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Multiplicities of eigenvalues of some linear search schemes

✍ Scribed by A.J. Pryde; R.M. Phatarfod

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
541 KB
Volume
291
Category
Article
ISSN
0024-3795

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✦ Synopsis

We consider the problem of dynamically reorganizing a linear list when the list is subject to a random number of requests during a unit time interval. Three different heuristics are considered in which the selected items are moved to the front of the list in random order. the same order and finally the opposite order to the previous one. We find the eigenvalues and their multiplicities for the corresponding transition probability matrices. These arc given in terms of the weights representing the probability of selection of tile individual items. The methods employed arc purely algebraic, being based on properties of permutations, and so our results arc valid fOf arbitrary complex weights.

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