The Relative Worst Order Ratio for On-Line Algorithms

  • Joan Boyar
  • Lene M. Favrholdt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2653)


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.


Competitive Ratio Large Item Small Item Request Sequence Order Ratio 
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  1. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    S. Ben-David and A. Borodin. A New Measure for the Study of On-Line Algorithms. Algorithmica, 11(1):73–91, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    J. Boyar, L. M. Favrholdt, and K. S. Larsen. Work in progress.Google Scholar
  4. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.Google Scholar
  6. 6.
    D. S. Johnson. Fast Algorithms for Bin Packing. Journal of Computer and System Sciences, 8:272–314, 1974.zbMATHMathSciNetGoogle Scholar
  7. 7.
    A. R. Karlin, M. S. Manasse, L. Rudolph, and D. D. Sleator. Competitive Snoopy Caching. Algorithmica, 3(1):79–119, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 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. 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. 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.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joan Boyar
    • 1
  • Lene M. Favrholdt
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  2. 2.Department of Computer ScienceUniversity of CopenhagenDenmark

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