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Bin Packing and Covering Problems with Rejection

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Computing and Combinatorics (COCOON 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3595))

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Abstract

In this paper we consider the following problems: We are given a set of n items {u 1, ⋯, u n }, each item u i is characterized by its size w i ∈ (0,1] and its penalty/profit p i ≥ 0, and a number of unit-capacity bins. An item can be either rejected, in which case we pay/get its penalty/profit, or put into one bin under the constraint that the total size of the items in the bin is not greater/smaller than 1. No item can be spread into more than one bin. The objective is to minimize/maximize the sum of the number of used/covered bins and the penalties/profits of all rejected items. We call the problems bin packing/covering with rejection penalties/profits, and denoted by BPR and BCR respectively. For the online BPR problem, we present an algorithm with an absolute competitive ratio of 2.618 while the lower bound is 2.343, and an algorithm with an asymptotic competitive ratio of arbitrarily close to 7/4 while the lower bound is 1.540. For the offline BPR problem, we present an algorithm with an absolute worst-case ratio of 2 while the lower bound is 3/2, and an algorithm with an asymptotic worst-case ratio of 3/2. For the online BCR problem, we show that no algorithm can have an absolute competitive ratio of greater than 0, and present an algorithm with an asymptotic competitive ratio of 1/2, which is the best possible. For the offline BCR problem, we also present an algorithm with an absolute worst-case ratio of 1/2 which matches the lower bound.

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Author information

Authors and Affiliations

  1. Department of Mathematics, and State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310027, P.R. China

    Yong He

  2. Department of Mathematics, University of Veszprém, Hungary

    György Dósa

Authors
  1. Yong He
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  2. György Dósa
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Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Lusheng Wang

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© 2005 Springer-Verlag Berlin Heidelberg

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He, Y., Dósa, G. (2005). Bin Packing and Covering Problems with Rejection. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_89

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  • DOI: https://doi.org/10.1007/11533719_89

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28061-3

  • Online ISBN: 978-3-540-31806-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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