scholarly journals TreeFuser: a framework for analyzing and fusing general recursive tree traversals

2017 ◽  
Vol 1 (OOPSLA) ◽  
pp. 1-30 ◽  
Author(s):  
Laith Sakka ◽  
Kirshanthan Sundararajah ◽  
Milind Kulkarni
Keyword(s):  
Recursive Tree ◽  
Tree Traversals

Using simulation to teach recursion and binary tree traversals

1985 ◽  
Vol 17 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Barry L. Kurtz ◽  
Dennis Johnson
Keyword(s):  
Binary Tree ◽  
Tree Traversals

scholarly journals On the Zagreb Index of Random Recursive Trees

2011 ◽  
Vol 48 (04) ◽  
pp. 1189-1196 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Random Process ◽  
Central Limit ◽  
Topological Indices ◽  
Zagreb Index ◽  
Martingale Central Limit Theorem ◽  
Recursive Tree ◽  
Recursive Trees

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments ofZn, the Zagreb index of a random recursive tree of sizen, are obtained. We also show that the random process {Zn− E[Zn],n≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.

scholarly journals On the Variety of Shapes on the Fringe of a Random Recursive Tree

2010 ◽  
Vol 47 (01) ◽  
pp. 191-200 ◽  
Author(s):  
Qunqiang Feng ◽  
Hosam M. Mahmoud
Keyword(s):  
Normal Distribution ◽  
Contraction Method ◽  
Tree Shape ◽  
Recursive Tree ◽  
Asymptotic Normal Distribution ◽  
Asymptotic Normal ◽  
The Given ◽  
Fixed Tree

We consider a variety of subtrees of various shapes lying on the fringe of a recursive tree. We prove that (under suitable normalization) the number of isomorphic images of a given fixed tree shape on the fringe of the recursive tree is asymptotically Gaussian. The parameters of the asymptotic normal distribution involve the shape functional of the given tree. The proof uses the contraction method.

Phase Changes in the Topological Indices of Scale-Free Trees

2013 ◽  
Vol 50 (02) ◽  
pp. 516-532 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu
Keyword(s):  
Nonnegative Integer ◽  
Topological Indices ◽  
Critical Values ◽  
Phase Changes ◽  
Zagreb Index ◽  
Asymptotic Behaviors ◽  
Scale Free ◽  
Recursive Tree ◽  
Free Tree ◽  
Recursive Trees

A scale-free tree with the parameter β is very close to a star if β is just a bit larger than −1, whereas it is close to a random recursive tree if β is very large. Through the Zagreb index, we consider the whole scene of the evolution of the scale-free trees model as β goes from −1 to + ∞. The critical values of β are shown to be the first several nonnegative integer numbers. We get the first two moments and the asymptotic behaviors of this index of a scale-free tree for all β. The generalized plane-oriented recursive trees model is also mentioned in passing, as well as the Gordon-Scantlebury and the Platt indices, which are closely related to the Zagreb index.

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