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网络流：理论、算法与应用 英文版
作者：拉文德拉K.阿胡亚（Ravindra K.Ahuja）等著
出版社：机械工业出版社
出版时间：2005-05-01
ISBN：9787111159193
定价：¥108.00
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内容简介
本书全面介绍了经典的和现代的网络流技术，包括综合的理论、算法与应用。主要内容包括：路径、树与周期，算法设计与分析，最大流与最小流算法，分派与匹配，最小生成树，拉格朗日松弛与网络优化等。书中包含大量练习题，拓展了本书的内容，便于教学。本书特点■深入介绍功能强大的算法策略和分析工具，如数据缩放和势函数变量。■讨论有关网络优化的重要主题及实际解决方案，如拉格朗日松弛法。■包括广泛的文献注解，提供宝贵的历史背景和指导。■包含800多道难度不一的练习题。
作者简介
RavindraK.Ahuja：印度理工学院坎普尔分校工业与管理工程系副教授。1986年至1988年，他曾在麻省理工学院斯隆管理学院做访问学者，与沃林教授合作研究若干网络流问题的快速算法，这期间的工作促成了本书的面世。他的研究方向为网络流、组合优化、算法的计算测试。ThomasL.Magnanti：麻省理工学院斯隆管理学院管理科学系教授。他曾任美国运筹学会的会长和《OperationsResearch》杂志的主编。他是美国国家工程院院士。他的研究方向为大规模优化，包括网络设计、整数规划及其在通信、制造和交通中的应用。JamesB.Orlin：麻省理工学院斯隆管理学院运筹学教授。从1985年至1990年，他荣膺美国国家自然科学基金会颁发的总统青年学者奖。目前，他的研究方向为网络流、组合优化及物流学。
目录
1 INTRODUCTION, 1
1.1 Introduction, 1
1.2 Network Flow Problems, 4
1.3 Applications, 9
1.4 Summary, 18
Reference Notes, 19
Exercises, 20
2 PATHS, TREES, AND CYCLES, 28
2.1 Introduction, 23
2.2 Notation and Definitions, 24
2.3 Network Representations, 31
2.4 Network Transformations, 38
2.5 Summary, 46
Reference Notes, 47
Exercises, 47
3 ALGORITHM DESIGN AND ANALYSIS, 58
3.1 Introduction, 53
3.2 Complexity Analysis, 56
3.3 Developing Polynomial-Time Algorithms, 66
3.4 Search Algorithms, 73
3.5 Flow Decomposition Algorithms, 79
3.6 Summary, 84
Reference Notes, 85
Exercises, 86
4 SHORTEST PATIO: LABEL-SETTING ALG-ORITHMS, 93
4.1 Introduction, 93
4.2 Applications, 97
4.3 Tree of Shortest Paths, 106
4.4 Shortest Path Problems in Acyclic Networks, 107
4.5 Dijkstra's Algorithm, 108
4.6 Dial's Implementation, 113
4.7 Heap Implementations, 115
4.8 Radix Heap Implementation, 116
4.9 Summary, 121
Reference Notes, 122
Exercises, 124
5 SHORTEST PATHS:LABEL-CORRECTING ALGORITHM,133
5.1 Introduction, 133
5.2 Optimality Conditions, 135
5.3 Generic Label-Correcting Algorithms, 136
5.4 Special Implementations of the Modified Label-Correcting Algorithm, 141
5.5 Detecting Negative Cycles, 143
5.6 All-Pairs Shortest Path Problem, 144
5.7 Minimum Cost-to-Time Ratio Cycle Problem, 150
5.8 Summary, 154
Reference Notes, 156
Exercises, 157
6 MAXIMUM FLOWS:BASICC IDEAS, 168
6.1 Introduction, 166
6.2 Applications, 169
6.3 Flows and Cuts, 177
6.4 Generic Augmenting Path Algorithm, 180
6.5 Labeling Algorithm and the Max-Flow Min-Cut Theorem, 184
6.6 Combinatorial Implications of the Max-Flow Min-Cut Theorem, 188
6.7 Flows with Lower Bounds, 191
6.8 Summary, 196
Reference Notes, 197
Exercises, 198
7 MAXIMUM FLOWS:POLYNOMIAL ALG-ORITHMS,2O7
7.1 Introduction, 207
7.2 Distance Labels, 209
7.3 Capacity Scaling Algorithm, 210
7.4 Shortest Augmenting Path Algorithm, 213
7.5 Distance Labels and Layered Networks, 221
7.6 Generic Prefiow-Push Algorithm, 223
7.7 FIFO Prefiow-Push Algorithm, 231
7.8 Highest-Label Prefiow-Push Algorithm, 233
7.9 Excess Scaling Algorithm, 237
7.10 Summary, 241
Reference Notes, 241
