DeepAI AI Chat
Log In Sign Up

A new compressed cover tree for k-nearest neighbour search and the stable-under-noise mergegram of a point cloud

by   Yury Elkin, et al.

This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies the classical problem of finding k nearest neighbors to m query points in a larger set of n reference points in any metric space. The second part is about the construction of a Minimum Spanning Tree (MST) on any finite metric space. The third part extends the key concept of persistence within Topological Data Analysis in a new direction.


page 20

page 22

page 24

page 27

page 29

page 34

page 37

page 38


The mergegram of a dendrogram and its stability

This paper extends the key concept of persistence within Topological Dat...

On the Complexity of the CSG Tree Extraction Problem

In this short note, we discuss the complexity of the search space for th...

On the law of the iterated logarithm and strong invariance principles in computational geometry

We study the law of the iterated logarithm (Khinchin (1933), Kolmogorov ...

Topological Art in Simple Galleries

Let P be a simple polygon, then the art gallery problem is looking for a...

Towards Stratified Space Learning: Linearly Embedded Graphs

In this paper, we consider the simplest class of stratified spaces – lin...