相关论文: Width and mode of the profile for some random tree…
We give a detailed asymptotic analysis of the profiles of random symmetric digital search trees, which are in close connection with the performance of the search complexity of random queries in such trees. While the expected profiles have…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
We consider planar rooted random trees whose distribution is even for fixed height $h$ and size $N$ and whose height dependence is of exponential form $e^{-\mu h}$. Defining the total weight for such trees of fixed size to be $Z^{(\mu)}_N$,…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
We consider the height of random k-trees and k-Apollonian networks. These random graphs are not really trees, but instead have a tree-like structure. The height will be the maximum distance of a vertex from the root. We show that w.h.p. the…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily…