Related papers: The Application of kd-tree in Astronomy

We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log…

Modern astronomy relies on massive databases collected by robotic telescopes and digital sky surveys, acquiring data in a much faster pace than what manual analysis can support. Among other data, these sky surveys collect information about…

We represent the further development of S-tree technique of the study the structure of clusters of galaxies. The S-tree technique developed by Gurzadyan et al enables one to analyse the substructures of clusters via self-consistent use of…

Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…

Machine learning is a field that has been growing in importance since the early 2010s due to the increasing accuracy of classification models and hardware advances that have enabled faster training on large datasets. In the field of…

We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…

Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…

Analysing and learning from spatio-temporal datasets is an important process in many domains, including transportation, healthcare and meteorology. In particular, data collected by sensors in the environment allows us to understand and…

We present an algorithm capable of detecting diffuse, dim sources of any size in an astronomical image. These sources often defeat traditional methods for source finding, which expand regions around points of high intensity. Extended…

This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…

Dust properties, such as mass and porosity, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, available ways to calculate the…

In the modern galaxy surveys photometric redshifts play a central role in a broad range of studies, from gravitational lensing and dark matter distribution to galaxy evolution. Using a dataset of about 25,000 galaxies from the second data…

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 present an application of a particular machine-learning method (Boosted Decision Trees, BDTs using AdaBoost) to separate stars and galaxies in photometric images using their catalog characteristics. BDTs are a well established machine…

The capability of classifying and clustering a desired set of data is an essential part of building knowledge from data. However, as the size and dimensionality of input data increases, the run-time for such clustering algorithms is…

Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…

Trees are key components of the terrestrial biosphere, playing vital roles in ecosystem function, climate regulation, and the bioeconomy. However, large-scale monitoring of individual trees remains limited by inadequate modelling. Available…

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…