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Comparison of self-organizing linear search rules

Published online by Cambridge University Press:  14 July 2016

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

Consider a file with n records denoted by R 1, R 2 , …, 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 p 1, p 2, …, 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 li th position without changing the relative ordering of other records where li , = 1, li , < i for i = 2, …, n and l i+1≧li . A move-forward rule R is said to be ≦ another move-forward rule R′ if l′i ≦li for all i. It is shown that when p 2 = p 3 = ··· = p n , R ≦ R ′, 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.

Keywords

TRANSPOSITION RULEMOVE-TO-FRONT RULEMOVE-UP-k-RULECOMPARISON OF SEARCH COSTMONOTONE MARKOV CHAIN

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984, pp. 763 - 776
Copyright
Copyright © Applied Probability Trust 1984 

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