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Dynamic Bin Packing of Unit Fractions Items

2005; Springer Science+Business Media; Linguagem: Inglês

10.1007/11523468_50

1611-3349

Wun-Tat Chan, Tak-Wah Lam, Prudence W. H. Wong,

Advanced Manufacturing and Logistics Optimization

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.