Exercises, 243
8 MAXIMUM FLOWS:ADDITIONAL TOPICS,25O
8.1 Introduction, 250
8.2 Flows in Unit Capacity Networks, 252
8.3 Flows in Bipartite Networks, 255
8.4 Flows in Planar Undirected Networks, 260
8.5 Dynamic Tree Implementations, 265
8.6 Network Connectivity, 273
8.7 All-Pairs Minimum Value Cut Problem, 277
8.8 Summary, 285
Reference Notes, 287
Exercises, 288
9 MINLMUM COST FLOWS:BASIC ALGORITHMS,294
9.1 Introduction, 294
9.2 Applications, 298
9.3 Optimality Conditions, 306
9.4 Minimum Cost Flow Duality, 310
9.5 Relating Optimal Flows to Optimal Node Potentials, 315
9.6 Cycle-Canceling Algorithm and the Integrality Property, 317
9.7 Successive Shortest Path Algorithm, 320
9.8 Primal-Dual Algorithm, 324
9.9 Out-of-Kilter Algorithm, 326
9.10 Relaxation Algorithm, 332
9.11 Sensitivity Analysis, 337
9.12 Summary, 339
Reference Notes, 341
Exercises, 344
10 MINIMUM COST FLOWS:POLYNOMIAL ALGORITHMS,357
10.1 Introduction, 357
10.2 Capacity Scaling Algorithm, 360
10.3 Cost Scaling Algorithm, 362
10.4 Double Scaling Algorithm, 373
10.5 Minimum Mean Cycle-Canceling Algorithm, 376
10.6 Repeated Capacity Scaling Algorithm, 382
10.7 Enhanced Capacity Scaling Algorithm, 387
10.8 Summary, 395
Reference Notes, 396
Exercises, 397
11 MINIMUM COST FLOWS: NETWORK SIMPLEX ALGORITHMS, 402
11.1 Introduction, 402
11.2 Cycle Free and Spanning Tree Solutions, 405
11.3 Maintaining a Spanning Tree Structure, 409
11.4 Computing Node Potentials and Flows, 411
11.5 Network Simplex Algorithm, 415
11.6 Strongly Feasible Spanning Trees, 421
11.7 Network Simplex Algorithm for the Shortest Path Problem, 425
11.8 Network Simplex Algorithm for the Maximum Flow Problem, 430
11.9 Related Network Simplex Algorithms, 433
11.10 Sensitivity Analysis, 439
11.11 Relationship to Simplex Method, 441
11.12 Unimodularity Property, 447
11.13 Summary, 450
Reference Notes, 451
Exercises, 453
12 ASSIGNMENTS AND MATCHINGS, 461
12.1 Introduction, 461
12.2 Applications, 463
12.3 Bipartite Cardinality Matching Problem, 469
12.4 Bipartite Weighted Matching Problem, 470
12.5 Stable Marriage Problem, 473
12.6 Nonbipartite Cardinality Matching Problem, 475
12.7 Matchings and Paths, 494
12.8 Summary, 498
Reference Notes, 499
Exercises, 501
13 MINIMUM SPANNING TREES, 510
13.1 Introduction, 510
13.2 Applications, 512
13.3 Optimality Conditions, 516
13.4 Kruskai's Algorithm, 520
13.5 Prim's Algorithm, 523
13.6 Sollin's Algorithm, 526
13.7 Minimum Spanning Trees and Matroids, 528
13.8 Minimum Spanning Trees and Linear Programming, 530
13.9 Summary, 533
Reference Notes, 535
Exercises, 536
14 CONVEX COST FLOWS, 543
14.1 Introduction, 543
14.2 Applications, 546
14.3 Transformation to a Minimum Cost Flow Problem, 551
14.4 Pseudopolynomial-Time Algorithms, 554
14.5 Polynomial-Time Algorithm, 556
14.6 Summary, 560
Reference Notes, 561
Exercises, 562
15 GENERALIXED FLOWS, 568
15.1 Introduction, 566
15.2 Applications, 568
