Abstract
In this paper we explore the effects of locality on the performance of paging algorithms. Traditional competitive analysis fails to explain important properties of paging assessed by practical experience. In particular, the competitive ratios of paging algorithms that are known to be efficient in practice (e.g. LRU) are as poor as those of naive heuristics (e.g. FWF). It has been recognized that the main reason for these discrepancies lies in an unsatisfactory modelling of locality of reference exhibited by real request sequences.
Following [13], we explicitely address this issue, proposing an adversarial model in which the probability of requesting a page is also a function of the page’s age. In this way, our approach allows to capture the effects of locality of reference. We consider several families of distributions and we prove that the competitive ratio of LRU becomes constant as locality increases, as expected. This result is strengthened when the distribution satisfies a further concavity/convexity property: in this case, the competitive ratio of LRU is always constant.
We also propose a family of distributions parametrized by locality of reference and we prove that the performance of FWF rapidly degrades as locality increases, while the converse happens for LRU.
We think, our results provide one contribution to explaining the behaviours of these algorithms in practice.
Partially supported by the EU projects AMORE, ALCOM-FT, COSIN and by the MIUR Project “Resource Allocation in Real Networks”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albers, S., Favrholdt, L.M., Giel, O.: On paging with locality of reference. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 258–267 (2002)
Belady, L.A.: A study of replacement algorithms for a virtual-storage computer. IBM Systems Journal 5(2), 78–101 (1966)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Borodin, A., Irani, S., Raghavan, P., Schieber, B.: Competitive paging with locality of reference. In: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pp. 249–259 (1991)
Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst case order ratio applied to paging. In: Proceedings of the 5th Italian Conference on Algorithms and Complexity, pp. 58–69 (2003)
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)
Denning, P.J.: The working set model for program behaviour. Communications of the ACM 11(5), 323–333 (1968)
Fiat, A., Karlin, A.R.: Randomized and multipointer paging with locality of reference. In: Proceedings of the Twenty-Seventh Annual ACM Symposium on the Theory of Computing, pp. 626–634 (1995)
Fiat, A., Karp, R., Luby, M., McGeoch, L., Sleator, D., Young, N.E.: Competitive paging algorithms. Journal of Algorithms 12(4), 685–699 (1991)
Fiat, A., Mendel, M.: Truly online paging with locality of reference. In: 38th IEEE Annual Symposium on Foundations of Computer Science, pp. 326–335 (1997)
Irani, S., Karlin, A.R., Phillips, S.: Strongly competitive algorithms for paging with locality of reference. SIAM Journal on Computing 25(3), 477–497 (1996)
Karlin, R., Phillips, S.J., Raghavan, P.: Markov paging. In: Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, pp. 208–217 (1992)
Koutsoupias, E., Papadimitriou, C.H.: Beyond competitive analysis. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 394–400 (1994)
Chrobak, M., Noga, J.: LRU is better than FIFO. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1998), pp. 78–81 (1998)
Sleator, D., Tarjan, R.E.: Amortized Efficiency of List Update and Paging Rules. Communications of the ACM 28, 202–208 (1985)
Tanenbaum, A.S.: Modern Operating Systems. Prentice-Hall, Englewood Cliffs (1992)
Torng, E.: A unified analysis of paging and caching. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science, pp. 194–203 (1995)
Young, N.: The k-server dual and loose competitiveness for paging. Algorithmica 11(6), 525–541 (1994)
Young, N.E.: On-line file caching. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1998), pp. 82–86 (1998)
Young, N.E.: On-line paging against adversarially biased random inputs. Journal of Algorithms 37(1), 218–235 (2000)
Young, N.: Competitive paging and dual-guided on-line weighted caching and matching algorithms. PhD thesis, Department of Computer Science, Princeton University (1991)
Young, N.E.: Bounding the diffuse adversary. In: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 420–425 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becchetti, L. (2004). Modeling Locality: A Probabilistic Analysis of LRU and FWF. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-30140-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23025-0
Online ISBN: 978-3-540-30140-0
eBook Packages: Springer Book Archive