Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-30T01:11:29.533Z Has data issue: false hasContentIssue false

Comparison of self-organizing linear search rules

Published online by Cambridge University Press:  14 July 2016

K. Lam*
Affiliation:
University of Hong Kong
*
Postal address: Department of Statistics, University of Hong Kong, Hong Kong.

Abstract

Consider a file with n records denoted by R1, R2, …, Rn. At each access of a record, the file has to be searched sequentially and it is assumed that the search cost is proportional to the number of probes needed to retrieve the records. The access probabilities p1, p2, …, pn are assumed to be unknown constants and accesses are assumed to be independent. A move-forward self-organizing rule moves a record accessed in the ith position to the lith position without changing the relative ordering of other records where li, = 1, li, < i for i = 2, …, n and li+1li. A move-forward rule R is said to be ≦ another move-forward rule R′ if lili for all i. It is shown that when p2 = p3 = ··· = pn, RR, implies cost R ≦ cost R. This is a generalization of some known results. A new consequence is that the move-up-k + 1 rule is more costly than the move-up-k rule and the move-to-front rule is the most costly of all move-forward rules.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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

Anderson, E. J., Nash, P. and Weber, R. R. (1982) A counterexample to a conjecture on optimal list ordering. J. Appl. Prob. 19, 730732.Google Scholar
Arnaud, J. P. (1977) Sur quelques propriétés de librairies. Thèse de 3ème cycle, Université Paul Sabatier, Toulouse.Google Scholar
Bitner, J. R. (1979) Heuristics that dynamically organize data structures. SIAMJ. Computing 8, 82110.Google Scholar
Daley, D. J. (1968) Stochastically monotone Markov chains. Z. Wahrscheinlichkeitsth. 10, 305317.Google Scholar
Gonnet, G. H., Munro, J. I. and Suwanda, H. (1981) Exegesis of self-organizing linear search. SIAM J. Computing 10, 613637.CrossRefGoogle Scholar
Hendricks, W. J. (1972) The stationary distribution of an interesting Markov chain. J. Appl. Prob. 9, 231233.Google Scholar
Hendricks, W. J. (1976) An account of self organizing systems. SIAMJ. Computing 5, 715723.CrossRefGoogle Scholar
Kan, Y. C. and Ross, S. M. (1980) Optimal list order under partial memory constraints. J. Appl. Prob. 17, 10041015.CrossRefGoogle Scholar
Keilson, J. and Kester, A. (1977) Monotone matrices and monotone Markov processes. Stoch. Proc. Appl. 5, 231241.Google Scholar
Lam, K., Leung, M. Y. and Siu, ?. K. (1984) Self-organizing files with dependent accesses. J. Appl. Prob. 21, 343359.Google Scholar
Lam, K., Siu, M. K. and Yu, C. T. (1981) A generalized counter scheme. Theoret. Computer Sci. 16, 271278.Google Scholar
Lehmann, E. (1955) Ordered families of distribution. Ann. Math. Statist. 26, 399419.CrossRefGoogle Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar
Mccabe, J. (1965) On serial files with relocatable records. Operat. Res. 12, 609618.Google Scholar
Nelson, P. R. (1982) The transposition replacement policy with a partial memory. J. Appl. Prob. 19, 733736.Google Scholar
Phelps, R. I. and Thomas, L. C. (1980) On optimal performance in self-organizing paging algorithms. J. Information Optimization Sci. 1, 8093.Google Scholar
Rivest, R. (1976) On self-organizing sequential search heuristics. Comm. ACM 19, 6367.CrossRefGoogle Scholar
Tenenbaum, A. M. and Nemes, R. M. (1982) Two spectra of self-organizing sequential search algorithms. SIAM J. Computing 11, 557566.Google Scholar