Related papers: Performance Evaluation: Ball-Tree and KD-Tree in t…
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set $S$ of $n$ point-sites in the plane. More precisely, we assume that $S$ resides in a random-access memory that can only be read. The edges of the…
Minimal spanning trees (MSTs) have been used in cosmology and astronomy to distinguish distributions of points in a multi-dimensional space. They are essentially unknown in particle physics, however. We briefly define MSTs and illustrate…
Recent results have shown that the MCTS algorithm (a new, adaptive, randomized optimization algorithm) is effective in a remarkably diverse set of applications in Artificial Intelligence, Operations Research, and High Energy Physics. MCTS…
In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…
Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…
The geometric $\delta$-minimum spanning tree problem ($\delta$-MST) is the problem of finding a minimum spanning tree for a set of points in a normed vector space, such that no vertex in the tree has a degree which exceeds $\delta$, and the…
The basic idea of the kd-tree algorithm is to recursively partition a point set P by hyperplanes, and to store the obtained partitioning in a binary tree. Due to its immense popularity, many applications in astronomy have been implemented.…
This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…
Most of the existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Therefore, we…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
In this paper we present and evaluate a parallel algorithm for solving a minimum spanning tree (MST) problem for supercomputers with distributed memory. The algorithm relies on the relaxation of the message processing order requirement for…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
We study the classic Euclidean Minimum Spanning Tree (MST) problem in the Massively Parallel Computation (MPC) model. Given a set $X \subset \mathbb{R}^d$ of $n$ points, the goal is to produce a spanning tree for $X$ with weight within a…
In this paper, we revisit the problem of indexing multi-dimensional data in memory for the efficient support of multi-dimensional range queries and nearest neighbor queries. This is a classic problem in main-memory databases, where there is…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
This work presents a fully integrated tree-based combined exploration-planning algorithm: Exploration-RRT (ERRT). The algorithm is focused on providing real-time solutions for local exploration in a fully unknown and unstructured…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…