Width and Mode of the Profile for Random Trees of Logarithmic Height1
نویسندگان
چکیده
We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in random trees of logarithmic height. The approach is simple but gives very precise estimates for expected width, central moments of the width, and almost sure convergence. It is widely applicable to random trees of logarithmic height, including recursive trees, binary search trees, quadtrees, plane-oriented ordered trees and other varieties of increasing trees. Abbreviated title: Width of random log trees. MSC 2000 subject classifications: Primary 60C05; secondary 05C05 68P10.
منابع مشابه
Width and Mode of the Profile for Some Random Trees of Logarithmic Height by Luc Devroye
We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise estimates for expected width, central moments of the width, and almost sure convergence. It is widely applicable to random trees of logarithmic height, including...
متن کاملProfiles of random trees: Plane-oriented recursive trees
We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of plane-oriented recursive trees (with ...
متن کاملProfiles of random trees: plane-oriented recursive trees1
We derive several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximation to the expected width and the correlation coefficients of two level sizes. Most of our proofs are based on a method of moments. We also discover an unexpected connection between 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 کاملThe Subtree Size Profile of Bucket Recursive Trees
Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...
متن کامل