Satisfiability characterizations of upward planarity problems
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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München
Verl. Dr. Hut
2014
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| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Informatik
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| 245 | 1 | 0 | |a Satisfiability characterizations of upward planarity problems |c Robert Zeranski |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 2014 A 3022 |
|---|---|
| DE-BY-TUM_katkey | 2004255 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040007902218 |
| _version_ | 1820876653560070144 |
| adam_text | CONTENTS
ABSTRACT I
ZUSAMMENFASSUNG III
ACKNOWLEDGEMENTS V
NOTATION VII
I INTRODUCTION 1
1 INTRODUCTION 3
1.1 THE THEOREM OF COOK 5
1.2 CONTRIBUTION AND OVERVIEW 6
2 PRELIMINARIES 9
2.1 COMPUTATIONAL COMPLEXITY 9
2.2 GRAPH THEORY 11
2.2.1 (DIRECTED) GRAPHS 11
2.2.2 DRAWINGS AND EMBEDDINGS 16
2.2.3 SPR-TREES 18
2.3 SATISFIABILITY 20
2.3.1 PROPOSITIONAL LOGIC 22
2.3.2 BASIC CONCEPTS OF SAT-SOLVING 25
2.3.3 PSEUDO-BOOLEAN SATISFIABILITY 28
3 AN EXEMPLARY APPLICATION OF SAT 31
3.1 MONOTONE NORMAL FORM EQUIVALENCE TEST 31
3.2 THE ALGORITHMS OF FREDMAN AND KHACHIYAN 33
3.3 SAT BASED FK-ALGORITHMS 36
3.3.1 UNIT PROPAGATION 36
3.3.2 SPLITTING VARIABLES 37
3.3.3 SIMULATING FK-ALGORITHM A 38
3.4 EVALUATION AND CONCLUSION 40
IX
HTTP://D-NB.INFO/1050732286
X
CONTENTS
II UPWARD DRAWINGS 45
4 UPWARD PLANARITY 47
4.1 UPWARD PLANAR DRAWINGS 47
4.1.1 BIMODALITY 48
4.1.2 OVERVIEW OF COMPLEXITY 50
4.2 QUASI-UPWARD PLANAR DRAWINGS 52
5 ALGORITHMS 55
5.1 FIXED EMBEDDINGS 55
5.1.1 ANGLE CHARACTERIZATION 55
5.1.2 UPWARD PLANARITY TESTING 59
5.1.3 BEND MINIMIZATION 63
5.2 EMBEDDING ENUMERATION (EE) 70
5.2.1 ENUMERATION METHOD 72
5.2.2 INCREMENTAL METHOD 72
5.2.3 SIMULTANEOUS METHOD 74
5.3 BRANCH-AND-BOUND (BB) 76
5.3.1 THE CORE ALGORITHM 77
5.3.2 MODIFICATIONS 78
5.3.3 BEND MINIMIZATION 82
5.4 PREPROCESSING 86
6 SAT FORMULATIONS 89
6.1 ORDERED EMBEDDING CHARACTERIZATION 89
6.1.1 ORDERED EMBEDDINGS 89
6.1.2 FORMULATION (OE) 90
6.1.3 VALIDITY 92
6.2 HANANI-TUTTE CHARACTERIZATION (FPSS) 99
6.3 HYBRID FORMULATIONS 100
6.4 ILP FORMULATIONS AND VARIANTS 101
7 OPTIMIZATION VARIANTS 103
7.1 UPWARD CROSSING MINIMIZATION 103
7.1.1 PBS FORMULATION 104
7.1.2 VALIDITY 106
7.1.3 ILP FORMULATION 115
7.2 MAXIMUM UPWARD PLANAR SUBGRAPH 115
7.2.1 PBS FORMULATION 117
7.2.2 VALIDITY 117
7.2.3 ILP FORMULATION AND VARIANTS 118
CONTENTS XI
III EXPERIMENTS & CONCLUSION 123
8 UPWARD PLANARITY: A COMPUTATIONAL STUDY 125
8.1 IMPLEMENTATION ISSUES 125
8.2 EXPERIMENTAL SETTING 127
8.3 INSTANCES 128
8.3.1 INSTANCES FROM LITERATURE 128
8.3.2 CONSTRUCTED INSTANCES 128
8.4 CENTRAL FINDINGS 131
8.5 ROME AND NORTH 131
8.6 GENERAL EVALUATION ON IHPRAND 133
8.7 SERIES-PARALLEL GRAPHS 149
8.8 DETAILS ON SAT 149
9 OPTIMIZATION VARIANTS: EXPERIMENTS 157
9.1 EXPERIMENTAL SETTING 157
9.2 INSTANCES 158
9.3 UPWARD CROSSING MINIMIZATION 159
9.3.1 COMPARISON OF EXACT APPROACHES 159
9.3.2 UPWARD PLANAR INSTANCES 160
9.3.3 EXPERIMENTS ON PBS AND HEURISTICS 162
9.4 MAXIMUM UPWARD PLANAR SUBGRAPH 170
10 CONCLUSION AND OUTLOOK 173
BIBLIOGRAPHY 177
LIST OF FIGURES 187
LIST OF TABLES 189
CURRICULUM VITAE 191
INDEX 193
|
| any_adam_object | 1 |
| author | Zeranski, Robert |
| author_facet | Zeranski, Robert |
| author_role | aut |
| author_sort | Zeranski, Robert |
| author_variant | r z rz |
| building | Verbundindex |
| bvnumber | BV041896866 |
| ctrlnum | (OCoLC)879879060 (DE-599)DNB1050732286 |
| dewey-full | 511.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.352 |
| dewey-search | 511.352 |
| dewey-sort | 3511.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| id | DE-604.BV041896866 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T04:08:21Z |
| institution | BVB |
| isbn | 9783843915557 3843915555 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027340677 |
| oclc_num | 879879060 |
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| owner_facet | DE-91 DE-BY-TUM DE-12 |
| physical | XII, 196 S. graph. Darst. 210 mm x 148 mm, 283 g |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Verl. Dr. Hut |
| record_format | marc |
| series2 | Informatik |
| spellingShingle | Zeranski, Robert Satisfiability characterizations of upward planarity problems Erfüllbarkeitsproblem (DE-588)4323820-8 gnd Gerichteter Graph (DE-588)4156815-1 gnd Graphenzeichnen (DE-588)4706480-8 gnd |
| subject_GND | (DE-588)4323820-8 (DE-588)4156815-1 (DE-588)4706480-8 (DE-588)4113937-9 |
| title | Satisfiability characterizations of upward planarity problems |
| title_auth | Satisfiability characterizations of upward planarity problems |
| title_exact_search | Satisfiability characterizations of upward planarity problems |
| title_full | Satisfiability characterizations of upward planarity problems Robert Zeranski |
| title_fullStr | Satisfiability characterizations of upward planarity problems Robert Zeranski |
| title_full_unstemmed | Satisfiability characterizations of upward planarity problems Robert Zeranski |
| title_short | Satisfiability characterizations of upward planarity problems |
| title_sort | satisfiability characterizations of upward planarity problems |
| topic | Erfüllbarkeitsproblem (DE-588)4323820-8 gnd Gerichteter Graph (DE-588)4156815-1 gnd Graphenzeichnen (DE-588)4706480-8 gnd |
| topic_facet | Erfüllbarkeitsproblem Gerichteter Graph Graphenzeichnen Hochschulschrift |
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