A two-phase algorithm for bin stretching with stretching factor 1.5

A Publisher's Erratum to this article was published on 24 February 2017

This article has been updated

Abstract

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin.We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We build on previous algorithms and use a two-phase approach. However, our analysis is technically more complicated and uses amortization over the bins with the help of two weight functions.

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  • 24 February 2017

    An erratum to this article has been published.

References

  1. Albers S, Hellwig M (2012) Semi-online scheduling revisited. Theor Comput Sci 443:1–9

    MathSciNet  Article  MATH  Google Scholar 

  2. Aspnes J, Azar Y, Fiat A, Plotkin S, Waarts O (1997) On-line load balancing with applications to machine scheduling and virtual circuit routing. J ACM 44:486–504

    MathSciNet  Article  MATH  Google Scholar 

  3. Azar Y, Regev O.(1998)On-line bin-stretching. In: Proceedings of randomization and approximation techniques in computer science (RANDOM). Springer, pp 71–81

  4. Azar Y, Regev O (2001) On-line bin-stretching. Theor Comput Sci 268(1):17–41

    MathSciNet  Article  MATH  Google Scholar 

  5. Berman P, Charikar M, Karpinski M (2000) On-line load balancing for related machines. J Algorithms 35:108–121

    MathSciNet  Article  MATH  Google Scholar 

  6. Böhm M, Sgall J, van Stee R, Veselý P (2015) Better algorithms for online bin stretching. In: Proceedings of the 12th workshop on approximation and online algorithms (WAOA 2014), Lecture Notes in Computer Science 8952. Springer, pp 23–34

  7. Böhm M, Sgall J, van Stee R, Veselý P (2016) Online bin stretching with three bins. arXiv preprint arXiv:1404.5569v3

  8. Coffman E Jr, Csirik J, Galambos G, Martello S, Vigo D (2013) Bin packing approximation algorithms: survey and classification. In: Pardalos PM, Du DZ, Graham RL (eds) Handbook of combinatorial optimization. Springer, New York, pp 455–531

    Chapter  Google Scholar 

  9. Ebenlendr T, Jawor W, Sgall J (2009) Preemptive online scheduling: optimal algorithms for all speeds. Algorithmica 53:504–522

    MathSciNet  Article  MATH  Google Scholar 

  10. Gabay M, Brauner N, Kotov V (2013) Computing lower bounds for semi-online optimization problems: application to the bin stretching problem. HAL preprint hal-00921663, version 2

  11. Gabay M, Brauner N, Kotov V (2015) Improved lower bounds for the online bin stretching problem. HAL preprint hal-00921663, version 3

  12. Gabay M, Kotov V, Brauner N (2013) Semi-online bin stretching with bunch techniques. HAL preprint hal-00869858

  13. Graham RL (1969) Bounds on multiprocessing timing anomalies. SIAM J Appl Math 17:263–269

    MathSciNet  MATH  Google Scholar 

  14. Johnson D (1973) Near-optimal bin packing algorithms. Massachusetts Institute of Technology Technical Report MAC TR-109, Project MAC, Cambridge, Massachusetts

  15. Kellerer H, Kotov V (2013) An efficient algorithm for bin stretching. Oper Res Lett 41(4):343–346

    MathSciNet  Article  MATH  Google Scholar 

  16. Kellerer H, Kotov V, Speranza MG, Tuza Z (1997) Semi on-line algorithms for the partition problem. Oper Res Lett 21:235–242

    MathSciNet  Article  MATH  Google Scholar 

  17. Pruhs K, Sgall J, Torng E (2004) Online scheduling. In: Leung JY-T (ed) Handbook of scheduling: algorithms, models, and performance analysis, chapter 15. CRC Press, Boca Raton, pp 15-1–15-41

    Google Scholar 

  18. Ullman J (1971) The performance of a memory allocation algorithm. Technical Report 100

Download references

Acknowledgements

The authors thank Emese Bittner for useful discussions during her visit to Charles University. We also thank to referees for many useful comments.

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Correspondence to Martin Böhm.

Additional information

The original version of this article was revised: The original title of this article is “A two-phase algorithm for bin stretching with 4 stretching factor 1.5”. The title was inadvertently changed to “A two-phase algorithm 5 for bin stretching with stretching factor 1:5’.

Supported by the project 14-10003S of GA ČR and by the GAUK project 548214.

An erratum to this article is available at https://doi.org/10.1007/s10878-017-0116-2.

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Böhm, M., Sgall, J., van Stee, R. et al. A two-phase algorithm for bin stretching with stretching factor 1.5. J Comb Optim 34, 810–828 (2017). https://doi.org/10.1007/s10878-017-0114-4

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Keywords

  • Online algorithms
  • Bin packing
  • Scheduling