Related papers: Average Case Analysis of Leaf-Centric Binary Tree …
Rooted and ranked binary trees are mathematical objects of great importance used to model hierarchical data and evolutionary relationships with applications in many fields including evolutionary biology and genetic epidemiology. Bayesian…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Recently, 2-protected nodes were studied in the context of ordered trees and $k$-trees. These nodes have a distance of at least 2 to each leaf. Here, we study digital search trees, which are binary trees, but with a different probability…
We develop basic cluster theory from an elementary point of view using a variation of binary trees which we call mixed cobinary trees. We show that the number of isomorphism classes of such trees is given by the Catalan number Cn where n is…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
Consider the Aldous Markov chain on the space of rooted binary trees with $n$ labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix $1\le k < n$ and project the leaf…
We study rooted planar random trees with a probability distribution which is proportional to a product of weight factors $w_n$ associated to the vertices of the tree and depending only on their individual degrees $n$. We focus on the case…
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…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…
We apply so-called tree straight-line programs to the problem of lossless compression of binary trees. We derive upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds obtained by Zhang,…
We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…
We give a simple characterisation of the distribution of the independence number, and equivalently the matching number, of a random tree on $n$ labelled vertices chosen uniformly among the $n^{n-2}$ such trees: Roll an $n$-sided die…
We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
To each generic complex polynomial $p(z)$ there is associated a labeled binary tree (here referred to as a "lemniscate tree") that encodes the topological type of the graph of $|p(z)|$. The branching structure of the lemniscate tree is…