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The Relative Worst Order Ratio for On-Line Algorithms

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Algorithms and Complexity (CIAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2653))

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Abstract

We consider a new measure for the quality of on-line algorithms, the relative worst order ratio, using ideas from the Max/Max ratio [2] and from the random order ratio [8]. The new ratio is used to compare on-line algorithms directly by taking the ratio of their performances on their respective worst orderings of a worst-case sequence. Two variants of the bin packing problem are considered: the Classical Bin Packing Problem and the Dual Bin Packing Problem. Standard algorithms are compared using this new measure. Many of the results obtained here are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier results are also shown to be possible with the relative worst order ratio.

Supported in part by the Danish Natural Science Research Council (SNF) and in part by the Future and Emerging Technologies program of the EU under contract number IST-1999-14186 (alcom-ft).

Part of this work was done while visiting the Computer Science Department, University of Toronto.

Part of this work was done while working at the Department of Mathematics and Computer Science, University of Southern Denmark.

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References

  1. Y. Azar, J. Boyar, L. Epstein, L. M. Favrholdt, K. S. Larsen, and M. N. Nielsen. Fair versus Unrestricted Bin Packing. Algorithmica, 34(2):181–196, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Ben-David and A. Borodin. A New Measure for the Study of On-Line Algorithms. Algorithmica, 11(1):73–91, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Boyar, L. M. Favrholdt, and K. S. Larsen. Work in progress.

    Google Scholar 

  4. J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function—a Generalization of the Competitive Ratio. SIAM Journal of Computation, 31(1):233–258, 2001. Also in WADS 99, pages 74–79.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.

    Google Scholar 

  6. D. S. Johnson. Fast Algorithms for Bin Packing. Journal of Computer and System Sciences, 8:272–314, 1974.

    MATH  MathSciNet  Google Scholar 

  7. A. R. Karlin, M. S. Manasse, L. Rudolph, and D. D. Sleator. Competitive Snoopy Caching. Algorithmica, 3(1):79–119, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. Kenyon. Best-Fit Bin-Packing with Random Order. In 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 359–364, 1996.

    Google Scholar 

  9. E. Koutsoupias and C. H. Papadimitriou. Beyond Competitive Analysis. In 35th Annual Symposium on Foundations of Computer Science, pages 394–400, 1994.

    Google Scholar 

  10. D. D. Sleator and R. E. Tarjan. Amortized Efficiency of List Update and Paging Rules. Communications of the ACM, 28(2):202–208, 1985.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Joan Boyar

  2. Department of Computer Science, University of Copenhagen, Denmark

    Lene M. Favrholdt

Authors
  1. Joan Boyar
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  2. Lene M. Favrholdt
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Editor information

Editors and Affiliations

  1. Dipartimento di Infornatica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Rome, Italy

    Rossella Petreschi  & Riccardo Silvestri  & 

  2. Dipartimento di Infornatica ed Applicazioni “R.M. Capocelli”, Università di Salerno, Via S. Allende 2, 84081, Baronissi, SA, Italy

    Giuseppe Persiano

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© 2003 Springer-Verlag Berlin Heidelberg

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Boyar, J., Favrholdt, L.M. (2003). The Relative Worst Order Ratio for On-Line Algorithms. In: Petreschi, R., Persiano, G., Silvestri, R. (eds) Algorithms and Complexity. CIAC 2003. Lecture Notes in Computer Science, vol 2653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44849-7_13

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  • DOI: https://doi.org/10.1007/3-540-44849-7_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40176-6

  • Online ISBN: 978-3-540-44849-5

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