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A counterexample to a conjecture on optimal list ordering

Published online by Cambridge University Press:  14 July 2016

E. J. Anderson ,
P. Nash  and
R. R. Weber
E. J. Anderson*
Affiliation:
University of Cambridge
P. Nash*
Affiliation:
University of Cambridge
R. R. Weber*
Affiliation:
University of Cambridge
*
∗Postal address: Clare College, Cambridge CB2 1TL, U.K.
∗∗Postal address: Churchill College, Cambridge CB3 0DS, U.K.
∗∗∗Postal address: Queens' College, Cambridge CB3 9ET, U.K.
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Abstract

A number of items are arranged in a line. At each unit of time one of the items is requested, the i th being requested with probability Pi. We consider rules which reorder the items between successive requests in a fashion which depends only on the position in which the most recently requested item was found. It has been conjectured that the rule which always moves the requested item one closer to the front of the line minimizes the average position of the requested item. An example with six items shows that the conjecture is false.

Keywords

OPTIMAL LIST ORDERMEMORY CONSTRAINTSTRANSPOSITION RULE
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 730 - 732
Copyright
Copyright © Applied Probability Trust 1982 

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References

Kan, Y. C. and Ross, S. M. (1980) Optimal list order under partial memory constraints. J. Appl. Prob. 17, 1004–1015.Google Scholar
Rivest, R. (1976) On self-organizing sequential search heuristics. Comm. ACM 19, 63–67.Google Scholar