A fast asymptotic approximation scheme for bin packing with rejection

Authors:
Wolfgang Bein;José R. Correa;Xin Han
Affiliations:
Center for the Advanced Study of Algorithms, School of Computer Science, University of Nevada, Las Vegas, NV;School of Business, Univesidad Adolfo Ibáñez, Santiago, Chile;School of Informatics, Kyoto University, Kyoto, Japan
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

The bin packing with rejection problem is the following: Given a list of items with associated sizes and rejection costs, find a packing into unit bins of a subset of the list, such that the number of bins used plus the sum of rejection costs of unpacked items is minimized. In this paper, we first show that bin packing with rejection can be reduced to n multiple knapsack problems. Then, based on techniques for the multiple knapsack problem we give a fast asymptotic polynomial time approximation scheme with time complexity O(nO(ε -2)). This improves a recent approximation scheme given by Epstein, which has time complexity O(nO(ε-4) ε-1))). Finally, we show that our algorithm can be extended to variable-sized bin packing with rejection and give an asymptotic polynomial time approximation scheme for it.