Complexity and approximation of fundamental problems in computational convexity:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130809-1140413-0-5 Inhaltsverzeichnis |
| Beschreibung: | VIII, 147 S. Ill., graph. Darst. |
Internformat
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Datensatz im Suchindex
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| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 OVERVIEW AND ORGANIZATION OF THE THESIS 1
1.2 COMPUTATIONAL CONVEXITY 2
1.2.1 CLASSIC PROBLEMS 3
1.2.2 APPLICATIONS IN PRACTICE 8
1.3 GENERAL NOTATION AND BACKGROUND 15
1.4 ACKNOWLEDGMENTS 17
2 SYMMETRY COEFFICIENTS IN GEOMETRIC INEQUALITIES 19
2.1 INTRODUCTION 19
2.2 RADII DEFINITIONS AND PRELIMINARIES 20
2.2.1 RADII DEFINITIONS 20
2.2.2 SOME SPECIFIC RADII 27
2.3 ASYMMETRY MEASURES 29
2.4 THE INEQUALITIES OF BOHNENBLUST AND LEICHTWEIFI 33
2.5 THE INEQUALITIES OF JUNG AND STEINHAGEN 36
2.6 AN INEQUALITY BETWEEN THE IN- AND CIRCUMRADIUS 37
2.7 JOHN S THEOREM 39
2.8 ASYMMETRY AND POLARITY 41
3 FIXED PARAMETER COMPLEXITY OF NORM MAXIMIZATION 45
3.1 INTRODUCTION AND PRELIMINARIES 45
3.2 FIXED PARAMETER COMPLEXITY OF NORM MAXIMIZATION 48
3.2.1 INTRACTABILITY 48
3.2.2 TRACTABILITY 56
3.3 APPROXIMATION 58
3.3.1 FPT-APPROXIMATION FOR FIXED ACCURACY 58
3.3.2 NO FPT-APPROXIMATION FOR VARIABLE ACCURACY 59
3.4 SOME IMPLICATIONS 60
4 CORE-SETS FOR CONTAINMENT UNDER HOMOTHETICS 63
4.1 INTRODUCTION 63
4.2 GEOMETRIC FOUNDATIONS 66
VII
HTTP://D-NB.INFO/1042923396
IMAGE 2
VIII CONTENTS
4.2.1 CORE-SETS AND CORE-RADII 66
4.2.2 OPTIMALITY CONDITIONS 68
4.2.3 SIDE NOTES 71
4.3 RADII IDENTITIES AND SMALL CORE-SETS 72
4.3.1 IDENTITIES BETWEEN DIFFERENT RADII 72
4.3.2 DIMENSION INDEPENDENCE FOR SPECIAL CONTAINER CLASSES 74
4.4 NO SUBLINEAR E-CORE-SETS 75
4.4.1 GENERAL (NON-SYMMETRIC) CONTAINERS 76
4.4.2 SYMMETRIC CONTAINERS/NORMED SPACES 77
5 HAUSDORFF MATCHING 83
5.1 INTRODUCTION 83
5.2 COMPUTING THE HAUSDORFF DISTANCE OF TWO POLY TOPES 84
5.2.1 PROBLEM STATEMENT AND GENERAL PROPERTIES 84
5.2.2 TRACTABILITY RESULTS 88
5.2.3 HARDNESS RESULTS 90
5.3 HAUSDORFF MATCHING UNDER HOMOTHETICS 95
5.3.1 OPTIMALITY CRITERION 96
5.3.2 HELLY-TYPE PROPERTIES 102
5.3.3 EXACT ALGORITHMS AND APPROXIMATIONS 104
6 BOUNDING THE PINNING NUMBER OF INTERSECTING BALLS 109
6.1 INTRODUCTION 109
6.2 CONES OF DIRECTIONS 112
6.2.1 ARBITRARY FAMILIES OF BALLS 112
6.2.2 ARBITRARY TRIPLE OF BALLS 114
6.3 PINNING THEOREM FOR INTERSECTING BALLS 120
6.4 EXTENSION TO OVALOIDS 121
6.4.1 BOUNDARY OF THE CONE OF DIRECTIONS OF THREE OVALOIDS 122
6.4.2 SCREENS 123
6.4.3 FIRST-ORDER APPROXIMATION OF CONES OF DIRECTIONS 125
6.4.4 PINNING THEOREM FOR OVALOIDS 126
SYMBOLS AND NOTIONS 131
BIBLIOGRAPHY 135
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| spelling | König, Stefan M. Verfasser aut Complexity and approximation of fundamental problems in computational convexity Stefan M. König 2013 VIII, 147 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Mit einer Zssfassung in dt. Sprache Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Computational convexity (DE-588)4618130-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Computational convexity (DE-588)4618130-1 s Komplexitätstheorie (DE-588)4120591-1 s Approximationstheorie (DE-588)4120913-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130809-1140413-0-5 http://mediatum.ub.tum.de/node?id=1140413 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130809-1140413-0-5 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026225051&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | König, Stefan M. Complexity and approximation of fundamental problems in computational convexity Komplexitätstheorie (DE-588)4120591-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Computational convexity (DE-588)4618130-1 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4120913-8 (DE-588)4618130-1 (DE-588)4113937-9 |
| title | Complexity and approximation of fundamental problems in computational convexity |
| title_auth | Complexity and approximation of fundamental problems in computational convexity |
| title_exact_search | Complexity and approximation of fundamental problems in computational convexity |
| title_full | Complexity and approximation of fundamental problems in computational convexity Stefan M. König |
| title_fullStr | Complexity and approximation of fundamental problems in computational convexity Stefan M. König |
| title_full_unstemmed | Complexity and approximation of fundamental problems in computational convexity Stefan M. König |
| title_short | Complexity and approximation of fundamental problems in computational convexity |
| title_sort | complexity and approximation of fundamental problems in computational convexity |
| topic | Komplexitätstheorie (DE-588)4120591-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Computational convexity (DE-588)4618130-1 gnd |
| topic_facet | Komplexitätstheorie Approximationstheorie Computational convexity Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1140413 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130809-1140413-0-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026225051&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT konigstefanm complexityandapproximationoffundamentalproblemsincomputationalconvexity |