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A New Lower Bound for Classic Online Bin Packing

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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.

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References

  1. Babel, L., Chen, B., Kellerer, H., Kotov, V.: Algorithms for on-line bin-packing problems with cardinality constraints. Discrete Appl. Math. 143(1–3), 238–251 (2004)

    Article  MathSciNet  Google Scholar 

  2. Balogh, J., Békési, J., Dósa, Gy., Epstein, L., Levin, A.: A new and improved algorithm for online bin packing. In: Proc. of the 26th European Symposium on Algorithms (ESA2018), pp. 5:1–5:14 (2018)

  3. Balogh, J., Békési, J., Dósa, Gy., Epstein, L., Levin, A.: A new lower bound for classic online bin packing. In: Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA2019), pp. 18–28 (2019)

  4. Online bin packing with cardinality constraints resolved: J. Comput. Syst. Sci. 112, 34–49 (2020)

    Article  Google Scholar 

  5. Balogh, J., Békési, J., Dósa, Gy., Galambos, G., Tan, Z.: Lower bound for 3-batched bin packing. Discrete Optim. 21, 14–24 (2016)

    Article  MathSciNet  Google Scholar 

  6. Balogh, J., Békési, J., Galambos, G.: New lower bounds for certain classes of bin packing algorithms. Theor. Comput. Sci. 440, 1–13 (2012)

    Article  MathSciNet  Google Scholar 

  7. Békési, J., Dósa, Gy.: Bounds for online bin packing with cardinality constraints. Inf. Comput. 249, 190–204 (2016)

    Article  MathSciNet  Google Scholar 

  8. Blitz, D.: Lower bounds on the asymptotic worst-case ratios of on-line bin packing algorithms. Technical Report 114682, University of Rotterdam, M.Sc. thesis (1996)

  9. Brown, D.J.: A lower bound for on-line one-dimensional bin packing algorithms. Coordinated Science Laboratory Report no. R-864 (UILU-ENG 78-2257) (1979)

  10. Csirik, J., Woeginger, G.J.: On-line packing and covering problems. In: Fiat, A., Woeginger, G. J. (eds.) Online Algorithms: The State of the Art, pp. 147–177 (1998)

  11. Epstein, L.: A survey on makespan minimization in semi-online environments. J. Scheduling 21(3), 269–284 (2018)

    Article  MathSciNet  Google Scholar 

  12. Fujiwara, H., Kobayashi, K.M.: Improved lower bounds for the online bin packing problem with cardinality constraints. J. Comb. Optim. 29(1), 67–87 (2015)

    Article  MathSciNet  Google Scholar 

  13. Heydrich, S., van Stee, R.: Beating the harmonic lower bound for online bin packing. In: Proc. of 43rd International Colloquium on Automata, Languages, and Programming (ICALP2016), pp. 41:1–41:14, (2016)

  14. Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis, MIT, Cambridge, MA (1973)

  15. Johnson, D.S.: Fast algorithms for bin packing. J. Comput. Syst. Sci. 8, 272–314 (1974)

    Article  MathSciNet  Google Scholar 

  16. Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3, 256–278 (1974)

    Article  MathSciNet  Google Scholar 

  17. Lee, C.C., Lee, D.T.: A simple online bin packing algorithm. J. ACM 32(3), 562–572 (1985)

    Article  Google Scholar 

  18. Liang, F.M.: A lower bound for on-line bin packing. Inf. Process. Lett. 10(2), 76–79 (1980)

    Article  MathSciNet  Google Scholar 

  19. Ramanan, P., Brown, D.J., Lee, C.C., Lee, D.T.: Online bin packing in linear time. J. Algorithms 10, 305–326 (1989)

    Article  MathSciNet  Google Scholar 

  20. Seiden, S.S.: On the online bin packing problem. J. ACM 49(5), 640–671 (2002)

    Article  MathSciNet  Google Scholar 

  21. Ullman, J.D.: The performance of a memory allocation algorithm. Technical Report 100, Princeton University, Princeton, NJ (1971)

  22. van Vliet, A.: An improved lower bound for online bin packing algorithms. Inf. Process. Lett. 43(5), 277–284 (1992)

    Article  Google Scholar 

  23. Yao, A.C.C.: New algorithms for bin packing. J. ACM 27, 207–227 (1980)

    Article  MathSciNet  Google Scholar 

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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, Veszprem, 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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Corresponding author

Correspondence to Leah Epstein.

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J. Balogh was supported by the projects “Extending the activities of the HU-MATHS-IN Hungarian Industrial and Innovation Mathematical Service Network” EFOP-3.6.2-16-2017-00015. J. Békési was supported by the EU-funded Hungarian Grant EFOP-3.6.2-16-2017-00015 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. 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). A. Levin was also partially supported by Grant number 308/18 of ISF - Israeli Science Foundation.

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Balogh, J., Békési, J., Dósa, G. et al. A New Lower Bound for Classic Online Bin Packing. Algorithmica 83, 2047–2062 (2021). https://doi.org/10.1007/s00453-021-00818-7

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  • DOI: https://doi.org/10.1007/s00453-021-00818-7

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