Bin packing with rejection revisited

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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 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 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 Dosa and He.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers
PublisherSpringer Verlag
Pages146-159
Number of pages14
ISBN (Print)9783540695134
DOIs
StatePublished - 2007
Event4th Workshop on Approximation and Online Algorithms, WAOA 2006 - Zurich, Switzerland
Duration: 14 Sep 200615 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4368 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th Workshop on Approximation and Online Algorithms, WAOA 2006
Country/TerritorySwitzerland
CityZurich
Period14/09/0615/09/06

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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