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ON CLIMBING TRIES

Published online by Cambridge University Press:  18 December 2007

Costas Christophi  and
Hosam Mahmoud
Costas Christophi
Affiliation:
Cyprus International Institute for the Environment and Public Health in Association with Harvard School of Public Health, 1105, Nicosia, Cyprus Biostatistics Center, The George Washington University, Rockville, MD 20852 E-mail: cchristophi@cyprusinstitute.org
Hosam Mahmoud
Affiliation:
Department of Statistics, The George Washington UniversityWashington, DC 20052 E-mail: hosam@gwu.edu
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Abstract

To sample a typical key in a “trie,” an appropriate climbing might consider generating random edges in the same manner as the data are generated. In the absence of the probability generating the keys, an uninformed random choice among the children still provides an alternative. We are also interested in extremal sampling, achieved by following a leftmost (or a rightmost) path. Each of these climbing strategies always generates a key, but one that might not necessarily be in the database. We investigate the altitude of the position at which climbing is terminated. Analytical techniques, including poissonization and the Mellin transform, are used for the accurate calculation of moments. In all strategies, the mean is always logarithmic. For typical and uninformed climbing, the variance is bounded in unbiased tries but grows logarithmically in biased tries. Consequently, in the biased case, one can find appropriate centering and scaling to produce a limit distribution for these two climbing strategies; the limit is normal. For extremal climbing, the variance is always bounded for both biased and unbiased cases, and no nontrivial limit exists under any scaling.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 1 , January 2008 , pp. 133 - 149
Copyright
Copyright © Cambridge University Press 2008

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