Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached parent chosen randomly proportionally its weight. Under some assumptions on the sequence of weights, first order for height such has been recently established one authors. In this paper, we obtain second and third orders in asymptotic expansion weighted trees, und...

As the early diagnosis of autism spectrum disorder (ASD) is critical high accuracy machine learning can be applied to achieve technology based diagnosis. In this context, present study demonstrates approach for ASD using decision tree (DT) modeling. The dataset employed in comprises two classes adults with a sample size 704 instances. DT model entails recursive partitioning implemented “rpart” ...

The generalized recursive circulant networking can be widely used in the design and implementation of interconnection networks. It consists a series processors, each is connected through bidirectional, point-to-point communication channels to different neighbors. In this work, we apply shortest path routing concept build independent spanning trees on graphs. proposed strategy loosen restricted ...

Increasing trees have been introduced by Bergeron, Flajolet and Salvy [1]. This kind of notion covers several well knows classes of random trees like binary search trees, recursive trees, and plane oriented (or heap ordered) trees. We consider the height of increasing trees and prove for several classes of trees (including the above mentioned ones) that the height satisfies EHn ∼ γ logn (for so...

Abstract We explore the tree limits recently defined by Elek and Tardos. In particular, we find for many classes of random trees. give general theorems three conditional Galton–Watson trees simply generated trees, split generalized (as here), a continuous-time branching process. These results include, example, labelled ordered recursive preferential attachment binary search

By a theorem of Dobrow and Smythe, the depth of the kth node in very simple families of increasing trees (which includes, among others, binary increasing trees, recursive trees and plane ordered recursive trees) follows the same distribution as the number of edges of the form j−(j+1) with j < k. In this short note, we present a simple bijective proof of this fact, which also shows that the resu...

We take a multivariate view of digital search trees by studying the number of nodes of different types that may coexist in a bucket digital search tree as it grows under an arbitrary memory management system. We obtain the mean of each type of node, as well as the entire covariance matrix between types, whereupon weak laws of large numbers follow from the orders of magnitude (the norming consta...

We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow...