Organizing Point Sets: Space-Filling Curves, Delaunay Tessellations of Random Point Sets, and FlowComplexes
Kevin Buchin · 2008
Cover, Abstract, Zusammenfassung, and Content 1\. Introduction 2\. Space-Filling Curves 2.1 Introduction 2.2 Space-Filling Curve Heuristic for the TSP 2.3 Discrete Space-Filling Curves 3\. Incremental Constructions along Space-Filling Curves 3.1 Introduction 3.2 Preliminaries 3.3 Incremental Constructions con BRIO Revisited 3.4 Expected-Case Analysis for Random Points 4\. Incremental Constructions along Space-Filling Curves in Higher Dimensions 4.1 Introduction 4.2 Analysis 4.3 Uniformly Distributed Points 4.4 Normally Distributed Points 4.5 Experiments 4.6 Constructing the Delaunay Tessellation using Nearest Neighbors 5\. Flow Complex 5.1 Introduction 5.2 Preliminaries 5.3 Flow and the Flow Complex 5.4 Properties of the Flow 5.5 Recursive Geometry 6\. Flow Shapes 6.1 Introduction 6.2 Preliminaries 6.3 Flow Shapes 6.4 Homotopy Equivalence of Union of Balls and Flow Shapes Bibliography