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Bin packing with rejection revisited
| Content Provider | CiteSeerX |
|---|---|
| Author | Epstein, Leah |
| Abstract | Abstract. 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 rst study the o ine 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 3 2, 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. 1 |
| File Format | |
| Journal | Algorithmica |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Rejection Cost Asymptotic Competitive Ratio Constant Number Fernandez De La Vega Standard Problem Absolute Approximation Bin Packing Competitive Ratio Bounded Space Variant Approximation Algorithm Ine Version Unit Sized Bin Unbounded Space Algorithm Possible Asymptotic Competitive Ratio Online Version Non-trivial Generalization Rejected Item Standard Bin Packing Problem Previous Result Following Generalization |
| Content Type | Text |
| Resource Type | Article |
