Davenport-Schinzel sequences and their geometric applications:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006874177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 372 S. |
| ISBN: | 0521470250 |
Internformat
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| 245 | 1 | 0 | |a Davenport-Schinzel sequences and their geometric applications |c Micha Sharir ; Pankaj K. Agarwal |
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Datensatz im Suchindex
| _version_ | 1819272316028190720 |
|---|---|
| adam_text | CONTENTS
PREFACE xi
1 INTRODUCTION 1
1.1 Davenport Schinzel sequences and lower envelopes 2
1.2 Simple bounds on As(n) 6
1.3 Bibliographic notes 10
2 DAVENPORT SCHINZEL SEQUENCES OF ORDER 3 12
2.1 Ackermann s function—A review 12
2.2 The upper bound 15
2.3 The lower bound 21
2.4 Path compressions on trees 29
2.5 Ackermann s functions and combinatorial problems 39
2.6 Bibliographic notes 41
Appendix 2.1 41
3 HIGHER ORDER SEQUENCES 43
3.1 Introduction 43
3.2 An upper bound for A4 (n) 44
3.3 A lower bound for A4(n) 52
3.4 Upper bounds for As(n) 56
3.5 Lower bounds for Xs(n) 67
3.6 Bibliographic notes 77
v
vi Contents
Appendix 3.1 77
Appendix 3.2 80
Appendix 3.3 82
4 GEOMETRIC REALIZATION 86
4.1 Introduction 86
4.2 Realizing the sequences S(k,m) by segments 87
4.3 An alternative construction 104
4.4 Discussion 112
4.5 Bibliographic notes 114
5 PLANAR ARRANGEMENTS 115
5.1 Introduction 115
5.2 Complexity of a single face 116
5.3 Zones in arrangements 122
5.4 Levels in arrangements 127
5.5 Bibliographic notes 130
6 ALGORITHMS FOR ARRANGEMENTS 133
6.1 Introduction 133
6.2 Computing lower envelopes 134
6.3 Computing a single face: Deterministic construction 137
6.4 Randomized divide and conquer construction 151
6.5 Randomized incremental construction 159
6.6 Incremental construction of arrangements 169
6.7 Bibliographic notes 172
7 ARRANGEMENTS IN HIGHER DIMENSIONS 175
7.1 Introduction 175
7.2 Lower envelopes of piecewise linear functions 178
7.3 Lower envelopes in three dimensions 187
7.4 Lower envelopes in higher dimensions 203
7.5 Lower envelopes in some special cases 215
7.6 Single cells in simplex arrangements 223
7.7 Zones 231
7.8 Other related results 234
7.9 Bibliographic notes 237
Appendix 7.1 239
Appendix 7.2 242
Contents vii
8 GEOMETRIC APPLICATIONS 246
8.1 Applications of DS(n, 2) sequences 246
8.2 Transversals of a set of objects 254
8.3 Decomposing arrangements of surfaces 263
8.4 Visibility problems for polyhedral terrains 273
8.5 Width in 3 space 287
8.6 Dynamic geometry 290
8.7 Hausdorff distance and Voronoi surfaces 298
8.8 Polygon placement 307
8.9 Motion planning 326
8.10 Other applications 335
8.11 Bibliographic notes 344
BIBLIOGRAPHY 349
INDEX 369
|
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| author | Šārîr, Mîkā 1950- Agarwal, Pankaj K. |
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| edition | 1. publ. |
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| id | DE-604.BV010329197 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:52:07Z |
| institution | BVB |
| isbn | 0521470250 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006874177 |
| oclc_num | 476816642 |
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| owner_facet | DE-12 DE-11 |
| physical | XII, 372 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Univ. Press |
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| spellingShingle | Šārîr, Mîkā 1950- Agarwal, Pankaj K. Davenport-Schinzel sequences and their geometric applications Davenport-Schinzel sequences Envelopes (Geometry) Sequenzielle Schätzung (DE-588)4181024-7 gnd Einhüllende (DE-588)4151321-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| subject_GND | (DE-588)4181024-7 (DE-588)4151321-6 (DE-588)4130267-9 |
| title | Davenport-Schinzel sequences and their geometric applications |
| title_auth | Davenport-Schinzel sequences and their geometric applications |
| title_exact_search | Davenport-Schinzel sequences and their geometric applications |
| title_full | Davenport-Schinzel sequences and their geometric applications Micha Sharir ; Pankaj K. Agarwal |
| title_fullStr | Davenport-Schinzel sequences and their geometric applications Micha Sharir ; Pankaj K. Agarwal |
| title_full_unstemmed | Davenport-Schinzel sequences and their geometric applications Micha Sharir ; Pankaj K. Agarwal |
| title_short | Davenport-Schinzel sequences and their geometric applications |
| title_sort | davenport schinzel sequences and their geometric applications |
| topic | Davenport-Schinzel sequences Envelopes (Geometry) Sequenzielle Schätzung (DE-588)4181024-7 gnd Einhüllende (DE-588)4151321-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| topic_facet | Davenport-Schinzel sequences Envelopes (Geometry) Sequenzielle Schätzung Einhüllende Algorithmische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006874177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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