منابع مشابه
The Height of Increasing Trees
Increasing trees have been introduced by Bergeron, Flajolet and Salvy [1]. This kind of notion covers several well knows classes of random trees like binary search trees, recursive trees, and plane oriented (or heap ordered) trees. We consider the height of increasing trees and prove for several classes of trees (including the above mentioned ones) that the height satisfies EHn ∼ γ logn (for so...
متن کاملThe height of increasing trees
We extend results about heights of random trees (Devroye, 1986, 1987, 1998b). In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to c logn for some constant c. We apply our results to obtain a law of large numbers for the height of all polynomial varie...
متن کاملOn the Average Height of b-Balanced Ordered Trees
An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...
متن کاملA bijection of plane increasing trees with relaxed binary trees of right height at most one
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We construct a bijection between these two combinatorial objects and study the therefrom arising connections of certain parameters. Furthermore, we show central limit t...
متن کاملProfile and Height of Random Binary Search Trees
The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2009
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-009-0009-x