The oscillatory distribution of distances in random tries

• 成果类型: Article
• 署名作者: Christophi, CA; Mahmoud, HM
• 署名单位: George Washington University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000106
• 发表日期: 2005
• 页码: 1536-1564
• 关键词: tree

摘要

We investigate A, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O (1), as n -> infinity. It is demonstrated that the centered random variable Delta(n)* = Delta(n) - [2 log(2) n] does not have a limit distribution, but rather oscillates between two distributions.