Related papers: Central Forests in Trees
Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…
The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…
In 1966, Cummins introduced the "tree graph": the tree graph $\mathbf{T}(G)$ of a graph $G$ (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge,…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-minimization problem for $1$-dimensional currents with…
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. However, when k = 1 the complexity of the problem is polynomial. In this paper, some tools for…
A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
Random forests are a scheme proposed by Leo Breiman in the 2000's for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Despite growing interest and practical use, there has been…
Minimum $k$-Section denotes the NP-hard problem to partition the vertex set of a graph into $k$ sets of sizes as equal as possible while minimizing the cut width, which is the number of edges between these sets. When $k$ is an input…
The aim of this paper is to provide an affirmative answer to a recent question by Bubeck and Linial on the local profile of trees. For a tree $T$, let $p^{(k)}_1(T)$ be the proportion of paths among all $k$-vertex subtrees (induced…
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is…
Among many topological indices of trees the sum of distances $\sigma(T)$ and the number of subtrees $F(T)$ have been a long standing pair of graph invariants that are well known for their negative correlation. That is, among various given…
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…