Average Mixing Matrix of Trees

On 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...

Average mixing of continuous quantum walks

The Average Height of Binary Trees and Other Simple Trees

The average height of a binary tree with n internal nodes is shown to be asymptotic to 2 6. This represents the average stack height of the simplest recursive tree traversal algorithm. The method used in this estimation is also applicable to the analysis of traversal algorithms of unary-binary trees, unbalanced 2-3 trees, t-ary trees for any t, and other families of trees. It yields the two pre...

Matrix Trees

We propose a new data representation for octrees and kd-trees that improves upon memory size and algorithm speed of existing techniques. While pointerless approaches exploit the regular structure of the tree to facilitate efficient data access, their memory footprint becomes prohibitively large as the height of the tree increases. Pointerbased trees require memory consumption proportional to th...

The Average Profile of Suffix Trees

The internal profile of a tree structure denotes the number of internal nodes found at a specific level of the tree. Similarly, the external profile denotes the number of leaves on a level. The profile is of great interest because of its intimate connection to many other parameters of trees. For instance, the depth, fill-up level, height, path length, shortest path, and size of trees can each b...