15.3 Augmented Forest Structures, 572
15.4 Determining Potentials and Flows for an Augmented Forest Structure, 577
15.5 Good Augmented Forests and Linear Programming Bases, 582
15.6 Generalized Network Simplex Algorithm, 583
15.7 Summary, 591
Reference Notes, 591
Exercises, 593
16 LAGRANGIAN RELAXATION AND NETWORK OPTLMIZATION, 598
16.1 Introduction, 598
16.2 Problem Relaxations and Branch and Bound, 602
16.3 Lagrangian Relaxation Technique, 605
16.4 Lagrangian Relaxation and Linear Programming, 615
16.5 Applications of Lagrangian Relaxation, 620
16.6 Summary, 635
Reference Notes, 637
Exercises, 638
17 MULTICOMMODITY FLOWS, 649
17.1 Introduction, 649
17.2 Applications, 653
17.3 Optimality Conditions, 657
17.4 Lagrangian Relaxation, 660
17.5 Column Generation Approach, 665
17.6 Dantzig-Woffe Decomposition, 671
17.7 Resource-Directive Decomposition, 674
17.8 Basis Partitioning, 678
17.9 Summary, 682
Reference Notes, 684
Exercises, 686
18 COMPUTATIONAL TESTING OF ALGORITHMS, 695
18.1 Introduction, 695
18.2 Representative Operation Counts, 698
18.3 Application to Network Simplex Algorithm, 702
18.4 Summary, 713
Reference Notes, 713
Exercises, 715
19 ADDITIONAL APPLICATIONS, 717
19.1 Introduction, 717
19.2 Maximum Weight Closure of a Graph, 719
19.3 Data Scaling, 725
19.4 Science Applications, 728
19.5 Project Management, 732
19.6 Dynamic Flows, 737
19.7 Arc Routing Problems, 740
19.8 Facility Layout and Location, 744
19.9 Production and Inventory Planning, 748
19.10 Summary, 755
Reference Notes, 759
Exercises, 760
APPENDIX A DATA STRUCTURES, 765
A.1 Introduction, 765
A.2 Elementary Data Structures, 766
A.3 d-Heaps, 773
A.4 Fibonacci Heaps, 779
Reference Notes, 787
APPENDIX B N9-COMPLETENESS, 788
B.1 Introduction, 788
B.2 Problem Reductions and Transformations, 790
B.3 Problem Classes 9,N9, N9-Complete, and N9-Hard, 792
B.4 Proving N9-Completeness Results, 796
B.5 Concluding Remarks, 800
Reference Notes, 801
APPENDIX C LINEAR PROGRAMMING, 802
C.1 Introduction, 802
C.2 Graphical Solution Procedure, 804
C.3 Basic Feasible Solutions, 805
C.4 Simplex Method, 810
C.5 Bounded Variable Simplex Method, 814
C.6 Linear Programming Duality, 816
Reference Notes, 820
REFERENCES, 821
INDEX, 84O
</font>
1.1 Introduction, 1
1.2 Network Flow Problems, 4
1.3 Applications, 9
1.4 Summary, 18
Reference Notes, 19
Exercises, 20
2 PATHS, TREES, AND CYCLES, 28
2.1 Introduction, 23
2.2 Notation and Definitions, 24
2.3 Network Representations, 31
2.4 Network Transformations, 38
2.5 Summary, 46
Reference Notes, 47
Exercises, 47
3 ALGORITHM DESIGN AND ANALYSIS, 58
3.1 Introduction, 53
3.2 Complexity Analysis, 56
3.3 Developing Polynomial-Time Algorithms, 66
3.4 Search Algorithms, 73
3.5 Flow Decomposition Algorithms, 79
3.6 Summary, 84
Reference Notes, 85
Exercises, 86
4 SHORTEST PATIO: LABEL-SETTING ALG-ORITHMS, 93
4.1 Introduction, 93
4.2 Applications, 97
4.3 Tree of Shortest Paths, 106
