Crossings, curves, and constraints in graph drawing: = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Würzburg
Würzburg University Press
2014
|
| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis |
| Beschreibung: | IX, 222 Seiten Illustrationen, Diagramme |
| ISBN: | 9783958260023 |
Internformat
MARC
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| 245 | 1 | 0 | |a Crossings, curves, and constraints in graph drawing |b = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |c Martin Fink |
| 246 | 1 | 1 | |a Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| 264 | 1 | |a Würzburg |b Würzburg University Press |c 2014 | |
| 300 | |a IX, 222 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Julius-Maximilians-Universität Würzburg |d 2014 | ||
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Datensatz im Suchindex
| _version_ | 1804152553922887680 |
|---|---|
| adam_text | CONTENTS
PREFACE V
1 INTRODUCTION 1
2 PRELIMINARIES 11
2.1 GRAPHS 11
2.2 GRAPH DRAWING 12
2.3 COMPLEXITY AND NP-HARDNESS 17
I METRO MAPS 21
3 DRAWING METRO MAPS USING BEZIER CURVES 23
3.1 INTRODUCTION 23
3.2 PRELIMINARIES 28
3.3 BASIC ALGORITHM 30
3.3.1 FORCES ON VERTICES 31
3.3.2 FORCES ON TANGENTS AND CONTROL POINTS 31
3.3.3 AVOIDING CROSSINGS BY LIMITING FORCES 33
3.4 DECREASING THE VISUAL COMPLEXITY 33
3.5 CREATING A FEASIBLE INPUT DRAWING 35
3.6 IMPLEMENTATION AND TESTS 37
3.7 CONCLUDING REMARKS 41
4 METRO-LINE CROSSING MINIMIZATION 43
4.1 INTRODUCTION 43
4.2 GENERAL METRO-LINE CROSSING MINIMIZATION 49
4.2.1 NP-COMPLETENESS 49
4.2.2 RECOGNITION OF CROSSING-FREE INSTANCES 51
4.3 METRO-LINE CROSSING MINIMIZATION WITH PERIPHERY CONDITION 55
4.3.1 A 2SAT MODEL FOR MLCM-P 55
4.3.2 CROSSING-FREE SOLUTIONS 57
4.3.3 FIXED-PARAMETER TRACTABILITY 58
4.3.4 APPROXIMATING MLCM-P 59
4.4 THE PROBLEM PROPER-MLCM-P 60
4.5 MLCM WITH BOUNDED MAXIMUM DEGREE AND EDGE MULTIPLICITY 65
4.6 PRACTICAL CONSIDERATIONS ON METRO-LINE CROSSING MINIMIZATION 68
4.7 CONCLUDING REMARKS 71
VII
HTTP://D-NB.INFO/1058837176
CONTENTS
5 ORDERING METRO LINES BY BLOCK CROSSINGS 73
5.1 INTRODUCTION 73
5.2 BLOCK CROSSINGS ON A SINGLE EDGE 77
5.3 BLOCK CROSSINGS ON A PATH 80
5.3.1 BCM ON A PATH 80
5.3.2 MBCM ON A PATH 85
5.4 BLOCK CROSSINGS ON TREES 87
5.4.1 GENERAL TREES 88
5.4.2 UPWARD TREES 90
5.5 BLOCK CROSSINGS ON GENERAL GRAPHS 91
5.6 INSTANCES WITH BOUNDED MAXIMUM DEGREE AND EDGE MULTIPLICITY 96
5.6.1 RESTRICTED (M)BCM ON TREES 96
5.6.2 NP-HARDNESS OF RESTRICTED BCM AND MBCM 97
5.7 CONCLUDING REMARKS 103
II POINT-SET EMBEDDABILITY 105
6 POINT-SET EMBEDDABILITY AND LARGE CROSSING ANGLES 107
6.1 INTRODUCTION 107
6.2 STRAIGHT-LINE RAC AND AAC POINT-SET EMBEDDABILITY 110
6.3 AACI POINT-SET EMBEDDINGS 113
6.4 AAC
2
POINT-SET EMBEDDINGS 115
6.5 RAC3 POINT-SET EMBEDDINGS 116
6.6 CONCLUDING REMARKS 117
7 ORTHOGONAL POINT-SET EMBEDDABILITY ON THE GRID 119
7.1 INTRODUCTION 119
7.2 ORTHOGONAL POINT-SET EMBEDDABILITY WITH AT MOST ONE BEND PER EDGE
122
7.3 ORTHOGONAL POINT-SET EMBEDDABILITY WITH TWO OR THREE BENDS PER EDGE
.... 124
7.3.1 GENERAL POINT SETS 124
7.3.2 AREA MINIMIZATION 126
7.3.3 1-SPACED POINT SETS 129
7.4 PLANAR ORTHOGONAL POINT-SET EMBEDDABILITY WITH UNBOUNDED BEND
NUMBERS . 131
7.5 ORTHOGONAL POINT-SET EMBEDDABILITY WITHOUT PRESCRIBED MAPPING 133
7.6 NPOI EMBEDDINGS ON 1-SPACED POINT SETS WITHOUT PRESCRIBED MAPPING
136
7.7 CONCLUDING REMARKS 141
III BOUNDARY LABELING 143
8 ALGORITHMS FOR LABELING FOCUS REGIONS 145
8.1 INTRODUCTION 145
8.2 PROBLEM STATEMENTS AND MOTIVATIONS 152
8.2.1 RADIAL LEADERS 153
VIII
CONTENTS
8.2.2 FREE LEADERS 156
8.3 ALGORITHMS FOR THE RADIAL-LEADER MODEL 158
8.3.1 LABEL MAXIMIZATION WITH GIVEN CENTER 158
8.3.2 WEIGHTED LABEL MAXIMIZATION WITH GIVEN CENTER 159
8.3.3 LABEL MAXIMIZATION WITH VARIABLE CENTER POSITION 160
8.3.4 SECTOR MAXIMIZATION 162
8.4 EXTENSIONS 162
8.4.1 SIMULTANEOUS CLUSTERING AND LABELING 163
8.4.2 BEZIER POST-PROCESSING 169
8.5 CONCLUDING REMARKS 175
