Spanning trees and optimization problems:
"With logical organization, well-chosen topics, and easy-to-understand pseudocode, this book is not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. It will be a welcome addition to your reference shelf, whether your intere...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
Chapman & Hall/CRC
2004
|
| Series: | Discrete mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "With logical organization, well-chosen topics, and easy-to-understand pseudocode, this book is not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. It will be a welcome addition to your reference shelf, whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems."--BOOK JACKET. |
| Physical Description: | XV, 184 S. |
| ISBN: | 1584884363 |
Staff View
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Record in the Search Index
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| adam_text | DISCRETE MATHEMATICS AND ITS APPLICATIONS SPANNING TREES AND
OPTIMIZATION PROBLEMS BANG YE WU DEPARTMENT OF COMPUTER SCIENCE AND
INFORMATION ENGINEERING, SHU-TE UNIVERSITY, YEN-CHAU, KAOHSIUNG COUNTY,
TAIWAN 824 KUN-MAO CHAO DEPARTMENT OF COMPUTER SCIENCE AND INFORMATION
ENGINEERING, NATIONAL TAIWAN UNIVERSITY, TAIPEI, TAIWAN 106 CHAPMAN &
HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS 1 SPANNING TREES 1 1.1 COUNTING SPANNING TREES 1 2 MINIMUM
SPANNING TREES 9 2.1 INTRODUCTION 9 2.2 BORUEVKA S ALGORITHM 11 2.3
PRIM S ALGORITHM 13 2.4 KRUSKAL S ALGORITHM 15 2.5 APPLICATIONS 17 2.5.1
CABLE TV 17 2.5.2 CIRCUIT DESIGN 17 2.5.3 ISLANDS CONNECTION 17 2.5.4
CLUSTERING GENE EXPRESSION DATA 17 2.5.5 MST-BASED APPROXIMATIONS 18 2.6
SUMMARY 18 BIBLIOGRAPHIE NOTES AND FURTHER READING 19 EXERCISES 20 3
SHORTEST-PATHS TREES 23 3.1 INTRODUCTION 23 3.2 DIJKSTRA S ALGORITHM 25
3.3 THE BELLMAN-FORD ALGORITHM 33 3.4 APPLICATIONS 35 3.4.1 MULTICAST 37
3.4.2 SPT-BASED APPROXIMATIONS 37 3.5 SUMMARY 38 BIBLIOGRAPHIE NOTES AND
FURTHER READING 38 EXERCISES 39 4 MINIMUM ROUTING COST SPANNING TREES 41
4.1 INTRODUCTION 41 4.2 APPROXIMATING BY A SHORTEST-PATHS TREE 44 4.2.1
A SIMPLE ANALYSIS 44 4.2.2 SOLUTION DECOMPOSITION 46 4.3 APPROXIMATING
BY A GENERAL STAR 47 4.3.1 SEPARATORS AND GENERAL STARS 47 4.3.2 A
15/8-APPROXIMATION ALGORITHM 52 XI XII CONTENTS 4.3.3 A
3/2-APPROXIMATION ALGORITHM 55 4.3.4 FURTHER IMPROVEMENT 57 4.4 A
REDUCTION TO THE METRIE CASE 58 4.5 A POLYNOMIAL TIME APPROXIMATION
SCHEME 62 4.5.1 OVERVIEW 62 4.5.2 THE 5-SPINE OF A TREE 66 4.5.3 LOWER
BOUND 69 4.5.4 FROM TREES TO STARS 70 4.5.5 FINDING AN OPTIMAL FC-STAR
74 4.6 APPLICATIONS 79 4.6.1 NETWORK DESIGN 79 4.6.2 COMPUTATIONAL
BIOLOGY 79 4.7 SUMMARY 82 BIBLIOGRAPHIE NOTES AND FURTHER READING 82
EXERCISES 83 5 OPTIMAL COMMUNICATION SPANNING TVEES 85 5.1 INTRODUCTION
85 5.2 PRODUCT-REQUIREMENT 87 5.2.1 OVERVIEW 87 5.2.2 PRELIMINARIES 88
5.2.3 APPROXIMATING BY 2-STARS 91 5.2.4 A POLYNOMIAL TIME APPROXIMATION
SCHEME 98 5.3 SUM-REQUIREMENT 104 5.4 MULTIPLE SOURCES 109 5.4.1
COMPUTATIONAL COMPLEXITY FOR FIXED P 110 5.4.2 A PTAS FOR THE 2-MRCT 115
5.5 APPLICATIONS 124 5.6 SUMMARY 125 BIBLIOGRAPHIE NOTES AND FURTHER
READING 125 EXERCISES 127 6 BALANCING THE TREE COSTS 129 6.1
INTRODUCTION 129 6.2 LIGHT APPROXIMATE SHORTEST-PATHS TREES 130 6.2.1
OVERVIEW 130 6.2.2 THE ALGORITHM 131 6.2.3 THE ANALYSIS OF THE ALGORITHM
134 6.3 LIGHT APPROXIMATE ROUTING COST SPANNING TREES 136 6.3.1 OVERVIEW
136 6.3.2 THE ALGORITHM 137 6.3.3 THE PERFORMANCE ANALYSIS 140 6.3.4 ON
GENERAL GRAPHS 143 6.4 APPLICATIONS 143 6.5 SUMMARY 144 CONTENTS XIII
