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Online Bin Packing with Advice

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Abstract

We consider the online bin packing problem under the advice complexity model where the “online constraint” is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with \(\log n + o(\log n)\) bits of advice, achieves a competitive ratio of \(3/2\) for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives \(2n + o(n)\) bits of advice and achieves a competitive ratio of \(4/3 + \varepsilon \). Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Joan Boyar & Kim S. Larsen

  2. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Shahin Kamali & Alejandro López-Ortiz

Authors
  1. Joan Boyar
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  2. Shahin Kamali
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  3. Kim S. Larsen
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  4. Alejandro López-Ortiz
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Corresponding author

Correspondence to Kim S. Larsen.

Additional information

The work of the first and third author was partially supported by the Danish Council for Independent Research, Natural Sciences, and the Villum Foundation, and most of the work was carried out while these authors were visiting the University of Waterloo.

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Boyar, J., Kamali, S., Larsen, K.S. et al. Online Bin Packing with Advice. Algorithmica 74, 507–527 (2016). https://doi.org/10.1007/s00453-014-9955-8

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