Algorithms for dynamic geometric data streams:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis |
| Beschreibung: | Paderborn, Univ., Diss., 2006 |
| Beschreibung: | 1 Online-Ressource |
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Datensatz im Suchindex
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| adam_text | Contents
Acknowledgements iii
Contents vi
1 Introduction 1
1.1 Motivation 4
1.2 Related Work 8
2 Preliminaries 13
2.1 General Notations 13
2.2 Data Streams 14
2.3 Clustering 17
2.4 Chernoff Bounds with Limited Independence 19
3 Sampling Data Streams 21
3.1 The Unique Element (UE) Data Structure 22
3.2 The Distinct Elements (DE) Data Structure 23
3.3 A Sample Data Structure using Totally Random Hash Functions 23
3.4 A Sample Data Structure using Random Number Generators 25
3.5 A Sample Data Structure using Pairwise Independent Hash Functions 29
4 Sampling Geometric Data Streams and Applications 33
4.1 Sampling Geometric Data Streams 34
4.2 e Nets and e Approximations in Data Streams 35
4.3 Random Sampling with Neighborhood Information 36
4.4 Estimating the Weight of a Euclidean Minimum Spanning Tree 39
5 The Coreset Method 47
5.1 Definitions 47
5.2 Coresets for k Median 54
5.3 Coresets for k Means 60
5.4 Coresets for Oblivious Optimization Problems 65
5.5 Constructing Solutions on the Coreset 69
5.6 Coresets via Sampling 76
6 Coresets in Data Streams 93
6.1 Insertions 95
6.2 Deletions 97
6.3 Maximum Spanning Tree 99
7 A Kinetic Data Structure for MaxCut 103
7.1 Kinetic Turnament Trees 104
7.2 Approximating the Bounding Cube 104
7.3 The Kinetic Data Structure for MaxCut 105
8 An Efficient k Means Implementation using Coresets 111
8.1 Definitions and Notations 112
8.2 The Algorithm 114
8.3 Experiments 120
9 Counting Motifs in Data Streams 133
9.1 Counting Triangles in Adjacency Streams 134
9.2 Counting Triangles in Incidence Streams 142
9.3 Counting Cliques of Arbitrary Size 149
9.4 Counting K33 in Incidence Streams 152
10 Conclusions 157
Bibliography 159
|
| adam_txt |
Contents
Acknowledgements iii
Contents vi
1 Introduction 1
1.1 Motivation 4
1.2 Related Work 8
2 Preliminaries 13
2.1 General Notations 13
2.2 Data Streams 14
2.3 Clustering 17
2.4 Chernoff Bounds with Limited Independence 19
3 Sampling Data Streams 21
3.1 The Unique Element (UE) Data Structure 22
3.2 The Distinct Elements (DE) Data Structure 23
3.3 A Sample Data Structure using Totally Random Hash Functions 23
3.4 A Sample Data Structure using Random Number Generators 25
3.5 A Sample Data Structure using Pairwise Independent Hash Functions 29
4 Sampling Geometric Data Streams and Applications 33
4.1 Sampling Geometric Data Streams 34
4.2 e Nets and e Approximations in Data Streams 35
4.3 Random Sampling with Neighborhood Information 36
4.4 Estimating the Weight of a Euclidean Minimum Spanning Tree 39
5 The Coreset Method 47
5.1 Definitions 47
5.2 Coresets for k Median 54
5.3 Coresets for k Means 60
5.4 Coresets for Oblivious Optimization Problems 65
5.5 Constructing Solutions on the Coreset 69
5.6 Coresets via Sampling 76
6 Coresets in Data Streams 93
6.1 Insertions 95
6.2 Deletions 97
6.3 Maximum Spanning Tree 99
7 A Kinetic Data Structure for MaxCut 103
7.1 Kinetic Turnament Trees 104
7.2 Approximating the Bounding Cube 104
7.3 The Kinetic Data Structure for MaxCut 105
8 An Efficient k Means Implementation using Coresets 111
8.1 Definitions and Notations 112
8.2 The Algorithm 114
8.3 Experiments 120
9 Counting Motifs in Data Streams 133
9.1 Counting Triangles in Adjacency Streams 134
9.2 Counting Triangles in Incidence Streams 142
9.3 Counting Cliques of Arbitrary Size 149
9.4 Counting K33 in Incidence Streams 152
10 Conclusions 157
Bibliography 159 |
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| spelling | Frahling, Gereon 1976- Verfasser (DE-588)132298899 aut Algorithms for dynamic geometric data streams von Gereon Frahling 2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Paderborn, Univ., Diss., 2006 Dynamische Datenstruktur (DE-588)4250628-1 gnd rswk-swf Algorithmische Programmierung (DE-588)4293504-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Dynamische Datenstruktur (DE-588)4250628-1 s Algorithmische Programmierung (DE-588)4293504-0 s DE-604 http://ubdata.uni-paderborn.de/ediss/17/2006/frahling/ kostenfrei Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015506637&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frahling, Gereon 1976- Algorithms for dynamic geometric data streams Dynamische Datenstruktur (DE-588)4250628-1 gnd Algorithmische Programmierung (DE-588)4293504-0 gnd |
| subject_GND | (DE-588)4250628-1 (DE-588)4293504-0 (DE-588)4113937-9 |
| title | Algorithms for dynamic geometric data streams |
| title_auth | Algorithms for dynamic geometric data streams |
| title_exact_search | Algorithms for dynamic geometric data streams |
| title_exact_search_txtP | Algorithms for dynamic geometric data streams |
| title_full | Algorithms for dynamic geometric data streams von Gereon Frahling |
| title_fullStr | Algorithms for dynamic geometric data streams von Gereon Frahling |
| title_full_unstemmed | Algorithms for dynamic geometric data streams von Gereon Frahling |
| title_short | Algorithms for dynamic geometric data streams |
| title_sort | algorithms for dynamic geometric data streams |
| topic | Dynamische Datenstruktur (DE-588)4250628-1 gnd Algorithmische Programmierung (DE-588)4293504-0 gnd |
| topic_facet | Dynamische Datenstruktur Algorithmische Programmierung Hochschulschrift |
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