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原文摘要

We study a generalization of online bin packing by introducing dispatch deadlines. Items arrive over time in an online fashion. Each item has an arrival time, a size in $(0,1]$, and a deadline, all of which are revealed only when the item arrives. The algorithm must immediately and irrevocably assign the item to a unit-capacity bin that has not yet been dispatched. Each bin must be dispatched no later than the earliest deadline of the items assigned to it, and once it is dispatched, it cannot be used for future items. The goal is to minimize the number of bins used. Applications arise naturally in logistics. Additionally, the offline version of this problem has appeared under several names, including the clique partition problem in weighted interval graphs and the BinSchedule problem. This problem is also a special case of online bin packing with conflicts and is closely related to online bin packing models with delay costs. We study the competitive ratios of several classical online bin packing algorithms when applied to this problem, and show that a similar hierarchy of competitive ratios carries over. Our main technical results are that the competitive ratio of First-Fit is exactly $16/7 \approx 2.28571$, and that no deterministic online algorithm has a competitive ratio less than $11/5 = 2.2$, showing that First-Fit is quite close to best possible. In addition, Next-Fit and Worst-Fit have competitive ratio exactly $3$, and every algorithm in the Any-Fit class has competitive ratio between $16/7$ and $3$.