Related papers: On exponentially height-penalized random trees
The goal of this note is to study the geometry of large size-conditioned Bienaym\'e trees whose offspring distribution is subcritical, belongs to the domain of attraction of a stable law of index $\alpha=1$ and satisfies a local regularity…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…
Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively (from the root) split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities…
In this paper we investigate the asymptotic optimality property of a randomized sampling based motion planner, namely RRT. We prove that a RRT planner is not an asymptotically optimal motion planner. Our result, while being consistent with…
We study the problem of detecting and recovering a planted spanning tree $M_n^*$ hidden within a complete, randomly weighted graph $G_n$. Specifically, each edge $e$ has a non-negative weight drawn independently from $P_n$ if $e \in M_n^*$…
Let $T$ be a random tree taken uniformly at random from the family of labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the number of sub-trees of $T$ that hold asymptotically almost surely. With computer support…
The Aho, Hopcroft and Ullman (AHU) algorithm has been the state of the art since the 1970s for determining in linear time whether two unordered rooted trees are isomorphic or not. However, it has been criticized (by Campbell and Radford)…
A monotone drawing of a graph G is a straight-line drawing of G such that every pair of vertices is connected by a path that is monotone with respect to some direction. Trees, as a special class of graphs, have been the focus of several…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
We study a general procedure that builds random $\mathbb R$-trees by gluing recursively a new branch on a uniform point of the pre-existing tree. The aim of this paper is to see how the asymptotic behavior of the sequence of lengths of…
We prove that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set converges in the Gromov-Hausdorff sense after a suitable rescaling to the Brownian continuum random tree. This proves a conjecture by…
The number of trees T in the random forest (RF) algorithm for supervised learning has to be set by the user. It is controversial whether T should simply be set to the largest computationally manageable value or whether a smaller T may in…
In this paper, we study the online nearest neighbor random tree in dimension $d\in \mathbb N$ (called $d$-NN tree for short) defined as follows. We fix the torus $\mathbb T^d_n$ of dimension $d$ and area $n$ and equip it with the metric…
We study two models of growing recursive trees. For both models, initially the tree only contains one vertex $u_1$ and at each time $n\geq 2$ a new vertex $u_n$ is added to the tree and its parent is chosen randomly according to some rule.…
We prove that the multiplicity of a fixed eigenvalue $\alpha$ in a random recursive tree on $n$ vertices satisfies a central limit theorem with mean and variance asymptotically equal to $\mu_{\alpha} n$ and $\sigma^2_{\alpha} n$…
Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning and are often viewed as…
We introduce a non-increasing tree growth process $((T_n,\sigma_n),\, n\ge 1)$, where $T_n$ is a rooted labeled tree on $n$ vertices and ${\sigma}_n$ is a permutation of the vertex labels. The construction of $(T_{n},{\sigma}_n)$ from…
This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal…