Towards dynamic randomized algorithms in computational geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in computer science
758 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 156 S. Ill., graph. Darst. |
| ISBN: | 3540575030 0387575030 |
Internformat
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| 100 | 1 | |a Teillaud, Monique |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Towards dynamic randomized algorithms in computational geometry |c Monique Teillaud |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a IX, 156 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in computer science |v 758 | |
| 502 | |a Zugl.: Paris, Univ., Diss., 1991 | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Geometry -- Data processing | |
| 650 | 4 | |a Algorithms | |
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| 689 | 0 | 1 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |D s |
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Datensatz im Suchindex
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|---|---|
| adam_text |
Table of Contents
Introduction 1
1 Fundamental structures 5
1.1 Convex hull 7
1.2 Voronoi diagram 8
1.2.1 Voronoi diagram for points in E 8
1.2.2 Higher order Voronoi diagrams 9
1.2.3 Voronoi diagram of line segments 13
1.3 Arrangements 14
1.3.1 Arrangements of hyperplanes 15
1.3.2 Trapezoidal map 16
1.4 Geometric transformations 17
2 Static randomized incremental algorithms 21
2.1 Formalization of the problem 23
2.2 A data structure : the conflict graph 25
2.3 Techniques of analysis 26
2.3.1 Random sampling 26
2.3.2 Probabilistic games and © series 32
2.3.3 Backwards analysis 32
3 The Delaunay Tree 35
3.1 Structure 37
3.2 Constructing the Delaunay triangulation 39
3.2.1 Location 39
3.2.2 Creating the new simplices 40
3.3 Another structure 42
4 A general structure : the Influence Graph 45
4.1 The general framework 47
4.1.1 Randomized analysis of the I DAG 48
4.1.2 Influence graph versus Conflict graph 51
4.1.3 Another analysis 51
4.1.4 Removing the update conditions 54
4.2 Locating with the influence graph 56
4.2.1 Faster object location 56
4.2.2 Queries 56
4.3 Applications 57
4.3.1 Convex hulls 57
4.3.2 Arrangements 61
4.3.3 Voronoi diagrams 66
4.3.3.1 Voronoi diagrams of point sites in Ed 66
4.3.3.2 Voronoi diagrams of line segments in the plane 69
4.4 About complexity results 72
4.4.1 Randomization 72
4.4.2 Amortization 72
4.4.3 Output sensitivity 74
5 The Jk Delaunay Tree 77
5.1 The fc Delaunay Tree in two dimensions 79
5.1.1 Including and excluding neighbors 80
5.1.2 A semi dynamic algorithm for constructing the order k Voronoi
diagrams 82
5.1.3 Construction of the Ar Delaunay Tree 82
5.1.3.1 Initialization 82
5.1.3.2 Inserting a new site 83
5.1.3.3 Structure of the Ar Delaunay Tree 85
5.1.3.4 Procedure location 86
5.1.3.5 Procedure creation 86
5.2 Analysis of the randomized construction 88
5.2.1 Results on triangles and bicycles 89
5.2.2 Analysis of the expected space used by the Jt Delaunay Tree . 92
5.2.3 Analysis of the expected cost of Procedure location 92
5.2.4 Analysis of the expected cost of Procedure creation 93
5.3 / nearest neighbors 93
5.3.1 Deducing the order / Voronoi diagram from the Jb Delaunay Tree
(/ k) 94
5.3.2 Finding the / nearest neighbors 94
5.4 The fc Delaunay Tree in higher dimensions 96
5.4.1 The d dimensional Jfc Delaunay Tree 97
5.4.2 Analysis of the randomized construction 97
5.5 Experimental results 99
5.5.1 Influence of randomization 99
5.5.2 Influence of it 100
5.5.3 Influence of the point distribution 100
6 Towards a fully dynamic structure 109
6.1 Removing a site from the Delaunay triangulation Ill
6.1.1 Different kinds of modified nodes 112
6.1.2 The Search step 113
6.1.3 The Reinsertion step 115
6.1.4 Analysis 123
6.1.5 d dimensional case 126
6.1.6 Practical results in the planar case 126
6.2 Removing a segment from an arrangement 126
6.2.1 The Search step 128
6.2.2 Corners and bridges 129
6.2.3 Reinsertion of a triplet (r,T, F) 129
6.3 Analysis 134
7 Parallel work 137
7.1 Accelerated static algorithms 139
7.2 Semi dynamic algorithms 140
7.3 Dynamic algorithms 140
7.3.1 With storage of the history 140
7.3.2 Without storing the history 141
7.4 Strategies 142
Conclusion 145
Bibliography 151
Index 157 |
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| author | Teillaud, Monique |
| author_facet | Teillaud, Monique |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SS 4800 |
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| ctrlnum | (OCoLC)320295620 (DE-599)BVBBV008308630 |
| dewey-full | 516/.13/02855120 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| indexdate | 2025-01-10T15:06:09Z |
| institution | BVB |
| isbn | 3540575030 0387575030 |
| language | English |
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| physical | IX, 156 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Teillaud, Monique Verfasser aut Towards dynamic randomized algorithms in computational geometry Monique Teillaud Berlin [u.a.] Springer 1993 IX, 156 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 758 Zugl.: Paris, Univ., Diss., 1991 Datenverarbeitung Geometry -- Data processing Algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Randomisierter Algorithmus (DE-588)4176929-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Randomisierter Algorithmus (DE-588)4176929-6 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Lecture notes in computer science 758 (DE-604)BV000000607 758 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005488805&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teillaud, Monique Towards dynamic randomized algorithms in computational geometry Lecture notes in computer science Datenverarbeitung Geometry -- Data processing Algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd Randomisierter Algorithmus (DE-588)4176929-6 gnd |
| subject_GND | (DE-588)4130267-9 (DE-588)4176929-6 (DE-588)4113937-9 |
| title | Towards dynamic randomized algorithms in computational geometry |
| title_auth | Towards dynamic randomized algorithms in computational geometry |
| title_exact_search | Towards dynamic randomized algorithms in computational geometry |
| title_full | Towards dynamic randomized algorithms in computational geometry Monique Teillaud |
| title_fullStr | Towards dynamic randomized algorithms in computational geometry Monique Teillaud |
| title_full_unstemmed | Towards dynamic randomized algorithms in computational geometry Monique Teillaud |
| title_short | Towards dynamic randomized algorithms in computational geometry |
| title_sort | towards dynamic randomized algorithms in computational geometry |
| topic | Datenverarbeitung Geometry -- Data processing Algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd Randomisierter Algorithmus (DE-588)4176929-6 gnd |
| topic_facet | Datenverarbeitung Geometry -- Data processing Algorithms Algorithmische Geometrie Randomisierter Algorithmus Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005488805&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT teillaudmonique towardsdynamicrandomizedalgorithmsincomputationalgeometry |