Economical Caching with Stochastic Prices

  • Matthias Englert
  • Berthold Vöcking
  • Melanie Winkler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5792)

Abstract

In the economical caching problem, an online algorithm is given a sequence of prices for a certain commodity. The algorithm has to manage a buffer of fixed capacity over time. We assume that time proceeds in discrete steps. In step i, the commodity is available at price ci ∈ [α,β], where β > α ≥ 0 and ci ∈ ℕ. One unit of the commodity is consumed per step. The algorithm can buy this unit at the current price ci, can take a previously bought unit from the storage, or can buy more than one unit at price ci and put the remaining units into the storage.

In this paper, we study the economical caching problem in a probabilistic analysis, that is, we assume that the prices are generated by a random walk with reflecting boundaries α and β. We are able to identify the optimal online algorithm in this probabilistic model and analyze its expected cost and its expected savings, i.e., the cost that it saves in comparison to the cost that would arise without having a buffer. In particular, we compare the savings of the optimal online algorithm with the savings of the optimal offline algorithm in a probabilistic competitive analysis and obtain tight bounds (up to constant factors) on the ratio between the expected savings of these two algorithms.

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References

  1. 1.
    Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press, New York (1998)MATHGoogle Scholar
  2. 2.
    Englert, M., Röglin, H., Spönemann, J., Vöcking, B.: Economical caching. In: Proceedings of the 26th Symposium on Theoretical Aspects of Computer Science (STACS), pp. 385–396 (2009)Google Scholar
  3. 3.
    Feller, W.: An Introduction to Probability Theory and Its Applications, 3rd edn. Wiley, Chichester (1971)MATHGoogle Scholar
  4. 4.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Matthias Englert
    • 1
  • Berthold Vöcking
    • 2
  • Melanie Winkler
    • 2
  1. 1.DIMAP and Department of Computer ScienceUniversity of WarwickUK
  2. 2.Department of Computer ScienceRWTH Aachen UniversityGermany

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