Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
On the online bin packing problem
Journal of the ACM (JACM)
Prediction, Learning, and Games
Prediction, Learning, and Games
The maximum resource bin packing problem
Theoretical Computer Science
Markov Decision Processes with Arbitrary Reward Processes
Mathematics of Operations Research
Bin packing and covering problems with rejection
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On sequential strategies for loss functions with memory
IEEE Transactions on Information Theory
Combining initial segments of lists
Theoretical Computer Science
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We consider a sequential version of the classical bin packing problem in which items are received one by one. Before the size of the next item is revealed, the decision maker needs to decide whether the next item is packed in the currently open bin or the bin is closed and a new bin is opened. If the new item does not fit, it is lost. If a bin is closed, the remaining free space in the bin accounts for a loss. The goal of the decision maker is to minimize the loss accumulated over n periods. We present an algorithm that has a cumulative loss not much larger than any strategy in a finite class of reference strategies for any sequence of items. Special attention is payed to reference strategies that use a fixed threshold at each step to decide whether a new bin is opened. Some positive and negative results are presented for this case.