Abstract
We consider a variant of the online paging problem where the online algorithm may buy additional cache slots at a certain cost. The overall cost incurred equals the total cost for the cache plus the number of page faults. This problem and our results are a generalization of both, the classical paging problem and the ski rental problem.
We derive the following three tight results: (1) For the case where the cache cost depends linearly on the cache size, we give a λ-competitive online algorithm where λ ≈ 3.14619 is a solution of λ = 2 + ln λ. This competitive ratio λ is best possible. (2) For the case where the cache cost grows like a polynomial of degree d in the cache size, we give an online algorithm whose competitive ratio behaves like d/lnd + o(d/lnd). No online algorithm can reach a competitive ratio better than d/lnd. (3) We exactly characterize the class of cache cost functions for which there exist online algorithms with finite competitive ratios.
Supported by the Hungarian National Foundation for Scientific Research, Grant T030074
Supported by the START program Y43-MAT of the Austrian Ministry of Science.
Supported by the Research Competitiveness Subprogram of the Louisiana Board of Regents.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
L.A. Belady. A study of replacement algorithms for virtual storage computers. IBM Systems Journal 5, 78–101, 1966.
A. Borodin and R. El Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.
R.M. Sccorless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, and D.E. Knuth. On The Lambert W Function. Maple Share Library.
Cs. Imreh and J. Noga. Scheduling with Machine Cost. Proceedings 2nd International Workshop on Approximation Algorithms, Springer LNCS 1671, 168–176, 1999.
S. Irani. Competitive analysis of paging. In A. Fiat and G.J. Woeginger (eds.) Online Algorithms-The State of the Art. Springer LNCS 1442, 52–73, 1998.
A. Karlin, M. Manasse, L. Mcgeoch, and S. Owicki. Competitive randomized algorithms for nonuniform problems. Algorithmica 11, 542–571, 1994.
D. Sleator and R.E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM 28, 202–208, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Csirik, J., Imreh, C., Noga, J., Seiden, S.S., Woeginger, G.J. (2001). Buying a Constant Competitive Ratio for Paging. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_8
Download citation
DOI: https://doi.org/10.1007/3-540-44676-1_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42493-2
Online ISBN: 978-3-540-44676-7
eBook Packages: Springer Book Archive