Graph Algorithms 3
Chapter 17．Graph Properties and Types 3
17.1 Glossary 7
17.2 Graph ADT 16
17.3 Adjacency-Matrix Representation 21
17.4 Adjacency-Lists Representation 27
17.5 Variations,Extensions,and Costs 31
17.6 Graph Generators 40
17.7 Simple,Euler,and Hamilton Paths 50
17.8 Graph-Processing Problems 64
Chapter 18．Graph Search 75
18.1 Exploring a Maze 76
18.2 Depth-First Search 81
18.3 Graph-Search ADT Functions 86
18.4 Properties of DFS Forests 91
18.5 DFS Algorithms 99
18.6 Separability and Biconnectivity 106
18.7 Breadth-First Search 114
18.8 Generalized Graph Search 124
18.9 Analysis of Graph Algorithms 133
Chapter 19．Digraphs and DAGs 141
19.1 Glossary and Rules of the Game 144
19.2 Anatomy of DFS in Digraphs 152
19.3 Reachability and Transitive Closure 161
19.4 Equivalence Relations and Partial Orders 174
19.5 DAGs 178
19.6 Topological Sorting 183
19.7 Reachability in DAGs 193
19.8 Strong Components in Digraphs 196
19.9 Transitive Closure Revisited 208
19.10 Perspective 212
Chapter 20．Minimum Spanning Trees 219
20.1 Representations 222
20.2 Underlying Principles of MST Algorithms 228
20.3 Prim's Algorithm and Priority-First Search 235
20.4 Kruskal's Algorithm 246
20.5 Boruvka's Algorithm 252
20.6 Comparisons and Improvements 255
20.7 Euclidean MST 261
Chapter 21．Shortest Paths 265
21.1 Underlying Principles 273
21.2 Dijkstra's algorithm 280
21.3 All-Pairs Shortest Paths 290
21.4 Shortest Paths in Acyclic Networks 300
21.5 Euclidean Networks 308
21.6 Reduction 314
21.7 Negative Weights 331
21.8 Perspective 350
Chapter 22．Network Flows 353
22.1 Flow Networks 359
22.2 Augmenting-Path Maxflow Algorithms 370
22.3 Preflow-Push Maxflow Algorithms 396
22.4 Maxflow Reductions 411
22.5 Mincost Flows 429
22.6 Network Simplex Algorithm 439
22.7 Mincost-Flow Reductions 457
22.8 Perspective 467
References for Part Five 473
Index 475