ON CLIMBING TRIES

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.