning scheme for cube packing and a d-dimensional hyperbox partitioning scheme for hypercube packing. We give a 5.43-competitive algorithm for cube packing and a 32/21 · 2dcompetitive algorithm for hypercube packing. To the best of our knowledge these are the first known results on 2-space bounded cube and hypercube packing.",

keywords = "2-bounded space, Asymptotic competitive ratio, Hypercube packing, Online algo-rithm",

author = "Xiaofan Zhao and Hong Shen",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 6th International Symposium on Parallel Architectures, Algorithms, and Programming, PAAP 2014 ; Conference date: 13-07-2014 Through 15-07-2014",

year = "2014",

month = oct,

day = "3",

doi = "10.1109/PAAP.2014.37",

language = "English",

series = "Proceedings - International Symposium on Parallel Architectures, Algorithms and Programming, PAAP",

publisher = "IEEE Computer Society",

pages = "87--92",

editor = "Hong Shen and Hong Shen and Yingpeng Sang and Hui Tian",

booktitle = "Proceedings - 6th International Symposium on Parallel Architectures, Algorithms, and Programming, PAAP 2014",

address = "United States",

}