2014 Sixth International Symposium on Parallel Architectures, Algorithms and Programming (PAAP) (2014)

Beijing, China

July 13, 2014 to July 15, 2014

ISSN: 2168-3034

ISBN: 978-1-4799-3844-5

pp: 87-92

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/PAAP.2014.37

ABSTRACT

We consider the problem of packing d-dimensional cubes into the minimum number of unit cubeswith 2-space bounded, as the generalization of the classic binpacking problem. Given a sequence of items, each of whichis a d-dimensional (d &ge; 3) hypercube with side length notgreater than 1 and an infinite number ofd-dimensional (d &ge; 3) hypercube bins with unit length on each side, we want to packall items in the sequence into a minimum number of bins. The constraint is that only two bins are active at anytimeduring the packing process. Each item should be orthogonallypacked without overlapping with others. Items are given inan on-line manner which means each item comes withoutknowing any information about the subsequent items. Weextend the technique of brick partitioning in paper [1] forsquare packing and obtain two results: a three dimensionalbox partitioning scheme for cube packing and ad-dimensionalhyperbox partitioning scheme for hypercube packing. We givea 5.43-competitive algorithm for cube packing and a3221 2d-competitive algorithm for hypercube packing. To the best ofour knowledge these are the first known results on 2-spacebounded cube and hypercube packing.

INDEX TERMS

Hypercubes, Partitioning algorithms, Harmonic analysis, Approximation algorithms, Educational institutions, Algorithm design and analysis, Electronic mail,asymptotic competitive ratio, hypercube packing, 2-bounded space, online algo-rithm

CITATION

Xiaofan Zhao,
Hong Shen,
"On-Line Algorithms for 2-Space Bounded Cube and Hypercube Packing",

*2014 Sixth International Symposium on Parallel Architectures, Algorithms and Programming (PAAP)*, vol. 00, no. , pp. 87-92, 2014, doi:10.1109/PAAP.2014.37