Related papers: Secant Tree Calculus
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986]. This paper studies the problem of finding an optimal approximating tree. The star decomposition scheme for sets of three binary…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
In this work a composition-decomposition technique is presented that correlates tree eigenvectors with certain eigenvectors of an associated so-called skeleton forest. In particular, the matching properties of a skeleton determine the…
Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…
The simulation of electrical discharges has been attracting a great deal of attention. In such simulations, the electric field computation dominates the computational time. In this paper, we propose a fast tree algorithm that helps to…
Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…
This note derives asymptotic upper and lower bounds for the number of planted plane trees on $n$ nodes assigned labels from the set $\{1,2,\ldots, k\}$ with the restriction that on any path from the root to a leaf, the labels must strictly…
We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted,…
We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula…
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
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…
In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…