4.4 Shortest Path Problems in Acyclic Networks, 107
4.5 Dijkstra's Algorithm, 108
4.6 Dial's Implementation, 113
4.7 Heap Implementations, 115
4.8 Radix Heap Implementation, 116
4.9 Summary, 121
Reference Notes, 122
Exercises, 124
5 SHORTEST PATHS:LABEL-CORRECTING ALGORITHM,133
5.1 Introduction, 133
5.2 Optimality Conditions, 135
5.3 Generic Label-Correcting Algorithms, 136
5.4 Special Implementations of the Modified Label-Correcting Algorithm, 141
5.5 Detecting Negative Cycles, 143
5.6 All-Pairs Shortest Path Problem, 144
5.7 Minimum Cost-to-Time Ratio Cycle Problem, 150
5.8 Summary, 154
Reference Notes, 156
Exercises, 157
6 MAXIMUM FLOWS:BASICC IDEAS, 168
6.1 Introduction, 166
6.2 Applications, 169
6.3 Flows and Cuts, 177
6.4 Generic Augmenting Path Algorithm, 180
6.5 Labeling Algorithm and the Max-Flow Min-Cut Theorem, 184
6.6 Combinatorial Implications of the Max-Flow Min-Cut Theorem, 188
6.7 Flows with Lower Bounds, 191
6.8 Summary, 196
Reference Notes, 197
Exercises, 198
7 MAXIMUM FLOWS:POLYNOMIAL ALG-ORITHMS,2O7
7.1 Introduction, 207
7.2 Distance Labels, 209
7.3 Capacity Scaling Algorithm, 210
7.4 Shortest Augmenting Path Algorithm, 213
7.5 Distance Labels and Layered Networks, 221
7.6 Generic Prefiow-Push Algorithm, 223
7.7 FIFO Prefiow-Push Algorithm, 231
7.8 Highest-Label Prefiow-Push Algorithm, 233
7.9 Excess Scaling Algorithm, 237
7.10 Summary, 241
Reference Notes, 241
Exercises, 243
8 MAXIMUM FLOWS:ADDITIONAL TOPICS,25O
8.1 Introduction, 250
8.2 Flows in Unit Capacity Networks, 252
8.3 Flows in Bipartite Networks, 255
8.4 Flows in Planar Undirected Networks, 260
8.5 Dynamic Tree Implementations, 265
8.6 Network Connectivity, 273
8.7 All-Pairs Minimum Value Cut Problem, 277
8.8 Summary, 285
Reference Notes, 287
Exercises, 288
9 MINLMUM COST FLOWS:BASIC ALGORITHMS,294
9.1 Introduction, 294
9.2 Applications, 298
9.3 Optimality Conditions, 306
9.4 Minimum Cost Flow Duality, 310
9.5 Relating Optimal Flows to Optimal Node Potentials, 315
9.6 Cycle-Canceling Algorithm and the Integrality Property, 317
9.7 Successive Shortest Path Algorithm, 320
9.8 Primal-Dual Algorithm, 324
9.9 Out-of-Kilter Algorithm, 326
9.10 Relaxation Algorithm, 332
9.11 Sensitivity Analysis, 337
9.12 Summary, 339
Reference Notes, 341
Exercises, 344
10 MINIMUM COST FLOWS:POLYNOMIAL ALGORITHMS,357
10.1 Introduction, 357
10.2 Capacity Scaling Algorithm, 360
10.3 Cost Scaling Algorithm, 362
10.4 Double Scaling Algorithm, 373
10.5 Minimum Mean Cycle-Canceling Algorithm, 376
10.6 Repeated Capacity Scaling Algorithm, 382
10.7 Enhanced Capacity Scaling Algorithm, 387
10.8 Summary, 395
Reference Notes, 396
Exercises, 397
11 MINIMUM COST FLOWS: NETWORK SIMPLEX ALGORITHMS, 402
11.1 Introduction, 402
11.2 Cycle Free and Spanning Tree Solutions, 405
11.3 Maintaining a Spanning Tree Structure, 409
11.4 Computing Node Potentials and Flows, 411
11.5 Network Simplex Algorithm, 415
11.6 Strongly Feasible Spanning Trees, 421
