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Algorithmic Aspects of Graph Connectivity
  • 著
  • 出版社： CAMBRIDGE UNIVERSITY PRESS
  • ISBN：9780521878647
  • 出版时间：2008
  • 标注页数：375页
  • 文件大小：152MB
  • 文件页数：390页
  • 主题词：

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图书目录

1 Introduction1

1.1 Preliminaries of Graph Theory1

1.2 Algorithms and Complexities13

1.3 Flows and Cuts20

1.4 Computing Connectivities34

1.5 Representations of Cut Structures45

1.6 Connectivity by Trees57

1.7 Tree Hypergraphs60

2 Maximum Adjacency Ordering and Forest Decompositions65

2.1 Spanning Subgraphs Preserving Connectivity65

2.2 MA Ordering73

2.3 3-Edge-Connected Components86

2.4 2-Approximation Algorithms for Connectivity100

2.5 Fast Maximum-Flow Algorithms107

2.6 Testing Chordality112

3 Minimum Cuts114

3.1 Pendent Pairs in MA Orderings114

3.2 A Minimum-Cut Algorithm117

3.3 s-Proper k-Edge-Connected Spanning Subgraphs119

3.4 A Hierarchical Structure of MA Orderings123

3.5 Maximum Flows Between a Pendent Pair127

3.6 A Generalization of Pendent Pairs130

3.7 Practically Efficient Minimum-Cut Algorithms131

4 Cut Enumeration137

4.1 Enumerating All Cuts137

4.2 Enumerating Small Cuts140

4.3 Enumerating Minimum Cuts145

4.4 Upper Bounds on the Number of Small Cuts149

5 Cactus Representations153

5.1 Canonical Forms of Cactus Representations153

5.2 （s，t）-Cactus Representations171

5.3 Constructing Cactus Representations180

6 Extreme Vertex Sets191

6.1 Computing Extreme Vertex Sets in Graphs192

6.2 Algorithm for Dynamic Edges Incident to a Specified Vertex198

6.3 Optimal Contraction Ordering200

6.4 Minimum k-Subpartition Problem207

7 Edge Splitting217

7.1 Preliminaries217

7.2 Edge Splitting in Weighted Graphs220

7.3 Edge Splitting in Multigraphs226

7.4 Other Splittings232

7.5 Detachments237

7.6 Applications of Splittings240

8 Connectivity Augmentation246

8.1 Increasing Edge-Connectivity by One247

8.2 Star Augmentation249

8.3 Augmenting Multigraphs252

8.4 Augmenting Weighted Graphs254

8.5 More on Augmentation276

9 Source Location Problems282

9.1 Source Location Problem Under Edge-Connectivity Requirements283

9.2 Source Location Problem Under Vertex-Connectivity Requirements295

10 Submodular and Posimodular Set Functions304

10.1 Set Functions304

10.2 Minimizing Submodular and Posimodular Functions306

10.3 Extreme Subsets in Submodular and Posimodular Systems315

10.4 Optimization Problems over Submodular and Posimodular Systems320

10.5 Extreme Points of Base Polyhedron336

10.6 Minimum Transversal in Set Systems342

Bibliography357

Index371

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