Abstract
We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. We analyze the problem using both the competitive ratio and the relative worst order ratio, observing that the two measures often lead to different conclusions.
A closely related problem was introduced by Zhang (Discrete Appl. Math. 72:193–197, 1997). Our main result answers a question posed in that paper in the affirmative: we give an algorithm with a competitive ratio strictly better than 2, for our problem as well as Zhang’s problem. For identical bins, the new algorithm has essentially the same performance as FFD (First-Fit-Decreasing).
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A preliminary version of some of this paper appeared in Algorithm Theory—SWAT 2006, pp. 17–28, 2006.
Supported in part by the Danish Natural Science Research Council (SNF).
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Boyar, J., Favrholdt, L.M. Scheduling Jobs on Grid Processors. Algorithmica 57, 819–847 (2010). https://doi.org/10.1007/s00453-008-9257-0
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DOI: https://doi.org/10.1007/s00453-008-9257-0