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Lower bounds for batched bin packing

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Abstract

We consider batched bin packing. Items are presented in a constant number of batches, and each batch should be packed before the next batch is presented. The cases of two, three, and four batches are studied. We prove improved lower bounds for the standard and parametric variants in some of the cases, and shorten the proofs for all other cases. To achieve this, we apply a new technique in our analysis, which differs from the ones previously used for proving such results.

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Funding

J. Balogh was supported by the project “Extending the activities of the HU-MATHS-IN Hungarian Industrial and Innovation Mathematical Service Network” EFOP-3.6.2-16-2017-00015, and by the project “Integrated program for training new generation of scientists in the fields of computer science”, EFOP-3.6.3-VEKOP-16-2017-00002. The project has been supported by the European Union and co-funded by the European Social Fund. J. Békési was supported by the EU-funded Hungarian grant “Integrated program for training new generation of scientists in the fields of computer science” EFOP-3.6.3-VEKOP-16-2017-0002, and by National Research, Development and Innovation Office NKFIH under the Grant SNN 129178. Gy. Dósa was supported by National Research, Development and Innovation Office–NKFIH under the Grant SNN 129364 and by Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015. A. Levin was partially supported by Grant Number 308/18 of ISF - Israeli Science Foundation.

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Authors and Affiliations

  1. Institute of Informatics, University of Szeged, Szeged, Hungary

    János Balogh & József Békési

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    György Dósa

  3. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

  4. Faculty of Industrial Engineering and Management, The Technion, Haifa, Israel

    Asaf Levin

Authors
  1. János Balogh
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  2. József Békési
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  3. György Dósa
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  4. Leah Epstein
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  5. Asaf Levin
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Correspondence to Leah Epstein.

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Balogh, J., Békési, J., Dósa, G. et al. Lower bounds for batched bin packing. J Comb Optim 43, 613–629 (2022). https://doi.org/10.1007/s10878-021-00797-z

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  • DOI: https://doi.org/10.1007/s10878-021-00797-z

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