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Algorithms for dynamic geometric data streams / Gereon Frahling. [2006]
Content
Acknowledgements
Contents
Introduction
Motivation
Related Work
Preliminaries
General Notations
Data Streams
Clustering
Chernoff Bounds with Limited Independence
Sampling Data Streams
The Unique Element (UE) Data Structure
The Distinct Elements (DE) Data Structure
A Sample Data Structure using Totally Random Hash Functions
A Sample Data Structure using Random Number Generators
A Sample Data Structure using Pairwise Independent Hash Functions
Sampling Geometric Data Streams and Applications
Sampling Geometric Data Streams
-Nets and -Approximations in Data Streams
Random Sampling with Neighborhood Information
Estimating the Weight of a Euclidean Minimum Spanning Tree
The Coreset Method
Definitions
Coresets for k-Median
Coresets for k-Means
Coresets for Oblivious Optimization Problems
Constructing Solutions on the Coreset
Coresets via Sampling
Coresets in Data Streams
Insertions
Deletions
Maximum Spanning Tree
A Kinetic Data Structure for MaxCut
Kinetic Turnament Trees
Approximating the Bounding Cube
The Kinetic Data Structure for MaxCut
An Efficient k-Means Implementation using Coresets
Definitions and Notations
The Algorithm
Experiments
Counting Motifs in Data Streams
Counting Triangles in Adjacency Streams
Counting Triangles in Incidence Streams
Counting Cliques of Arbitrary Size
Counting K3,3 in Incidence Streams
Conclusions
Bibliography
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