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Spanning Trees and Optimization Problems [Kietas viršelis]

(National Taiwan University, Taipei, Taiwan), (Shu-Te University, KaoShiung, Taiwan)
  • Formatas: Hardback, 200 pages, aukštis x plotis: 234x156 mm, weight: 417 g, 1 Tables, black and white; 67 Illustrations, black and white
  • Serija: Discrete Mathematics and Its Applications
  • Išleidimo metai: 27-Jan-2004
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584884363
  • ISBN-13: 9781584884361
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 200 pages, aukštis x plotis: 234x156 mm, weight: 417 g, 1 Tables, black and white; 67 Illustrations, black and white
  • Serija: Discrete Mathematics and Its Applications
  • Išleidimo metai: 27-Jan-2004
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584884363
  • ISBN-13: 9781584884361
Kitos knygos pagal šią temą:
A textbook for graduate or advanced undergraduate students in computer science, electrical or industrial engineering, and mathematics on an area important to algorithm design. It covers the full spectrum of spanning tree algorithms from classical computer science to modern applications. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under one cover spanning tree properties, classical results, and recent research developments.Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees.With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book 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

Recenzijos

" will supplement nicely undergraduate courses in discrete mathematics and graph theory Summing Up: Recommended for upper-division undergraduates through faculty." - CHOICE, November 2004, Vol. 42, No. 3

Spanning Trees
1(9)
Counting Spanning Trees
1(8)
Minimum Spanning Trees
9(14)
Introduction
9(2)
Boruvka's Algorithm
11(2)
Prim's Algorithm
13(2)
Kruskal's Algorithm
15(2)
Applications
17(1)
Cable TV
17(1)
Circuit design
17(1)
Islands connection
17(1)
Clustering gene expression data
17(1)
MST-based approximations
18(1)
Summary
18(5)
Bibliographic Notes and Further Reading
19(1)
Exercises
20(3)
Shortest-Paths Trees
23(18)
Introduction
23(2)
Dijkstra's Algorithm
25(8)
The Bellman-Ford Algorithm
33(2)
Applications
35(3)
Multicast
37(1)
SPT-based approximations
37(1)
Summary
38(3)
Bibliographic Notes and Further Reading
38(1)
Exercises
39(2)
Minimum Routing Cost Spanning Trees
41(44)
Introduction
41(3)
Approximating by a Shortest-Paths Tree
44(3)
A simple analysis
44(2)
Solution decomposition
46(1)
Approximating by a General Star
47(11)
Separators and general stars
47(5)
A 15/8-approximation algorithm
52(3)
A 3/2-approximation algorithm
55(2)
Further improvement
57(1)
A Reduction to the Metric Case
58(4)
A Polynomial Time Approximation Scheme
62(17)
Overview
62(4)
The δ-spine of a tree
66(3)
Lower bound
69(1)
From trees to stars
70(4)
Finding an optimal k-star
74(5)
Applications
79(3)
Network design
79(1)
Computational biology
79(3)
Summary
82(3)
Bibliographic Notes and Further Reading
82(1)
Exercises
83(2)
Optimal Communication Spanning Trees
85(44)
Introduction
85(2)
Product-Requirement
87(17)
Overview
87(1)
Preliminaries
88(3)
Approximating by 2-stars
91(7)
A polynomial time approximation scheme
98(6)
Sum-Requirement
104(5)
Multiple Sources
109(15)
Computational complexity for fixed p
110(5)
A PTAS for the 2-MRCT
115(9)
Applications
124(1)
Summary
125(4)
Bibliographic Notes and Further Reading
125(2)
Exercises
127(2)
Balancing the Tree Costs
129(18)
Introduction
129(1)
Light Approximate Shortest-Paths Trees
130(6)
Overview
130(1)
The algorithm
131(3)
The analysis of the algorithm
134(2)
Light Approximate Routing Cost Spanning Trees
136(7)
Overview
136(1)
The algorithm
137(3)
The performance analysis
140(3)
On general graphs
143(1)
Applications
143(1)
Summary
144(3)
Bibliographic Notes and Further Reading
144(1)
Exercises
145(2)
Steiner Trees and Some Other Problems
147(28)
Steiner Minimal Trees
147(7)
Approximation by MST
148(3)
Improved approximation algorithms
151(3)
Trees and Diameters
154(8)
Eccentricities, diameters, and radii
154(3)
The minimum diameter spanning trees
157(5)
Maximum Leaf Spanning Trees
162(6)
Leafy trees and leafy forests
162(3)
The algorithm
165(1)
Performance ratio
166(2)
Some Other Problems
168(7)
Network design
169(1)
Computational biology
170(3)
Bibliographic Notes and Further Reading
173(1)
Exercises
174(1)
References 175(8)
Index 183


Wu\, Bang Ye; Chao\, Kun-Mao