Related papers: Leaf Stripping on Uniform Attachment Trees
We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
We consider special cases of the two tree degree sequences problem. We show that if two tree degree sequences do not have common leaves then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove…
Automated segmentation of individual leaves of a plant in an image is a prerequisite to measure more complex phenotypic traits in high-throughput phenotyping. Applying state-of-the-art machine learning approaches to tackle leaf instance…
Most computational models of dependency syntax consist of distributions over spanning trees. However, the majority of dependency treebanks require that every valid dependency tree has a single edge coming out of the ROOT node, a constraint…
We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…
We investigate a degree-biased cutting process on random recursive trees, where each vertex is deleted with probability proportional to its degree. We establish the splitting property and derive the explicit distribution of the number of…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
The prevailing mindset is that a single decision tree underperforms classic random forests in testing accuracy, despite its advantages in interpretability and lightweight structure. This study challenges such a mindset by significantly…
We introduce a $k$-leaf removal algorithm as a generalization of the so-called leaf removal algorithm. In this pruning algorithm, vertices of degree smaller than $k$, together with their first nearest neighbors and all incident edges are…
In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively…
The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…
Finding the set of leaves for an unbounded tree is a nontrivial process in both the Weihrauch and reverse mathematics settings. Despite this, many combinatorial principles for trees are equivalent to their restrictions to trees with leaf…
The size of the largest common subtree (maximum agreement subtree) of two independent uniform random binary trees on $n$ leaves is known to be between orders $n^{1/8}$ and $n^{1/2}$. By a construction based on recursive splitting and…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…
Disjoint-Set forests, consisting of Union-Find trees, are data structures having a widespread practical application due to their efficiency. Despite them being well-known, no exact structural characterization of these trees is known (such a…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
When genetic algorithms are used to evolve decision trees, key tree quality parameters can be recursively computed and re-used across generations of partially similar decision trees. Simply storing instance indices at leaves is enough for…