Skip to main content
SpringerLink
Log in

The Relative Worst Order Ratio Applied to Seat Reservation

  • Conference paper
Algorithm Theory - SWAT 2004 (SWAT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3111))

Included in the following conference series:

Abstract

The relative worst order ratio is a new measure for the quality of on-line algorithms, which has been giving new separations and even new algorithms for a variety of problems. Here, we apply the relative worst order ratio to the seat reservation problem, the problem of assigning seats to passengers in a train. For the unit price problem, where all tickets have the same cost, we show that First-Fit and Best-Fit are better than Worst-Fit, even though they have not been separated using the competitive ratio. The same relative worst order ratio result holds for the proportional price problem, where the ticket price is proportional to the distance travelled. In contrast, no deterministic algorithm has a competitive ratio, or even a competitive ratio on accommodating sequences, which is bounded below by a constant. It is also shown that the worst order ratio for seat reservation algorithms is very closely related to the competitive ratio on accommodating sequences.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Awerbuch, B., Azar, Y., Fiat, A., Leonardi, S., Rosén, A.: On-line competitive algorithms for call admission in optical networks. In: Díaz, J. (ed.) ESA 1996. LNCS, vol. 1136, pp. 431–444. Springer, Heidelberg (1996)

    Google Scholar 

  2. Awerbuch, B., Bartal, Y., Fiat, A., Rosén, A.: Competitive non-preemptive call control. In: 5th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 312–320 (1994)

    Google Scholar 

  3. Bach, E., Boyar, J., Epstein, L., Favrholdt, L.M., Jiang, T., Larsen, K.S., Lin, G.-H., van Stee, R.: Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem. J. Sched. 6, 131–147 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bar-Noy, R., Canetti, S., Kutten, Y., Mansour, Y., Schieber, B.: Bandwidth allocation with preemption. In: 27th Annual ACM Symposium on the Theory of Computing, pp. 616–625 (1995)

    Google Scholar 

  5. Ben-David, S., Borodin, A.: A new measure for the study of on-line algorithms. Algorithmica 11(1), 73–91 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653, pp. 58–69. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Boyar, J., Favrholdt, L.M.: The relativeworst order ratio for on-line bin packing algorithms. Tech. report PP–2003–13, Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University (2003)

    Google Scholar 

  8. Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst order ratio applied to paging. Tech. report ALCOMFT-TR-03-32, Future and Emerging Technologies program under the EU, contract number IST-1999-14186 (2003)

    Google Scholar 

  9. Boyar, J., Favrholdt, L.M., Larsen, K.S., Nielsen, M.N.: Extending the accommodating function. Acta Informatica 40, 3–35 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Boyar, J., Larsen, K.S.: The seat reservation problem. Algorithmica 25, 403–417 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Boyar, J., Larsen, K.S., Nielsen, M.N.: The accommodating function:A generalization of the competitive ratio. SIAM J. Comput. 31(1), 233–258 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Epstein, L., Favrholdt, L.M., Kohrt, J.S.: The relativeworst order ratio applied to scheduling problems. Work in progress (2004)

    Google Scholar 

  13. Garay, J.A., Gopal, I.S., Kutten, S., Mansour, Y., Yung, M.: Efficient on-line call control algorithms. J. Algorithms 23, 180–194 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  14. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45, 1563–1581 (1966)

    Google Scholar 

  15. Jensen, T.R., Toft, B.: Graph Coloring Problems. JohnWiley & Sons, West Sussex (1995)

    MATH  Google Scholar 

  16. Johnson, D.S.: Fast algorithms for bin packing. Journal of Computer and System Sciences 8, 272–314 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  17. Karlin, R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kenyon, C.: Best-Fit bin-packing with random order. In: 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 359–364 (1996)

    Google Scholar 

  19. Kierstead, H.A., Trotter, W.T.: An extremal problem in recursive combinatorics. Congr. Numer. 33, 143–153 (1981)

    MathSciNet  Google Scholar 

  20. Kohrt, J.S.: The relative worst order ratio applied to bin coloring. Work in progress (2004)

    Google Scholar 

  21. Lipton, R.J.,Tomkins, A .: Online interval scheduling. In: 5th AnnualACM-SIAMSymposium on Discrete Algorithms, pp. 302–311 (1994)

    Google Scholar 

  22. Raghavan, P., Upfal, E.: Efficient routing in all-optical networks. In: 26th Annual ACM Symposium on the Theory of Computing, pp. 134–143 (1994)

    Google Scholar 

  23. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Comm. of the ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  24. Yannakakis, M., Gavril, F.: The maximum k-colorable subgraph problem for chordal graphs. Information Processing Letters 24(2), 133–137 (1987)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Joan Boyar & Paul Medvedev

Authors
  1. Joan Boyar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Medvedev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Augsburg, 86135, Augsburg, Germany

    Torben Hagerup

  2. Department of Computing, University of Copenhagen, Denmark

    Jyrki Katajainen

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Boyar, J., Medvedev, P. (2004). The Relative Worst Order Ratio Applied to Seat Reservation. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27810-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22339-9

  • Online ISBN: 978-3-540-27810-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation