We study depth properties of a general class of random recursive trees where each node n attaches to the random node !nXn" and X0, . . . , Xn is a sequence of i.i.d. random variables taking values in [0, 1). We call such trees scaled attachment random recursive trees (SARRT). We prove that the height Hn of a SARRT is asymptotically given by Hn ∼ αmax log n where αmax is a constant depending onl...

Introduction Many widely used file organizations can be logically partitioned into two components; the index (also called directory) component and the data leaves component. The file records are maintained in data leaves where each data leaf (leaf for short) is one logical unit which is stored in contiguous disk pages. The index component is a search structure, usually a tree or a hash table, w...

We propose a uniform approach to describing the phase change of the limiting distribution of space measures in random m-ary search trees: the space requirement, when properly normalized, is asymptotically normally distributed for m ≤ 26 and does not have a fixed limit distribution for m > 26. The tools are based on the method of moments and asymptotic solutions of differential equations, and ar...

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process, e.g., recursive trees, plane-oriented recursive trees and binary increasing trees, we can determine the limiting distribution which can be characterized as a generalized Dickman’s infinitely divisible distribution.