Probability theory of classical euclidean optimization problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Lecture notes in mathematics
1675 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 152 S. graph. Darst. |
| ISBN: | 3540636668 |
Internformat
MARC
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| 100 | 1 | |a Yukich, Joseph E. |d 1956- |e Verfasser |0 (DE-588)118121766 |4 aut | |
| 245 | 1 | 0 | |a Probability theory of classical euclidean optimization problems |c J. E. Yukich |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a X, 152 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1675 | |
| 650 | 4 | |a Combinatorial probabilities | |
| 650 | 4 | |a Mathematical optimization | |
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| 650 | 0 | 7 | |a Kombinatorische Optimierung |0 (DE-588)4031826-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804126318588067840 |
|---|---|
| adam_text | CONTENTS
1. Introduction 1
1.1. Chief Goals 1
1.2. A Brief History 3
1.3. Methods 5
1.4. Definitions 7
2. Subadditivity and Superadditivity 9
2.1. Geometric Subadditivity 9
2.2. Geometric Superadditivity, Boundary Punctionals 12
3. Subadditive and Superadditive Euclidean Functional .... 18
3.1. Definitions 18
3.2. Growth Bounds 20
3.3. Smoothness 22
3.4. Closeness of a Functional to Its Canonical Boundary Functional . . 25
4. Asymptotics for Euclidean Functional: The Uniform Case . . 32
4.1. Limit Theorems for Euclidean Functionals Lp, 1 p d 34
4.2. Limit Theorems for Euclidean Functionals Lp, p d 37
4.3. Applications to Problems in Combinatorial Optimization 41
4.4. Ergodic Theorems, Superadditive Functionals 47
4.5. Concluding Remarks 51
5. Rates of Convergence and Heuristics 53
5.1. Rates of Convergence in the Basic Limit Theorem 53
5.2. Sharper Rates of Convergence in the Basic Limit Theorem 54
5.3. Optimally of Rates 56
5.4. Analysis of Partitioning Heuristics 57
5.5. Concluding Remarks, Open Questions 62
6. Isoperimetry and Concentration Inequalities 64
6.1. Azuma s Inequality 64
6.2. The Rhee Talagrand Concentration Inequalities 67
6.3. Isoperimetry 70
6.4. Isoperimetry and the Power Weighted MST 72
6.5. Large Deviations 74
7. Umbrella Theorems for Euclidean Functionals 78
7.1. The Basic Umbrella Theorem 78
7.2. Proof of the Basic Umbrella Theorem 80
7.3. Extensions of the Umbrella Theorem 84
X
8. Applications and Examples 97
8.1. Steiner Minimal Spanning Trees 97
8.2. Semi Matchings 98
8.3. k Nearest Neighbors Graph 101
8.4. The Many Traveling Salesman Problem 105
8.5. The Greedy Matching Heuristic 107
8.6. The Directed TSP 108
9. Minimal Triangulations 110
9.1. Introduction 110
9.2. The Boundary Triangulation Functional 114
9.3. Minimal Triangulations are Subadditive and Smooth 115
9.4. Boundary Minimal Triangulations 117
9.5. Closeness in Mean 118
9.6. The Probabilistic Plateau Functional 122
10. Geometric Location Problems 126
10.1. Statement of Problem 126
10.2. Additional Remarks 129
11. Worst Case Growth Rates 131
11.1. Introduction 131
11.2. Superadditivity 132
11.3. Closeness 134
11.4. Concluding Remarks 136
Bibliography 138
Index 149
|
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| author | Yukich, Joseph E. 1956- |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:33Z |
| institution | BVB |
| isbn | 3540636668 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007947080 |
| oclc_num | 246274264 |
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| physical | X, 152 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Yukich, Joseph E. 1956- Verfasser (DE-588)118121766 aut Probability theory of classical euclidean optimization problems J. E. Yukich Berlin [u.a.] Springer 1998 X, 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1675 Combinatorial probabilities Mathematical optimization Random graphs Stochastic geometry Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 s Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 s Kombinatorische Optimierung (DE-588)4031826-6 s Stochastische Geometrie (DE-588)4133202-7 s DE-604 Lecture notes in mathematics 1675 (DE-604)BV000676446 1675 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007947080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yukich, Joseph E. 1956- Probability theory of classical euclidean optimization problems Lecture notes in mathematics Combinatorial probabilities Mathematical optimization Random graphs Stochastic geometry Zufallsgraph (DE-588)4277661-2 gnd Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| subject_GND | (DE-588)4277661-2 (DE-588)4132446-8 (DE-588)4031826-6 (DE-588)4133202-7 |
| title | Probability theory of classical euclidean optimization problems |
| title_auth | Probability theory of classical euclidean optimization problems |
| title_exact_search | Probability theory of classical euclidean optimization problems |
| title_full | Probability theory of classical euclidean optimization problems J. E. Yukich |
| title_fullStr | Probability theory of classical euclidean optimization problems J. E. Yukich |
| title_full_unstemmed | Probability theory of classical euclidean optimization problems J. E. Yukich |
| title_short | Probability theory of classical euclidean optimization problems |
| title_sort | probability theory of classical euclidean optimization problems |
| topic | Combinatorial probabilities Mathematical optimization Random graphs Stochastic geometry Zufallsgraph (DE-588)4277661-2 gnd Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| topic_facet | Combinatorial probabilities Mathematical optimization Random graphs Stochastic geometry Zufallsgraph Kombinatorische Wahrscheinlichkeitstheorie Kombinatorische Optimierung Stochastische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007947080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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