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Harmonic Algorithm for Bin Packing

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Encyclopedia of Algorithms

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Years and Authors of Summarized Original Work

1985; Lee, Lee

Problem Definition

One of the goals of the design of the harmonic algorithm (or class of algorithms) was to provide an online algorithm for the classic bin packing problem that performs well with respect to the asymptotic competitive ratio, which is the standard measure for online algorithms for bin packing type problems. The competitive ratio for a given input is the ratio between the costs of the algorithm and of an optimal off-line solution. The asymptotic competitive ratio is the worst-case competitive ratio of inputs for which the optimal cost is sufficiently large. In the online(standard) bin packing problem, items of rational sizes in (0, 1] are presented one by one. The algorithm must pack each item into a bin before the following item is presented. The total size of items packed into a bin cannot exceed 1, and the goal is to use the minimum number of bins, where a bin is used if at least one item was packed into...

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Recommended Reading

  1. Balogh J, Békési J, Galambos G (2012) New lower bounds for certain classes of bin packing algorithms. Theor Comput Sci 440–441:1–13

    Article  Google Scholar 

  2. Chrobak M, Sgall J, Woeginger GJ (2011) Two-bounded-space bin packing revisited. In: Proceedings of the 19th annual European symposium on algorithms (ESA2011), Saarbrücken, Germany, pp 263–274

    Google Scholar 

  3. Csirik J, Johnson DS (2001) Bounded space on-line bin packing: best is better than first. Algorithmica 31:115–138

    Article  MATH  MathSciNet  Google Scholar 

  4. Csirik J, Woeginger GJ (2002) Resource augmentation for online bounded space bin packing. J Algorithms 44(2):308–320

    Article  MATH  MathSciNet  Google Scholar 

  5. Epstein L (2006) Online bin packing with cardinality constraints. SIAM J Discret Math 20(4):1015–1030

    Article  MATH  Google Scholar 

  6. Epstein L (2010) Bin packing with rejection revisited. Algorithmica 56(4):505–528

    Article  MATH  MathSciNet  Google Scholar 

  7. Lee CC, Lee DT (1985) A simple online bin packing algorithm. J ACM 32(3):562–572

    Article  MATH  Google Scholar 

  8. Liang FM (1980) A lower bound for on-line bin packing. Inf Process Lett 10(2):76–79

    Article  MATH  Google Scholar 

  9. Ramanan P, Brown DJ, Lee CC, Lee DT (1989) Online bin packing in linear time. J Algorithms 10:305–326

    Article  MATH  MathSciNet  Google Scholar 

  10. Seiden SS (2001) An optimal online algorithm for bounded space variable-sized bin packing. SIAM J Discret Math 14(4):458–470

    Article  MATH  MathSciNet  Google Scholar 

  11. Seiden SS (2002) On the online bin packing problem. J ACM 49(5):640–671

    Article  MathSciNet  Google Scholar 

  12. Ullman JD (1971) The performance of a memory allocation algorithm. Technical report 100, Princeton University, Princeton

    Google Scholar 

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

    Article  MATH  Google Scholar 

  14. van Vliet A (1996) On the asymptotic worst case behavior of Harmonic Fit. J Algorithms 20(1):113–136

    Article  MATH  MathSciNet  Google Scholar 

  15. Woeginger GJ (1993) Improved space for bounded-space online bin packing. SIAM J Discret Math 6(4):575–581

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

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

    Leah Epstein

Authors
  1. Leah Epstein
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Correspondence to Leah Epstein .

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Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Epstein, L. (2014). Harmonic Algorithm for Bin Packing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_490-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_490-1

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  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

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