Probability theory and combinatorial optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Siam
1997
|
| Series: | National Science Foundation / Conference Board of the Mathematical Sciences: CBMS-NSF regional conference series in applied mathematics
69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 159 S. graph. Darst. |
| ISBN: | 0898713803 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | J. MICHAEL STEELE WHARTON SCHOOL UNIVERSITY OF PENNSYLVANIA
PHILADELPHIA, PENNSYLVANIA PROBABILITY THEORY AND COMBINATORIAL
OPTIMIZATION SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA
CONTENTS PREFACE VII CHAPTER 1. FIRST VIEW OF PROBLEMS AND METHODS 1
1.1. A FIRST EXAMPLE: LONG COMMON SUBSEQUENCES 1 1.2. SUBADDITIVITY AND
EXPECTED VALUES 2 1.3. AZUMA S INEQUALITY AND A FIRST APPLICATION 4 1.4.
A SECOND EXAMPLE: THE INCREASING-SUBSEQUENCE PROBLEM 6 1.5. FLIPPING
AZUMA S INEQUALITY. 10 1.6. CONCENTRATION ON RATES 13 1.7. DYNAMIC
PROGRAMMING 16 1.8. KINGMAN S SUBADDITIVE ERGODIC THEOREM 18 1.9.
OBSERVATIONS ON SUBADDITIVE SUBSEQUENCES 21 1.10. ADDITIONAL NOTES. 24
CHAPTER 2. CONCENTRATION OF MEASURE AND THE CLASSICAL THEOREMS 27 2.1.
THE TSP AND A QUICK APPLICATION OF AZUMA S INEQUALITY. 27 2.2. EASY SIZE
BOUNDS 30 2.3. ANOTHER MEAN POISSONIZATION 30 2.4. THE
BEARDWOOD-HALTON-HAMMERSLEY THEOREM 33 2.5. KARP S PARTITIONING
ALGORITHMS 40 2.6. INTRODUCTION TO THE SPACE-FILLING CURVE HEURISTIC 41
2.7. ASYMPTOTICS FOR THE SPACE-FILLING CURVE HEURISTIC 43 2.8.
ADDITIONAL NOTES 49 CHAPTER 3. MORE GENERAL METHODS 53 3.1. SUBADDITIVE
EUCLIDEAN FUNCTIONALS 53 3.2. EXAMPLES: GOOD, BAD, AND FORTHCOMING 58
3.3. A GENERAL L BOUND 59 3.4. SIMPLE SUBADDITIVITY AND GEOMETRIC
SUBADDITIVITY 60 V VI CONTENTS 3.5. A CONCENTRATION INEQUALITY 61 3.6.
MINIMAL MATCHING 63 3.7. TWO-SIDED BOUNDS AND FIRST CONSEQUENCES 65 3.8.
ROOTED DUALS AND THEIR APPLICATIONS 68 3.9. LOWER BOUNDS AND BEST
POSSIBILITIES 71 3.10. ADDITIONAL REMARKS 75 CHAPTER 4. PROBABILITY IN
GREEDY ALGORITHMS AND LINEAR PROGRAMMING 77 4.1. ASSIGNMENT PROBLEM 77
4.2. SIMPLEX METHOD FOR THEORETICIANS 82 4.3. DYER-FRIEZE-MCDIARMID
INEQUALITY 84 4.4. DEALING WITH INTEGRAL CONSTRAINTS 88 4.5.
DISTRIBUTIONAL BOUNDS 89 4.6. BACK TO THE FUTURE 91 4.7. ADDITIONAL
REMARKS 93 CHAPTER 5. DISTRIBUTIONAL TECHNIQUES AND THE OBJECTIVE METHOD
95 5.1. MOTIVATION FOR A METHOD 95 5.2. SEARCHING FOR A CANDIDATE OBJECT
96 5.3. TOPOLOGY FOR NICE SETS 100 5.4. INFORMATION ON THE INFINITE TREE
102 5.5. DENOUMENT 103 5.6. CENTRAL LIMIT THEORY 108 5.7. CONDITIONING
METHOD FOR INDEPENDENCE 110 5.8. DEPENDENCY GRAPHS AND THE CLT 112 5.9.
ADDITIONAL REMARKS 117 CHAPTER 6. TALAGRAND S ISOPERIMETRIC THEORY 119
6.1. TALAGRAND S ISOPERIMETRIC THEORY 119 6.2. TWO GEOMETRIC
APPLICATIONS OF THE ISOPERIMETRIC INEQUALITY. . . . . 121 6.3.
APPLICATION TO THE LONGEST-INCREASING-SUBSEQUENCE PROBLEM. . . . 125
6.4. PROOF OF THE ISOPERIMETRIC INEQUALITY. 128 6.5. APPLICATION AND
COMPARISON IN THE THEORY OF HEREDITARY SETS. . . . 131 6.6. SUPREMA OF
LINEAR FUNCTIONALS 133 6.7. TAIL OF THE ASSIGNMENT PROBLEM 135 6.8.
FURTHER APPLICATIONS OF TALAGRAND S ISOPERIMETRIC INEQUALITIES. . . 140
6.9. FINAL CONSIDERATIONS ON RELATED WORK 140 BIBLIOGRAPHY 143 INDEX 157
|
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| author | Steele, John Michael 1949- |
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| callnumber-raw | QA273.45.S74 1997 |
| callnumber-search | QA273.45.S74 1997 |
| callnumber-sort | QA 3273.45 S74 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 196 SK 800 SK 890 |
| classification_tum | MAT 602f |
| ctrlnum | (OCoLC)312915418 (DE-599)BVBBV011269313 |
| dewey-full | 519.7 519.720 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 519.7 20 |
| dewey-search | 519.7 519.7 20 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:53Z |
| institution | BVB |
| isbn | 0898713803 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007567104 |
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| physical | VIII, 159 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Siam |
| record_format | marc |
| series2 | National Science Foundation / Conference Board of the Mathematical Sciences: CBMS-NSF regional conference series in applied mathematics |
| spelling | Steele, John Michael 1949- Verfasser (DE-588)122585534 aut Probability theory and combinatorial optimization J. Michael Steele Philadelphia Siam 1997 VIII, 159 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier National Science Foundation / Conference Board of the Mathematical Sciences: CBMS-NSF regional conference series in applied mathematics 69 Probabilities Combinatorial optimization Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Conference Board of the Mathematical Sciences: CBMS-NSF regional conference series in applied mathematics National Science Foundation 69 (DE-604)BV000016696 69 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007567104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steele, John Michael 1949- Probability theory and combinatorial optimization Probabilities Combinatorial optimization Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4031826-6 |
| title | Probability theory and combinatorial optimization |
| title_auth | Probability theory and combinatorial optimization |
| title_exact_search | Probability theory and combinatorial optimization |
| title_full | Probability theory and combinatorial optimization J. Michael Steele |
| title_fullStr | Probability theory and combinatorial optimization J. Michael Steele |
| title_full_unstemmed | Probability theory and combinatorial optimization J. Michael Steele |
| title_short | Probability theory and combinatorial optimization |
| title_sort | probability theory and combinatorial optimization |
| topic | Probabilities Combinatorial optimization Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Probabilities Combinatorial optimization Wahrscheinlichkeitstheorie Kombinatorische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007567104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016696 |
| work_keys_str_mv | AT steelejohnmichael probabilitytheoryandcombinatorialoptimization |