Related papers: Nearest Embedded and Embedding Self-Nested Trees
Given a graph G, the {\em maximum internal spanning tree problem} (MIST for short) asks for computing a spanning tree T of G such that the number of internal vertices in T is maximized. MIST has possible applications in the design of…
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…
Aerial remote sensing using multispectral and RGB imagers has provided a critical impetus to precision agriculture. Analysis of the hyperspectral images with limited or no labels is challenging. This paper focuses on self-supervised…
In this paper we investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$. We analyze a modified version of a $k$-nearest…
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
Tree edit distance is a well-studied measure of dissimilarity between rooted trees with node labels. It can be computed in $O(n^3)$ time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007], and fine-grained hardness results suggest that the…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2}…
Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees.…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance.…
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…
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…
In this paper, we propose a physically inspired graph-theoretical clustering method, which first makes the data points organized into an attractive graph, called In-Tree, via a physically inspired rule, called Nearest Descent (ND). In…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…
We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with $n$ nodes can be drawn on a $\sqrt n$ by $\sqrt n$ grid. We also show that testing whether a given binary tree has…
Nearest-neighbor search dominates the asymptotic complexity of sampling-based motion planning algorithms and is often addressed with k-d tree data structures. While it is generally believed that the expected complexity of nearest-neighbor…