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Published in:
2005 | OriginalPaper | Chapter
Dynamic Bin Packing of Unit Fractions Items
Authors : Wun-Tat Chan, Tak-Wah Lam, Prudence W. H. Wong
Published in: Automata, Languages and Programming
Publisher: Springer Berlin Heidelberg
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This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1/
w
for some integer
w
≥ 1) into unit-size bins such that the maximum number of bins used over all time is minimized. Tight and almost-tight performance bounds are found for the family of any-fit algorithms, including first-fit, best-fit, and worst-fit. We show that the competitive ratio of best-fit and worst-fit is 3, which is tight, and the competitive ratio of first-fit lies between 2.45 and 2.4985. We also show that no on-line algorithm is better than 2.428-competitive. This result improves the lower bound of dynamic bin packing problem even for general items.