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Online LIB problems: Heuristics for Bin Covering and lower boundsfor Bin Packing

Published online by Cambridge University Press:  25 January 2006

Luke Finlay and
Prabhu Manyem
Luke Finlay
Affiliation:
Centre for Industrial and Applied Mathematics (CIAM), University of South Australia, Mawson Lakes, SA 5095, Australia; luke.finlay@unisa.edu.au
Prabhu Manyem
Affiliation:
Centre for Informatics and Applied Optimisation (CIAO), University of Ballarat, Mount Helen, VIC 3350, Australia; p.manyem@ballarat.edu.au
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Abstract

We consider the NP Hard problems of online Bin Covering and Packing whilerequiring that larger (or longer, in the one dimensional case)items be placed at the bottom of the bins, below smaller (orshorter) items — we call such a version, the LIBversion of problems. Bin sizes can be uniform or variable. We lookat computational studies for both the Best Fit and Harmonic Fitalgorithms for uniform sized bin covering. The Best Fit heuristic forthis version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upperbounds. For variable sized bin covering, a more thorough analysis revealeddefinite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform sizebins, no heuristic can guarantee an approximation ratio better than1.76 under the online model considered.

Keywords

Online approximation algorithmasymptotic worst case ratiobin covering problembin packing problemlongest itemuniform sized bins.

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 3 , July 2005, pp. 163 - 183
Copyright
© EDP Sciences, 2006

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