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The Accomodating Function — A Generalization of the Competitive Ratio

  • Joan Boyar
  • Kim S. Larsen
  • Morten N. Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

A new measure, the accommodating function, for the quality of on-line algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the accommodating ratio, measures the quality of an on-line algorithm as a function of the resources that would be sufficient for some algorithm to fully grant all requests. More precisely, if we have some amount of resources n, the function value at α is the usual ratio (still on some fixed amount of resources n), except that input sequences are restricted to those where all requests could have been fully granted by some algorithm if it had had the amount of resources αn. The accommodating functions for two specific on-line problems are investigated: a variant of bin-packing in which the goal is to maximize the number of objects put in n bins and the seat reservation problem.

Keywords

Input Sequence Competitive Ratio Online Algorithm Request Sequence Usual Ratio 
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.

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References

  1. 1.
    S. Ben-David and A. Borodin. A New Measure for the Study of On-Line Algorithms. Algorithmica, 11:73–91, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Allan Borodin, Sandy Irani, Prabhakar Raghavan, and Baruch Schieber. Competitive Paging with Locality of Reference. Journal of Computer and System Sciences, 50:244–258, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Joan Boyar and Kim S. Larsen. The Seat Reservation Problem. Algorithmica. To appear.Google Scholar
  4. 4.
    Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. The Accommodating Function-a generalization of the competitive ratio. Tech. report 24, Department of Mathematics and Computer Science, Odense University, 1998.Google Scholar
  5. 5.
    Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. Separating the Accommodating Ratio from the Competitive Ratio. Submitted., 1999.Google Scholar
  6. 6.
    M. Chrobak and J. Noga. LRU Is Better than FIFO. In 9th ACM-SIAM SODA, pages 78–81, 1998.Google Scholar
  7. 7.
    E. G. Coffman, Jr., J. Y-T. Leung, and D. W. Ting. Bin packing: Maximizing the number of pieces packed. Acta Informat., 9:263–271, 1978.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    E. G. Coffman, Jr. and Joseph Y-T. Leung. Combinatorial Analysis of an Efficient Algorithm for Processor and Storage Allocation. SIAM J. Comput., 8:202–217, 1979.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    János Csirik and Gerhard Woeginger. On-Line Packing and Covering Problems. In Gerhard J. Woeginger Amos Fiat, editor, Lecture Notes in Computer Science, Vol. 1442: Online Algorithms, chapter 7, pages 147–177. Springer-Verlag, 1998.Google Scholar
  10. 10.
    Amos Fiat and Gerhard J. Woeginger. Competitive Odds and Ends. In Gerhard J. Woeginger Amos Fiat, editor, Lecture Notes in Computer Science, Vol. 1442: Online Algorithms, chapter 17, pages 385–394. Springer-Verlag, 1998.Google Scholar
  11. 11.
    R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.Google Scholar
  12. 12.
    Sandy Irani and Anna R. Karlin. Online Computation. In Dorit S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems, chapter 13, pages 521–564. PWS Publishing Company, 1997.Google Scholar
  13. 13.
    Sandy Irani, Anna R. Karlin, and Steven Philips. Strongly Competitive Algorithms for Paging with Locality of Reference. In 3rd ACM-SIAM SODA, pages 228–236, 1992.Google Scholar
  14. 14.
    Bala Kalyanasundaram and Kirk Pruhs. Speed is as Powerful as Clairvoyance. In 36th IEEE FOCS, pages 214–221, 1995.Google Scholar
  15. 15.
    Anna R. Karlin, Mark S. Manasse, Larry Rudolph, and Daniel D. Sleator. Competitive Snoopy Caching. Algorithmica, 3:79–119, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Elias Koutsoupias and Christos H. Papadimitriou. Beyond Competitive Analysis. In 35th IEEE FOCS, pages 394–400, 1994.Google Scholar
  17. 17.
    Stefano Leonardi and Danny Raz. Approximating Total Flow Time on Parallel Machinces. In 29th ACM STOC, pages 110–119, 1997.Google Scholar
  18. 18.
    Cynthia A. Philips, Cliff Stein, Eric Torng, and Joel Wein. Optimal Time-Critical Scheduling via Resource Augmentation. In 29th ACM STOC, pages 140–149, 1997.Google Scholar
  19. 19.
    Daniel D. Sleator and Robert E. Tarjan. Amortized E.ciency of List Update and Paging Rules. Comm. of the ACM, 28(2):202–208, 1985.MathSciNetCrossRefGoogle Scholar
  20. 20.
    E. Torng. A Unified Analysis of Paging and Caching. Algorithmica, 20:175–200, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    N. Young. The k-Server Dual and Loose Competitiveness for Paging. Algorithmica, 11:525–541, 1994.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Joan Boyar
    • 1
  • Kim S. Larsen
    • 1
  • Morten N. Nielsen
    • 1
  1. 1.University of Southern DenmarkOdenseDenmark

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