9 MANY-TO-ONE BOUNDARY LABELING WITH BACKBONES 177
9.1 INTRODUCTION 178
9.2 MINIMIZING THE TOTAL NUMBER OF LABELS 180
9.2.1 INFINITE BACKBONES 180
9.2.2 FINITE BACKBONES 186
9.3 LENGTH MINIMIZATION 188
9.3.1 INFINITE BACKBONES 188
9.3.2 FINITE BACKBONES 192
9.4 CROSSING MINIMIZATION 195
9.4.1 FIXED Y-ORDER OF LABELS 195
9.4.2 FLEXIBLE Y-ORDER OF LABELS 196
9.5 CONCLUDING REMARKS 204
10 CONCLUSION 207
BIBLIOGRAPHY 209
IX
|
| any_adam_object | 1 |
| author | Fink, Martin 1985- |
| author_GND | (DE-588)1058828150 |
| author_facet | Fink, Martin 1985- |
| author_role | aut |
| author_sort | Fink, Martin 1985- |
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| building | Verbundindex |
| bvnumber | BV042094343 |
| classification_rvk | SK 890 ST 134 ST 320 |
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| ctrlnum | (OCoLC)892491703 (DE-599)BVBBV042094343 |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| spelling | Fink, Martin 1985- Verfasser (DE-588)1058828150 aut Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Martin Fink Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Würzburg Würzburg University Press 2014 IX, 222 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Dissertation Julius-Maximilians-Universität Würzburg 2014 Beschriftung (DE-588)4298755-6 gnd rswk-swf NP-hartes Problem (DE-588)4621705-8 gnd rswk-swf Graphenzeichnen (DE-588)4706480-8 gnd rswk-swf Untergrundbahnlinie (DE-588)4467503-3 gnd rswk-swf Kreuzung (DE-588)4132427-4 gnd rswk-swf Digitale Karte (DE-588)4745787-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Graphenzeichnen (DE-588)4706480-8 s Untergrundbahnlinie (DE-588)4467503-3 s Digitale Karte (DE-588)4745787-9 s Beschriftung (DE-588)4298755-6 s Kreuzung (DE-588)4132427-4 s NP-hartes Problem (DE-588)4621705-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:20-opus-98235 978-3-95826-003-0 https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-98235 Resolving-System kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027535143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fink, Martin 1985- Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Beschriftung (DE-588)4298755-6 gnd NP-hartes Problem (DE-588)4621705-8 gnd Graphenzeichnen (DE-588)4706480-8 gnd Untergrundbahnlinie (DE-588)4467503-3 gnd Kreuzung (DE-588)4132427-4 gnd Digitale Karte (DE-588)4745787-9 gnd |
| subject_GND | (DE-588)4298755-6 (DE-588)4621705-8 (DE-588)4706480-8 (DE-588)4467503-3 (DE-588)4132427-4 (DE-588)4745787-9 (DE-588)4113937-9 |
| title | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| title_alt | Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| title_auth | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| title_exact_search | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| title_full | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Martin Fink |
| title_fullStr | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Martin Fink |
| title_full_unstemmed | Crossings, curves, and constraints in graph drawing = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen Martin Fink |
| title_short | Crossings, curves, and constraints in graph drawing |
| title_sort | crossings curves and constraints in graph drawing kreuzungen kurven und constraints beim zeichnen von graphen |
| title_sub | = Kreuzungen, Kurven und Constraints beim Zeichnen von Graphen |
| topic | Beschriftung (DE-588)4298755-6 gnd NP-hartes Problem (DE-588)4621705-8 gnd Graphenzeichnen (DE-588)4706480-8 gnd Untergrundbahnlinie (DE-588)4467503-3 gnd Kreuzung (DE-588)4132427-4 gnd Digitale Karte (DE-588)4745787-9 gnd |
| topic_facet | Beschriftung NP-hartes Problem Graphenzeichnen Untergrundbahnlinie Kreuzung Digitale Karte Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-98235 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027535143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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