A storage-size selection problem
Information Processing Letters - Lecture Notes in Computer Science, no. 173
Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Online variable-sized bin packing
Discrete Applied Mathematics
An on-line algorithm for variable-sized bin packing
Acta Informatica
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
New Bounds for Variable-Sized and Resource Augmented Online Bin Packing
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Tight bounds for online vector bin packing
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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One of the open problems in on-line packing is the gap between the lower bound Ω(1) and the upper bound O(d) for vector packing of d-dimensional items into d-dimensional bins. We address a more general packing problem with variable sized bins. In this problem, the set of allowed bins contains the traditional "all-1" vector, but also a finite number of other d-dimensional vectors. The study of this problem can be seen as a first step towards solving the classical problem. It is not hard to see that a simple greedy algorithm achieves competitive ratio O(d) for every set of bins. We show that for all small ε 0 there exists a set of bins for which the competitive ratio is 1 + ε. On the other hand we show that there exists a set of bins for which every deterministic or randomized algorithm has competitive ratio Ω(d). We also study one special case for d = 2.