相关论文: Trimmed trees and embedded particle systems

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…

Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

We study the evolution of branching trees embedded in Euclidean spaces with suppressed branching of spatially close nodes. This cooperative branching process accounts for the effect of overcrowding of nodes in the embedding space and mimics…

We study the distribution of the number of leaves of the subtree chosen uniformly at random among all the subtrees of the critical branching process tree at extinction.

The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…

We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…

The goal of this work is to decompose random populations with a genealogy in subfamilies of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We model the genealogical structure of a population by…

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…

The question whether a partition $\mathcal{P}$ and a hierarchy $\mathcal{H}$ or a tree-like split system $\mathfrak{S}$ are compatible naturally arises in a wide range of classification problems. In the setting of phylogenetic trees, one…

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…

The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at constant rate, to iid copies of themselves. It also established…

A split system on a multiset $\mathcal M$ is a set of bipartitions of $\mathcal M$. Such a split system $\mathfrak S$ is compatible if it can be represented by a tree in such a way that the vertices of the tree are labelled by the elements…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure…

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…