Planar graph drawing
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai
World Scientific
[2004]
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| Schriftenreihe: | Lecture notes series on computing
vol. 12 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Nishizeki, Takao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Planar graph drawing |c Takao Nishizeki, Saidur Rahman |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai |b World Scientific |c [2004] | |
| 264 | 4 | |c © 2004 | |
| 300 | |a xiii, 295 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes series on computing |v vol. 12 | |
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| 689 | 1 | 2 | |a Algorithmus |0 (DE-588)4001183-5 |D s |
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| 700 | 1 | |a Rahman, Saidur |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804133527514513408 |
|---|---|
| adam_text | Contents
Preface v
1. Graph Drawing 1
1.1 Introduction............................................... 1
1.2 Historical Background...................................... 2
1.3 Drawing Styles............................................. 3
1.3.1 Planar Drawing...................................... 4
1.3.2 Polyline Drawing.................................... 5
1.3.3 Straight Line Drawing............................... 5
1.3.4 Convex Drawing ..................................... 6
1.3.5 Orthogonal Drawing.................................. 6
1.3.6 Box-Orthogonal Drawing.............................. 7
1.3.7 Rectangular Drawing................................. 8
1.3.8 Box-Rectangular Drawing............................. 8
1.3.9 Grid Drawing........................................ 8
1.3.10 Visibility Drawing ................................. 9
1.4 Properties of Drawings.................................... 10
1.5 Applications of Graph Drawing............................. 11
1.5.1 Floorplanning...................................... 12
1.5.2 VLSI Layout ....................................... 13
1.5.3 Software Engineering............................... 14
1.5.4 Simulating Molecular Structures.................... 15
1.6 Scope of This Book....................................... 15
2. Graph Theoretic Foundations 19
2.1 Basic Terminology......................................... 19
ix
X
Planar Graph Drawing
2.1.1 Graphs and Multigraphs........................... 19
2.1.2 Subgraphs........................................ 20
2.1.3 Paths and Cycles................................. 21
2.1.4 Chains........................................... 21
2.1.5 Connectivity..................................... 22
2.1.6 Trees and Forests................................ 22
2.1.7 Complete Graphs..................................... 23
2.1.8 Bipartite Graphs.................................... 24
2.1.9 Subdivisions ....................................... 24
2.2 Planar Graphs.............................................. 24
2.2.1 Plane Graphs........................................ 26
2.2.2 Euler’s Formula.................................... 29
2.2.3 Dual Graph.......................................... 30
2.3 Bibliographic Notes........................................ 31
3. Algorithmic Foundations 33
3.1 What is an Algorithm?..................................... 33
3.2 Machine Model and Complexity............................... 34
3.2.1 The 0( ) notation.................................. 34
3.2.2 Polynomial Algorithms............................... 35
3.2.3 NP-Complete Problems............................. 35
3.3 Data Structures and Graph Representation.................. 36
3.4 Exploring a Graph.......................................... 38
3.4.1 Depth-First Search.................................. 38
3.4.2 Breadth-First Search................................ 39
3.5 Data Structures for Plane Graphs........................... 42
3.6 Bibliographic Notes........................................ 44
4. Straight Line Drawing 45
4.1 Introduction............................................... 45
4.2 Shift Method............................................... 46
4.2.1 Canonical Ordering.................................. 46
4.2.2 Shift Algorithm..................................... 50
4.2.3 Linear-Time Implementation.......................... 54
4.3 Realizer Method............................................ 58
4.3.1 Barycentric Representation ......................... 58
4.3.2 Schnyder Labeling................................... 62
4.3.3 Realizer............................................ 66
Contents
XI
4.3.4 Drawing Algorithm with Realizer.................... 69
4.4 Compact Grid Drawing..................................... 72
4.4.1 Four-Canonical Ordering............................ 74
4.4.2 Algorithm Four-Connected-Draw...................... 77
4.4.3 Drawing Gf......................................... 79
4.5 Bibliographic Notes...................................... 87
5. Convex Drawing 89
5.1 Introduction............................................. 89
5.2 Convex Drawing .......................................... 90
5.3 Convex Testing........................................... 94
5.3.1 Definitions........................................ 95
5.3.2 Condition II....................................... 98
5.3.3 Testing Algorithm ................................ 101
5.4 Convex Grid Drawings of 3-Connected Plane Graphs .... 105
5.4.1 Canonical Decomposition .......................... 105
5.4.2 Algorithm for Convex Grid Drawing................. 110
5.5 Convex Grid Drawings of 4-Connected Plane Graphs .... 117
5.5.1 Four-Canonical Decomposition...................... 117
5.5.2 Algorithm......................................... 119
5.5.2.1 How to Compute ^-Coordinates............. 119
5.5.2.2 How to Compute ^-Coordinates............. 123
5.6 Bibliographic Notes..................................... 127
6. Rectangular Drawing 129
6.1 Introduction............................................ 129
6.2 Rectangular Drawing and Matching ....................... 130
