scholarly journals Limit laws for terminal nodes in random circuits with restricted fan-out: a family of graphs generalizing binary search trees

2004 ◽  
Vol 41 (2-3) ◽  
pp. 99-110 ◽  
Author(s):  
Hosam Mahmoud ◽  
Tatsuie Tsukiji
Keyword(s):  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Limit Laws ◽  
Random Circuits

Limit Theorems for Subtree Size Profiles of Increasing Trees

2012 ◽  
Vol 21 (3) ◽  
pp. 412-441 ◽  
Author(s):  
MICHAEL FUCHS
Keyword(s):  
Limit Theorems ◽  
Mean Value ◽  
Binary Search ◽  
Analytic Method ◽  
Binary Search Trees ◽  
Search Trees ◽  
Limit Laws ◽  
Special Cases ◽  
Recursive Trees ◽  
Complex Analytic Method

Simple families of increasing trees were introduced by Bergeron, Flajolet and Salvy. They include random binary search trees, random recursive trees and random plane-oriented recursive trees (PORTs) as important special cases. In this paper, we investigate the number of subtrees of size k on the fringe of some classes of increasing trees, namely generalized PORTs and d-ary increasing trees. We use a complex-analytic method to derive precise expansions of mean value and variance as well as a central limit theorem for fixed k. Moreover, we propose an elementary approach to derive limit laws when k is growing with n. Our results have consequences for the occurrence of pattern sizes on the fringe of increasing trees.

scholarly journals The Wiener Index of Random Trees

2002 ◽  
Vol 11 (6) ◽  
pp. 587-597 ◽  
Author(s):  
RALPH NEININGER
Keyword(s):  
Path Length ◽  
Probabilistic Models ◽  
Wiener Index ◽  
Binary Search ◽  
Random Trees ◽  
Binary Search Trees ◽  
Search Trees ◽  
Limit Laws ◽  
Recursive Trees ◽  
Asymptotic Correlations

The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations. Covariances, asymptotic correlations, and bivariate limit laws for the Wiener index and the internal path length are given.

scholarly journals Adaptive structuring of binary search trees using conditional rotations

1993 ◽  
Vol 5 (4) ◽  
pp. 695-704 ◽  
Author(s):  
R.P. Cheetham ◽  
B.J. Oommen ◽  
D.T.H. Ng
Keyword(s):  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees
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