Extending the Accommodating Function

  • Joan Boyar
  • Lene M. Favrholdt
  • Kim S. Larsen
  • Morten N. Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2387)


The applicability of the accommodating function, a relatively new measure for the quality of on-line algorithms, is extended. If a limited amount n of some resource is available, the accommodating function \( \mathcal{A} \) (α) is the competitive ratio when input sequences are restricted to those for which the amount α n of resources suffices for an optimal off-line algorithm. The accommodating function was originally used only for α ≥ 1. We focus on α < 1, observe that the function now appears interesting for a greater variety of problems, and use it to make new distinctions between known algorithms and to find new ones.


Input Sequence Competitive Ratio Interval Graph Performance Guarantee Request Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Azar, J. Boyar, L. Epstein, L. M. Favrholdt, K. S. Larsen, and M. N. Nielsen. Fair versus Unrestricted Bin Packing. Algorithmica. To appear. Preliminary version in SWAT 2000.Google Scholar
  2. 2.
    Y. Azar, L. Epstein, and R. van Stee. Resource Augmentation in Load Balancing. In SWAT 2000, volume 1851 of LNCS, pages 189–199, 2000.CrossRefGoogle Scholar
  3. 3.
    E. Bach, J. Boyar, L. Epstein, L. M. Favrholdt, T. Jiang, K. S. Larsen, G.-H. Lin, and R. van Stee. Tight Bounds on the Competitive Ratio on Accommodating Sequences for the Seat Reservation Problem. Journal of Scheduling. To appear. Preliminary version in COCOON 2000.Google Scholar
  4. 4.
    J. Boyar, L. M. Favrholdt, K. S. Larsen, and M. N. Nielsen. Extending the Accommodating Function. Technical report PP-2002-02, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, 2002.Google Scholar
  5. 5.
    J. Boyar and K. S. Larsen. The Seat Reservation Problem. Algorithmica, 25:403–417, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. The Accommodating Function: a generalization of the competitive ratio. SIAM Journal on Computing, 31(1):233–258, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    M. Brehop, E. Torng, and P. Uthaisombut. Applying Extra Resource Analysis to Load Balancing. Journal of Scheduling, 3:273–288, 2000.CrossRefMathSciNetGoogle Scholar
  8. 8.
    M. Chrobak and M. Slusarek. On Some Packing Problems Related to Dynamic Storage Allocation. RAIRO Informatique Théoretique et Applications, 22:487–499, 1988.MathSciNetzbMATHGoogle Scholar
  9. 9.
    E. Koutsoupias. Weak Adversaries for the k-Server Problem. In FOCS, pages 444–449, 1999.Google Scholar
  10. 10.
    R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.Google Scholar
  11. 11.
    T. R. Jensen and B. Toft. Graph Coloring Problems. John Wiley & Sons, 1995.Google Scholar
  12. 12.
    B. Kalyanasundaram and K. Pruhs. Speed is as powerful as clairvoyance. In FOCS, pages 214–221, 1995.Google Scholar
  13. 13.
    H. A. Kierstead and J. Qin. Coloring Interval Graphs with First-Fit. Discrete Mathematics, 144:47–57, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    H. A. Kierstead and W. T. Trotter. An Extremal Problem in Recursive Combinatorics. Congressus Numerantium, 33:143–153, 1981.MathSciNetGoogle Scholar
  15. 15.
    M. S. Manasse, L. A. McGeoch, and D. D. Sleator. Competitive Algorithms for Server Problems. Journal of Algorithms, 11(2):208–230, June 1990.Google Scholar
  16. 16.
    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
  17. 17.
    N. Young. On-Line Caching as Cache Size Varies. In SODA, pages 241–250, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joan Boyar
    • 1
  • Lene M. Favrholdt
    • 1
  • Kim S. Larsen
    • 1
  • Morten N. Nielsen
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense

Personalised recommendations