Steiner minimal trees:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Academic Publishers
1998
|
| Series: | Nonconvex Optimization and Its Applications
23 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XI, 319 Seiten |
| ISBN: | 0792349830 |
Staff View
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| 245 | 1 | 0 | |a Steiner minimal trees |c by Dietmar Cieslik, Ernst-Moritz-Arndt University, Greifswald, Germany |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Academic Publishers |c 1998 | |
| 300 | |a XI, 319 Seiten | ||
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| 490 | 1 | |a Nonconvex Optimization and Its Applications |v 23 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE ix
1 INTRODUCTION 1
1.1 The Historical Genesis 2
1.2 Networks 8
1.3 Spaces 15
1.4 Steiner s Problem 42
1.5 How to Attack Steiner s Problem 46
2 SMT AND MST IN METRIC SPACES A
SURVEY 49
2.1 Basic Properties 50
2.2 The Algorithmic Complexity to find an MST 54
2.3 Examples 71
2.4 Approximations and Heuristics 83
3 FERMAT S PROBLEM IN BANACH
MINKOWSKI SPACES 91
3.1 Introduction to Fermat s Problem 92
3.2 Hulls of a Finite Set and the Set of Torricelli Points 95
3.3 Fermat s Problem in Several Specific Planes 99
3.4 Geometric Constructions for Torricelli Points in Banach
Minkowski Planes 110
3.5 General Solution Methods 112
3.6 Generalizations 122
4 THE DEGREES OF THE VERTICES IN
SHORTEST TREES 125
4.1 Upper Bounds for the Degrees of the Vertices 125
4.2 The Degrees of Vertices in a k SMT 128
4.3 The Degrees of Vertices in an SMT 137
4.4 The First Special Case: Finite Dimensional £p Spaces 143
4.5 The Second Special Case: Banach Minkowski Planes 150
4.6 Degree Constraint Trees 154
4.7 Further Results and Remarks 160
5 1 STEINER MINIMAL TREES 163
5.1 A Polynomially Bounded Algorithm 164
5.2 Examples 168
5.3 The Generalization to k SMT 172
6 METHODS TO CONSTRUCT SHORTEST
TREES 177
6.1 The Essentials of Steiner s Problem 178
6.2 The Geometric Structure of Shortest Trees 179
6.3 Reductions 189
6.4 Methods to Minimize the Function SZB 195
6.5 A Discretization 204
6.6 Approximation of Shortest Trees by Replacing One Space
by Another 213
6.7 A Graph Theoretical Approximation 218
6.8 Heuristic Approaches 224
6.9 Concluding Remarks 232
7 THE STEINER RATIO OF BANACH
MINKOWSKI SPACES 235
7.1 Basic Facts 236
7.2 An Upper Bound for the Steiner Ratio 239
7.3 Euclidean Spaces 242
7.4 A Lower Bound for the Steiner Ratio 246
7.5 The Steiner Ratio and several other Parameters in Discrete
Geometry 251
7.6 The Steiner ratio and the Embedding of Spaces 256
7.7 The Steiner Ratio for fc SMT s 264
7.8 Concluding Remarks 267
8 GENERALIZATIONS 271
8.1 Reasons why Steiner s Problem Should be Generalized 271
8.2 Shortest Networks with a Given Combinatorial Structure 273
8.3 Spanners 276
8.4 Searching More than one Tree 278
8.5 Fermat s Problem with Weighted Nodes 278
8.6 Steiner s Problem which is Steiner Point Weighted 281
8.7 Steiner s Problem in the Plane with Obstacles 282
8.8 Steiner s Problem in Spaces with a Weaker Triangle Inequal¬
ity 283
REFERENCES 287
INDEX 315
|
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| indexdate | 2024-12-20T10:29:04Z |
| institution | BVB |
| isbn | 0792349830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008389909 |
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| owner_facet | DE-703 DE-11 DE-188 |
| physical | XI, 319 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Nonconvex Optimization and Its Applications |
| series2 | Nonconvex Optimization and Its Applications |
| spellingShingle | Cieslik, Dietmar Steiner minimal trees Nonconvex Optimization and Its Applications Metrische ruimten gtt Netwerken gtt Steiner systems Steiner-Baum (DE-588)4228498-3 gnd |
| subject_GND | (DE-588)4228498-3 |
| title | Steiner minimal trees |
| title_auth | Steiner minimal trees |
| title_exact_search | Steiner minimal trees |
| title_full | Steiner minimal trees by Dietmar Cieslik, Ernst-Moritz-Arndt University, Greifswald, Germany |
| title_fullStr | Steiner minimal trees by Dietmar Cieslik, Ernst-Moritz-Arndt University, Greifswald, Germany |
| title_full_unstemmed | Steiner minimal trees by Dietmar Cieslik, Ernst-Moritz-Arndt University, Greifswald, Germany |
| title_short | Steiner minimal trees |
| title_sort | steiner minimal trees |
| topic | Metrische ruimten gtt Netwerken gtt Steiner systems Steiner-Baum (DE-588)4228498-3 gnd |
| topic_facet | Metrische ruimten Netwerken Steiner systems Steiner-Baum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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