A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On-line bin packing in linear time
Journal of Algorithms
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
New Algorithms for Bin Packing
Journal of the ACM (JACM)
Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
On the online bin packing problem
Journal of the ACM (JACM)
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Preemptive Scheduling with Rejection
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Fast algorithms for bin packing
Journal of Computer and System Sciences
Linear time-approximation algorithms for bin packing
Operations Research Letters
A fast asymptotic approximation scheme for bin packing with rejection
Theoretical Computer Science
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A fast asymptotic approximation scheme for bin packing with rejection
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Online coupon consumption problem
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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We consider the following generalization of bin packing. Each item is associated with a size bounded by 1, as well as a rejection cost, that an algorithm must pay if it chooses not to pack this item. The cost of an algorithm is the sum of all rejection costs of rejected items plus the number of unit sized bins used for packing all other items. We first study the offline version of the problem and design an APTAS for it. This is a non-trivial generalization of the APTAS given by Fernandez de la Vega and Lueker for the standard bin packing problem. We further give an approximation algorithm of absolute approximation ratio $\frac 32$, this value is best possible unless P=NP. Finally, we study an online version of the problem. For the bounded space variant, where only a constant number of bins can be open simultaneously, we design a sequence an algorithms whose competitive ratios tend to the best possible asymptotic competitive ratio. We show that our algorithms have the same asymptotic competitive ratios as these known for the standard problem, whose ratios tend to Π∞≈1.691. Furthermore, we introduce an unbounded space algorithm which achieves a much smaller asymptotic competitive ratio. All our results improve upon previous results of Dósa and He.