BIBLIOGRAPHIE NOTES AND FURTHER READING 144 EXERCISES 145 7 STEINER
TREES AND SOME OTHER PROBLEMS 147 7.1 STEINER MINIMAL TREES 147 7.1.1
APPROXIMATION BY MST 148 7.1.2 INIPROVED APPROXIMATION ALGORITHNIS 151
7.2 TREES AND DIAMETERS 154 7.2.1 ECCENTRICITIES, DIAMETERS, AND RADII
154 7.2.2 THE MINIMUM DIAMETER SPANNING TREES 157 7.3 MAXIMUM LEAF
SPANNING TREES 162 7.3.1 LEAFY TREES AND LEAFY FORESTS 162 7.3.2 THE
ALGORITHM 165 7.3.3 PERFORMANCE RATIO 166 7.4 SOME OTHER PROBLEMS 168
7.4.1 NETWORK DESIGN 169 7.4.2 COMPUTATIONAL BIOLOGY 170 BIBLIOGRAPHIE
NOTES AND FURTHER READING 173 EXERCISES 174 REFERENCES 175 INDEX 183
|
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| spelling | Wu, Bang Ye Verfasser aut Spanning trees and optimization problems Bang Ye Wu ; Kun-Mao Chao Boca Raton, FL [u.a.] Chapman & Hall/CRC 2004 XV, 184 S. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications "With logical organization, well-chosen topics, and easy-to-understand pseudocode, this book is not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. It will be a welcome addition to your reference shelf, whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems."--BOOK JACKET. Algorithme rasuqam Algoritmen gtt Arbre (Théorie des graphes) rasuqam Arbre couvrant rasuqam Bomen (wiskunde) gtt Optimaliseren gtt Optimisation mathématique rasuqam Otimização matemática larpcal Teoria dos grafos larpcal Datenverarbeitung Mathematical optimization Trees (Graph theory) Data processing Algorithmus (DE-588)4001183-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Algorithmus (DE-588)4001183-5 s Optimierung (DE-588)4043664-0 s DE-604 Chao, Kun-Mao Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010613541&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wu, Bang Ye Spanning trees and optimization problems Algorithme rasuqam Algoritmen gtt Arbre (Théorie des graphes) rasuqam Arbre couvrant rasuqam Bomen (wiskunde) gtt Optimaliseren gtt Optimisation mathématique rasuqam Otimização matemática larpcal Teoria dos grafos larpcal Datenverarbeitung Mathematical optimization Trees (Graph theory) Data processing Algorithmus (DE-588)4001183-5 gnd Optimierung (DE-588)4043664-0 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4043664-0 (DE-588)4113782-6 |
| title | Spanning trees and optimization problems |
| title_auth | Spanning trees and optimization problems |
| title_exact_search | Spanning trees and optimization problems |
| title_full | Spanning trees and optimization problems Bang Ye Wu ; Kun-Mao Chao |
| title_fullStr | Spanning trees and optimization problems Bang Ye Wu ; Kun-Mao Chao |
| title_full_unstemmed | Spanning trees and optimization problems Bang Ye Wu ; Kun-Mao Chao |
| title_short | Spanning trees and optimization problems |
| title_sort | spanning trees and optimization problems |
| topic | Algorithme rasuqam Algoritmen gtt Arbre (Théorie des graphes) rasuqam Arbre couvrant rasuqam Bomen (wiskunde) gtt Optimaliseren gtt Optimisation mathématique rasuqam Otimização matemática larpcal Teoria dos grafos larpcal Datenverarbeitung Mathematical optimization Trees (Graph theory) Data processing Algorithmus (DE-588)4001183-5 gnd Optimierung (DE-588)4043664-0 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Algorithme Algoritmen Arbre (Théorie des graphes) Arbre couvrant Bomen (wiskunde) Optimaliseren Optimisation mathématique Otimização matemática Teoria dos grafos Datenverarbeitung Mathematical optimization Trees (Graph theory) Data processing Algorithmus Optimierung Graphentheorie |
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