Skip to main content

Price Fluctuations: To Buy or to Rent

  • Conference paper
Book cover Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

Included in the following conference series:

Abstract

We extend the classic online ski rental problem, so that the rental price may change over time. We consider several models which differ in the knowledge given to the algorithm: whereas the price development is unknown, an algorithm may have full, partial or no knowledge about the duration of the game. We construct algorithms whose competitive ratios are up to constant or logarithmic factors optimal.

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

Access this chapter

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. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  2. Damaschke, P.: Nearly optimal strategies for special cases of on-line capital investment. Theoretical Computer Science 302(1–3), 35–44 (2003)

    Article  MATH  Google Scholar 

  3. Dooly, D.R., Goldman, S.A., Scott, S.D.: On-line analysis of the TCP acknowledgment delay problem. Journal of the ACM 48(2), 243–273 (2001); Also appeared as TCP Dynamic Acknowledgment Delay: Theory and Practice. In: Proc. of the 30th STOC, pp. 389–398 (1998)

    Article  MathSciNet  Google Scholar 

  4. El-Yaniv, R.: Competitive solutions for online financial problems. ACM Computing Surveys 30(1), 28–69 (1998)

    Article  MathSciNet  Google Scholar 

  5. El-Yaniv, R., Fiat, A., Karp, R.M., Turpin, G.: Competitive analysis of financial games. In: Proc. of the 33rd IEEE Symp. on Foundations of Computer Science (FOCS), pp. 327–333 (1992)

    Google Scholar 

  6. Fleischer, R.: On the bahncard problem. In: Hsu, W.-L., Kao, M.-Y. (eds.) COCOON 1998. LNCS, vol. 1449, pp. 12–14. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  7. Fujiwara, H., Iwama, K.: Average-case competitive analyses for ski-rental problems. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 476–488. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Garg, N., Gupta, A., Leonardi, S., Sankowski, P.: Stochastic analyses for online combinatorial optimization problems. In: Proc. of the 19th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 942–951 (2008)

    Google Scholar 

  9. Karlin, A.R., Kenyon, C., Randall, D.: Dynamic TCP acknowledgement and other stories about e/(e - 1). Algorithmica 36, 209–224 (2003); Also appeared in: Proc. of the 33rd STOC, pp. 502–509 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Karlin, A.R., Manasse, M.S., McGeoch, L.A., Owicki, S.: Competitive randomized algorithms for non-uniform problems. Algorithmica 11, 542–571 (1994); Also appeared in: Proc. of the 1st SODA, pp. 301–309 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 77–119 (1988); Also appeared in: Proc. of the 27th FOCS, pp. 244–254 (1986)

    Article  MathSciNet  Google Scholar 

  12. Karp, R.M.: On-line algorithms versus off-line algorithms: How much is it worth to know the future? In: Proc. of the IFIP 12th World Computer Congress, pp. 416–429 (1992)

    Google Scholar 

  13. Lotker, Z., Patt-Shamir, B., Rawitz, D.: Rent, lease or buy: Randomized algorithms for multislope ski rental. In: Proc. of the 25th Symp. on Theoretical Aspects of Computer Science (STACS), pp. 503–514 (2008)

    Google Scholar 

  14. Schäfer, G., Sivadasan, N.: Topology matters: Smoothed competitiveness of metrical task systems. Theoretical Computer Science 341(1–3), 216–246 (2005); Also appeared in: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 489–500. Springer, Heidelberg (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yao, A.C.-C.: Probabilistic computation: towards a uniform measure of complexity. In: Proc. of the 18th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 222–227 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bienkowski, M. (2010). Price Fluctuations: To Buy or to Rent. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12450-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics