- The Competitive Ratio for On-Line Dual Bin Packing with Restricted Input Sequences.
- Joan Boyar, Lene M. Favrholdt, Kim S. Larsen, and Morten N. Nielsen.
Nordic Journal of Computing, 8(4): 463-472, 2001.
We consider the On-Line Dual Bin Packing problem where we have a fixed
number n of bins of equal size and a sequence of items.
The goal is to maximize the number of items that are packed
in the bins by an on-line algorithm.
An investigation of First-Fit and an algorithm called Log shows that,
in the special case where all sequences can be completely packed by an
optimal off-line algorithm,
First-Fit has a constant competitive ratio, but Log does not.
In contrast, if there is no restriction on the input sequences,
Log is exponentially better than First-Fit.
This is the first separation of
this sort with a difference of more than a constant factor. We also
design randomized and deterministic algorithms for which the competitive
ratio is constant on sequences which the optimal off-line algorithm can
pack using at most alpha n bins, if alpha is constant and
known to the algorithm in advance.
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