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Workshop on Algorithms and Data Structures

WADS 1999: Algorithms and Data Structures pp 74–79Cite as

The Accomodating Function — A Generalization of the Competitive Ratio

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Part of the book series: Lecture Notes in Computer Science ((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.

Supported in part by the esprit Long Term Research Programme of the EU under project number 20244 (alcom-it) and in part by SNF, Denmark.

Dept. of Mathematics and Computer Science, University of Southern Denmark, Main campus: Odense University, Campusvej 55, DK-5230 Odense M, Denmark.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  3. Joan Boyar and Kim S. Larsen. The Seat Reservation Problem. Algorithmica. To appear.

    Google Scholar 

  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. Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. Separating the Accommodating Ratio from the Competitive Ratio. Submitted., 1999.

    Google Scholar 

  6. M. Chrobak and J. Noga. LRU Is Better than FIFO. In 9th ACM-SIAM SODA, pages 78–81, 1998.

    Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  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. 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. Bala Kalyanasundaram and Kirk Pruhs. Speed is as Powerful as Clairvoyance. In 36th IEEE FOCS, pages 214–221, 1995.

    Google Scholar 

  15. Anna R. Karlin, Mark S. Manasse, Larry Rudolph, and Daniel D. Sleator. Competitive Snoopy Caching. Algorithmica, 3:79–119, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  16. Elias Koutsoupias and Christos H. Papadimitriou. Beyond Competitive Analysis. In 35th IEEE FOCS, pages 394–400, 1994.

    Google Scholar 

  17. Stefano Leonardi and Danny Raz. Approximating Total Flow Time on Parallel Machinces. In 29th ACM STOC, pages 110–119, 1997.

    Google Scholar 

  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. 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.

    Article  MathSciNet  Google Scholar 

  20. E. Torng. A Unified Analysis of Paging and Caching. Algorithmica, 20:175–200, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  21. N. Young. The k-Server Dual and Loose Competitiveness for Paging. Algorithmica, 11:525–541, 1994.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Southern Denmark, Odense, Denmark

    Joan Boyar, Kim S. Larsen & Morten N. Nielsen

Authors
  1. Joan Boyar
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  2. Kim S. Larsen
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  3. Morten N. Nielsen
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Canada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. School of Computer Science, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

    Arvind Gupta

  3. Center for Geometric Computing Providence, Brown University, RI, 02912-1910, USA

    Roberto Tamassia

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© 1999 Springer-Verlag Berlin Heidelberg

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Boyar, J., Larsen, K.S., Nielsen, M.N. (1999). The Accomodating Function — A Generalization of the Competitive Ratio. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_9

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  • DOI: https://doi.org/10.1007/3-540-48447-7_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66279-2

  • Online ISBN: 978-3-540-48447-9

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