THE DEGREE PROFILE AND GINI INDEX OF RANDOM CATERPILLAR TREES

Profile 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.

The Degree Profile of Pólya Trees

We investigate the profile of random Pólya trees of size n when only nodes of degree d are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process converges weakly to a Brownian excursion local time. Moreover, we investigate the joint distribution of the number of nodes of degree d1 and d2 in the levels of the tree.

The degree distribution of random k-trees

A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and copying mechanisms that existing evolving graph processes fail to model due to technical obstacles. The result also serves as a further cautionary ...

The Gini Index of Speech

In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator and length should be used to create the sparsest decomposition? To answer these questions, we propose the Gini index, which is twice the area between the Lorenz curve and the 45 degree line, as a measure of signal sparsity. The Gini index, introduced in 1912, is one of the most common measures of i...

Wiener index of random trees