Combinatorial geometry and its algorithmic applications: the Alcalá lectures
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2009]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 152 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 235 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821846919 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804145332130414592 |
|---|---|
| adam_text | Titel: Combinatorial geometry and its algorithmic applications
Autor: Pach, János
Jahr: 2009
Contents
Preface and Apology vii
Chapter 1. Sylvester-Gallai Problem:
The Beginnings of Combinatorial Geometry 1
1. James Joseph Sylvester and the Beginnings 1
2. Connecting Lines and Directions 3
3. Directions in Space vs. Points in the Plane 6
4. Proof of the Generalized Ungar Theorem 7
5. Colored Versions of the Sylvester-Gallai Theorem 10
Chapter 2. Arrangements of Surfaces:
Evolution of the Basic Theory 13
1. Introduction 13
2. Preliminaries 16
3. Lower Envelopes 20
4. Single Cells 27
5. Zones 29
6. Levels 32
7. Many Cells and Related Problems 37
8. Generalized Voronoi Diagrams 40
9. Union of Geometric Objects 42
10. Decomposition of Arrangements 49
11. Representation of Arrangements 54
12. Computing Arrangements 56
13. Computing Substructures in Arrangements 58
14. Applications 63
15. Conclusions 70
Chapter 3. Davenport-Schinzel Sequences:
The Inverse Ackermann Function in Geometry 73
1. Introduction 73
2. Davenport-Schinzel Sequences and Lower Envelopes 74
3. Simple Bounds and Variants 79
4. Sharp Upper Bounds on Xs(n) 81
5. Lower Bounds on As(n) 86
6. Davenport-Schinzel Sequences and Arrangements 89
Chapter 4. Incidences and Their Relatives:
From Szemeredi and Trotter to Cutting Lenses 99
1. Introduction 99
2. Lower Bounds 102
3. Upper Bounds for Incidences via the Partition Technique 104
4. Incidences via Crossing Numbers?Szekely s Method 106
5. Improvements by Cutting into Pseudo-segments 109
6. Incidences in Higher Dimensions 112
7. Applications 114
Chapter 5. Crossing Numbers of Graphs:
Graph Drawing and its Applications 119
1. Crossings?the Brick Factory Problem 119
2. Thrackles?Conway s Conjecture 120
3. Different Crossing Numbers? 122
4. Straight-Line Drawings 125
5. Angular Resolution and Slopes 126
6. An Application in Computer Graphics 127
7. An Unorthodox Proof of the Crossing Lemma 129
Chapter 6. Extremal Combinatorics:
Repeated Patterns and Pattern Recognition 133
1. Models and Problems 133
2. A Simple Sample Problem: Equivalence under Translation 135
3. Equivalence under Congruence in the Plane 137
4. Equivalence under Congruence in Higher Dimensions 139
5. Equivalence under Similarity 141
6. Equivalence under Homothety or Affine Transformations 143
7. Other Equivalence Relations for Triangles in the Plane 144
Chapter 7. Lines in Space:
From Ray Shooting to Geometric Transversals 147
1. Introduction 147
2. Geometric Preliminaries 149
3. The Orientation of a Line Relative to n Given Lines 152
4. Cycles and Depth Order 158
5. Ray Shooting and Other Visibility Problems 163
6. Transversal Theory 167
7. Open Problems 170
Chapter 8. Geometric Coloring Problems:
Sphere Packings and Frequency Allocation 173
1. Multiple Packings and Coverings 173
2. Cover-Decomposable Families and Hypergraph Colorings 175
3. Frequency Allocation and Conflict-Free Coloring 178
4. Online Conflict-Free Coloring 181
Chapter 9. From Sain Loyd to Laszlo Fejes Toth:
The 15 Puzzle and Motion Planning 183
1. Sam Loyd and the Fifteen Puzzle 183
2. Unlabeled Coins in Graphs and Grids 185
3. Laszlo Fejes Toth and Sliding Coins 187
4. Pushing Squares Around 194
Bibliography 197
Index 227
|
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| dewey-full | 516/.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.13 |
| dewey-search | 516/.13 |
| dewey-sort | 3516 213 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:17:46Z |
| institution | BVB |
| isbn | 9780821846919 |
| language | English |
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| physical | viii, 235 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
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| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
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| spelling | Pach, János 1954- Verfasser (DE-588)138916543 aut Combinatorial geometry and its algorithmic applications the Alcalá lectures János Pach ; Micha Sharir Providence, Rhode Island American Mathematical Society [2009] © 2009 viii, 235 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 152 Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Šārîr, Mîkā 1950- Verfasser (DE-588)138916675 aut Erscheint auch als Online-Ausgabe 978-1-4704-1379-8 Mathematical surveys and monographs Volume 152 (DE-604)BV000018014 152 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022260294&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pach, János 1954- Šārîr, Mîkā 1950- Combinatorial geometry and its algorithmic applications the Alcalá lectures Mathematical surveys and monographs Kombinatorische Geometrie (DE-588)4140733-7 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| subject_GND | (DE-588)4140733-7 (DE-588)4130267-9 |
| title | Combinatorial geometry and its algorithmic applications the Alcalá lectures |
| title_auth | Combinatorial geometry and its algorithmic applications the Alcalá lectures |
| title_exact_search | Combinatorial geometry and its algorithmic applications the Alcalá lectures |
| title_full | Combinatorial geometry and its algorithmic applications the Alcalá lectures János Pach ; Micha Sharir |
| title_fullStr | Combinatorial geometry and its algorithmic applications the Alcalá lectures János Pach ; Micha Sharir |
| title_full_unstemmed | Combinatorial geometry and its algorithmic applications the Alcalá lectures János Pach ; Micha Sharir |
| title_short | Combinatorial geometry and its algorithmic applications |
| title_sort | combinatorial geometry and its algorithmic applications the alcala lectures |
| title_sub | the Alcalá lectures |
| topic | Kombinatorische Geometrie (DE-588)4140733-7 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| topic_facet | Kombinatorische Geometrie Algorithmische Geometrie |
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