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asymptotic worst case ratio

RAIRO - Operations Research (1)

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Online LIB problems: Heuristics for Bin Covering and lower boundsfor Bin Packing
Luke Finlay, Prabhu Manyem
Journal:

RAIRO - Operations Research / Volume 39 / Issue 3 / July 2005

Published online by Cambridge University Press:

25 January 2006, pp. 163-183

Print publication:

July 2005
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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.