Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T17:45:11.307Z Has data issue: false hasContentIssue false
  • English
  • Français

On the distribution of the search cost for the move-to-front rule with random weights

Part of: Theory of data Algorithms - Computer Science Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Javiera Barrera  and
Christian Paroissin
Javiera Barrera*
Affiliation:
Universidad de Chile, Santiago
Christian Paroissin*
Affiliation:
Universidad de Chile, Santiago
*
∗ Postal address: CMM – UMR 2071, UCHILE-CNRS, Casilla 170-3, Correo 7, Santiago, Chile. Email address: [email protected]
∗∗ Current address: Université Paris X Nanterre, MODAL’X, 200 avenue de la République, 92001 Nanterre Cedex, France. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a countable list of files updated according to the move-to-front rule. Files have independent random weights, which are used to construct request probabilities. Exact and asymptotic formulae for the Laplace transform of the stationary search cost are given for i.i.d. weights. Similar expressions are derived for the first two moments. Some results are extended to the case of independent weights.

Keywords

Move-to-front ruleLaplace transformLaplace integral

MSC classification

Primary: 68W40: Analysis of algorithms
Secondary: 68P10: Searching and sorting 44A10: Laplace transform
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 250 - 262
Copyright
Copyright © Applied Probability Trust 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bender, C. M., and Orszag, S. A. (1999). Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory. Springer, New York.Google Scholar
Bodell, J. (1997). Cost of searching—probabilistic analysis of the self-organizing move-to-front and move-to-root sorting rules. Doctoral Thesis, Royal Institute of Technology, Stockholm.Google Scholar
Diaconis, P. (1998). From shuffling cards to walking around the building: an introduction to modern Markov chain theory. In Proc. Internat. Congress Math. (Berlin, 1998), Documenta Mathematica 1, 187–204.Google Scholar
Donnelly, P. (1991). The heaps process, libraries and size-biased permutations. J. Appl. Prob. 28, 321–335.Google Scholar
Fill, J. A. (1996). Limits and rates of convergence for the distribution of search cost under the move-to-front rule. Theory Comput. Sci. 164, 185–206.Google Scholar
Fill, J. A., and Holst, L. (1996). On the distribution of search cost for the move-to-front rule. Random Structures Algorithms 8, 179–186.Google Scholar
Flajolet, P., Gardy, D., and Thimonier, L. (1992). Birthday paradox, coupon collectors, caching algorithms and self-organizing search. Discrete Appl. Math. 39, 207–229.Google Scholar
Hendricks, W. J. (1972). The stationary distribution of an interesting Markov chain. J. Appl. Prob. 9, 231–233.CrossRefGoogle Scholar
Hofri, M. (1995). Analysis of Algorithms: Computational Methods and Mathematical Tools. Oxford University Press.Google Scholar
Hofri, M., and Shachnai, H. (1991). On the optimality of the counter scheme for dynamic linear lists. Inf. Process. Lett. 37, 175–179.CrossRefGoogle Scholar
Holst, L. (2001). Extreme value distributions for random coupon collector and birthday problems. Extremes 4, 129–145.CrossRefGoogle Scholar
Jelenković, P. R. (1999). Asymptotic approximation for the move-to-front search cost distribution and least-recently-used caching fault probabilities. Ann. Appl. Prob. 9, 430–464.Google Scholar
Kingman, J. F. C. (1975). Random discrete distributions. J. R. Statist. Soc. B 37, 1–22.Google Scholar
Knuth, D. E. (1973). The Art of Computer Programming, Vol. 3, Sorting and Searching. Addison-Wesley, Reading, MA.Google Scholar
McCabe, J. (1965). On serial files with relocatable records. Operat. Res. 13, 609–618.Google Scholar
Papanicolaou, V. G., Kokolakis, G. E., and Boneh, S. (1998). Asymptotics for the random coupon collector problem. J. Comput. Appl. Math. 93, 95–105.Google Scholar
Pitman, J., and Yor, M. (1996). Random discrete distributions derived from self-similar random sets. Electron. J. Prob. 1, No. 4.CrossRefGoogle Scholar