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A New Lower Bound for Classic Online Bin Packing

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Approximation and Online Algorithms (WAOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11926))

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Abstract

We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278.

We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of lower bounds for the classic online bin packing problem. We apply a new method for weight based analysis, which is usually applied only in proofs of upper bounds. The values of previous lower bounds were approximately 1.5401 and 1.5403.

J. Balogh was supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002). J. Békési was supported by the EU-funded Hungarian grant EFOP-3.6.2-16-2017-00015 and by the National Research, Development and Innovation Office of Hungary (NKFIH), grant no. 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. L. Epstein and A. Levin were partially supported by a grant from GIF - the German-Israeli Foundation for Scientific Research and Development (grant number I-1366-407.6/2016).

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Author information

Authors and Affiliations

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

    János Balogh

  2. Department of Applied Informatics, Gyula Juhász Faculty of Education, University of Szeged, Szeged, Hungary

    József Békési

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

    György Dósa

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

    Leah Epstein

  5. 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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Corresponding author

Correspondence to Leah Epstein .

Editor information

Editors and Affiliations

  1. LIP6, Sorbonne University, Paris, France

    Evripidis Bampis

  2. Department for Mathematics and Computer Science, University of Bremen, Bremen, Germany

    Nicole Megow

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Balogh, J., Békési, J., Dósa, G., Epstein, L., Levin, A. (2020). A New Lower Bound for Classic Online Bin Packing. In: Bampis, E., Megow, N. (eds) Approximation and Online Algorithms. WAOA 2019. Lecture Notes in Computer Science(), vol 11926. Springer, Cham. https://doi.org/10.1007/978-3-030-39479-0_2

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