Lower bounds for batched bin packing

János Balogh, József Békési, György Dósa, Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)613-629
Number of pages17
JournalJournal of Combinatorial Optimization
Issue number3
StatePublished - 2021

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Batched problems
  • Bin packing
  • Competitive analysis
  • Online algorithms

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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