Subtree sizes in recursive trees and binary search trees: Berry–esseen bounds and poisson approximations

Authors:
Michael Fuchs
Affiliations:
Department of applied mathematics, national chiao tung university, hsinchu, 300, taiwan (e-mail: mfuchs@math.nctu.edu.tw)
Venue:
Combinatorics, Probability and Computing
Year:
2008

Citing 5
Cited 1

Patterns in random binary search trees

Random Structures & Algorithms
Profiles of Random Trees: Limit Theorems for Random Recursive Trees and Binary Search Trees

Algorithmica
Profiles of random trees: Plane-oriented recursive trees

Random Structures & Algorithms
Phase changes in random point quadtrees

ACM Transactions on Algorithms (TALG)
Phase Changes in Subtree Varieties in Random Recursive and Binary Search Trees

SIAM Journal on Discrete Mathematics

On the subtree size profile of binary search trees

Combinatorics, Probability and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry–Esseen bounds and local limit theorems for the normal range and prove a Poisson approximation result as the subtree size tends to infinity.