6.3 Linear Algorithm for Rectangular Drawings of Plane Graphs 135
6.3.1 Thomassen’s Theorem............................... 135
6.3.2 Sufficiency....................................... 137
6.3.3 Rectangular Drawing Algorithm..................... 152
6.3.4 Rectangular Grid Drawing.......................... 156
6.4 Rectangular Drawings without Designated Corners .... 159
6.5 Rectangular Drawings of Planar Graphs................... 161
6.5.1 Case for a Subdivision of a Planar 3-connected Cubic
Graph............................................ 163
6.5.2 The Other Case................................... 169
6.6 Bibliographic Notes.................................... 173
xii Planar Graph Drawing
7. Box-Rectangular Drawing 175
7.1 Introduction............................................ 175
7.2 Preliminaries.......................................... 175
7.3 Box-Rectangular Drawings with Designated Corner Boxes . 178
7.4 Box-Rectangular Drawings without Designated Corners . . 182
7.4.1 Box-Rectangular Drawings of G with A 3......... 183
7.4.2 Box-Rectangular Drawings of G with A 4......... 193
7.5 Bibliographic Notes..................................... 195
8. Orthogonal Drawing 197
8.1 Introduction............................................ 197
8.2 Orthogonal Drawing and Network Flow..................... 198
8.2.1 Orthogonal Representation........................ 198
8.2.2 Flow Network..................................... 201
8.2.3 Finding Bend-Optimal Drawing..................... 202
8.3 Linear Algorithm for Bend-Optimal Drawing............... 208
8.3.1 Genealogical Tree................................ 211
8.3.2 Assignment and Labeling ..........................213
8.3.3 Feasible Orthogonal Drawing...................... 217
8.3.4 Algorithm........................................ 224
8.4 Orthogonal Grid Drawing................................. 227
8.5 Orthogonal Drawings without Bends....................... 229
8.6 Bibliographic Notes.................................... 231
9. Octagonal Drawing 233
9.1 Introduction............................................ 233
9.2 Good Slicing Graphs . .................................. 235
9.3 Octagonal Drawing....................................... 238
9.3.1 Algorithm Octagonal-Draw......................... 239
9.3.2 Embedding a Slicing Path......................... 243
9.3.3 Correctness and Time Complexity ................. 249
9.4 Bibliographic Notes.................................... 250
Appendix A Planar Embedding 253
A.l Introduction............................................ 253
A.2 Planarity Testing....................................... 254
A. 2.1 si-Numbering..................................... 255
A.2.2 Bush Form and PQ-Tree............................. 259
Contents xiii
A.2.3 Planarity Testing Algorithm..........................263
A.3 Finding Planar Embedding...................................266
A.3.1 Algorithm for Extending Au into Adj..................267
A.3.2 Algorithm for Constructing Au........................271
A.4 Bibliographic Notes....................................... 277
Bibliography 281
Index 291
|
| any_adam_object | 1 |
| author | Nishizeki, Takao Rahman, Saidur |
| author_facet | Nishizeki, Takao Rahman, Saidur |
| author_role | aut aut |
| author_sort | Nishizeki, Takao |
| author_variant | t n tn s r sr |
| building | Verbundindex |
| bvnumber | BV019984496 |
| classification_rvk | SK 890 ST 132 |
| ctrlnum | (OCoLC)253308613 (DE-599)BVBBV019984496 |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV019984496 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:08Z |
| institution | BVB |
| isbn | 9812560335 9789812560339 |
| language | English |
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| owner_facet | DE-384 DE-20 DE-188 DE-739 |
| physical | xiii, 295 Seiten Illustrationen, Diagramme |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | World Scientific |
| record_format | marc |
| series | Lecture notes series on computing |
| series2 | Lecture notes series on computing |
| spelling | Nishizeki, Takao Verfasser aut Planar graph drawing Takao Nishizeki, Saidur Rahman New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai World Scientific [2004] © 2004 xiii, 295 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes series on computing vol. 12 Graphenzeichnen (DE-588)4706480-8 gnd rswk-swf Visualisierung (DE-588)4188417-6 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Planarer Graph (DE-588)4174783-5 gnd rswk-swf Graphenzeichnen (DE-588)4706480-8 s DE-604 Planarer Graph (DE-588)4174783-5 s Visualisierung (DE-588)4188417-6 s Algorithmus (DE-588)4001183-5 s Rahman, Saidur Verfasser aut Lecture notes series on computing vol. 12 (DE-604)BV007221225 12 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013306513&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nishizeki, Takao Rahman, Saidur Planar graph drawing Lecture notes series on computing Graphenzeichnen (DE-588)4706480-8 gnd Visualisierung (DE-588)4188417-6 gnd Algorithmus (DE-588)4001183-5 gnd Planarer Graph (DE-588)4174783-5 gnd |
| subject_GND | (DE-588)4706480-8 (DE-588)4188417-6 (DE-588)4001183-5 (DE-588)4174783-5 |
| title | Planar graph drawing |
| title_auth | Planar graph drawing |
| title_exact_search | Planar graph drawing |
| title_full | Planar graph drawing Takao Nishizeki, Saidur Rahman |
| title_fullStr | Planar graph drawing Takao Nishizeki, Saidur Rahman |
| title_full_unstemmed | Planar graph drawing Takao Nishizeki, Saidur Rahman |
| title_short | Planar graph drawing |
| title_sort | planar graph drawing |
| topic | Graphenzeichnen (DE-588)4706480-8 gnd Visualisierung (DE-588)4188417-6 gnd Algorithmus (DE-588)4001183-5 gnd Planarer Graph (DE-588)4174783-5 gnd |
| topic_facet | Graphenzeichnen Visualisierung Algorithmus Planarer Graph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013306513&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007221225 |
| work_keys_str_mv | AT nishizekitakao planargraphdrawing AT rahmansaidur planargraphdrawing |