11.7 Network Simplex Algorithm for the Shortest Path Problem, 425
11.8 Network Simplex Algorithm for the Maximum Flow Problem, 430
11.9 Related Network Simplex Algorithms, 433
11.10 Sensitivity Analysis, 439
11.11 Relationship to Simplex Method, 441
11.12 Unimodularity Property, 447
11.13 Summary, 450
Reference Notes, 451
Exercises, 453
12 ASSIGNMENTS AND MATCHINGS, 461
12.1 Introduction, 461
12.2 Applications, 463
12.3 Bipartite Cardinality Matching Problem, 469
12.4 Bipartite Weighted Matching Problem, 470
12.5 Stable Marriage Problem, 473
12.6 Nonbipartite Cardinality Matching Problem, 475
12.7 Matchings and Paths, 494
12.8 Summary, 498
Reference Notes, 499
Exercises, 501
13 MINIMUM SPANNING TREES, 510
13.1 Introduction, 510
13.2 Applications, 512
13.3 Optimality Conditions, 516
13.4 Kruskai's Algorithm, 520
13.5 Prim's Algorithm, 523
13.6 Sollin's Algorithm, 526
13.7 Minimum Spanning Trees and Matroids, 528
13.8 Minimum Spanning Trees and Linear Programming, 530
13.9 Summary, 533
Reference Notes, 535
Exercises, 536
14 CONVEX COST FLOWS, 543
14.1 Introduction, 543
14.2 Applications, 546
14.3 Transformation to a Minimum Cost Flow Problem, 551
14.4 Pseudopolynomial-Time Algorithms, 554
14.5 Polynomial-Time Algorithm, 556
14.6 Summary, 560
Reference Notes, 561
Exercises, 562
15 GENERALIXED FLOWS, 568
15.1 Introduction, 566
15.2 Applications, 568
15.3 Augmented Forest Structures, 572
15.4 Determining Potentials and Flows for an Augmented Forest Structure, 577
15.5 Good Augmented Forests and Linear Programming Bases, 582
15.6 Generalized Network Simplex Algorithm, 583
15.7 Summary, 591
Reference Notes, 591
Exercises, 593
16 LAGRANGIAN RELAXATION AND NETWORK OPTLMIZATION, 598
16.1 Introduction, 598
16.2 Problem Relaxations and Branch and Bound, 602
16.3 Lagrangian Relaxation Technique, 605
16.4 Lagrangian Relaxation and Linear Programming, 615
16.5 Applications of Lagrangian Relaxation, 620
16.6 Summary, 635
Reference Notes, 637
Exercises, 638
17 MULTICOMMODITY FLOWS, 649
17.1 Introduction, 649
17.2 Applications, 653
17.3 Optimality Conditions, 657
17.4 Lagrangian Relaxation, 660
17.5 Column Generation Approach, 665
17.6 Dantzig-Woffe Decomposition, 671
17.7 Resource-Directive Decomposition, 674
17.8 Basis Partitioning, 678
17.9 Summary, 682
Reference Notes, 684
Exercises, 686
18 COMPUTATIONAL TESTING OF ALGORITHMS, 695
18.1 Introduction, 695
18.2 Representative Operation Counts, 698
18.3 Application to Network Simplex Algorithm, 702
18.4 Summary, 713
Reference Notes, 713
Exercises, 715
19 ADDITIONAL APPLICATIONS, 717
19.1 Introduction, 717
19.2 Maximum Weight Closure of a Graph, 719
19.3 Data Scaling, 725
19.4 Science Applications, 728
19.5 Project Management, 732
19.6 Dynamic Flows, 737
19.7 Arc Routing Problems, 740
19.8 Facility Layout and Location, 744
19.9 Production and Inventory Planning, 748
19.10 Summary, 755
Reference Notes, 759
Exercises, 760
APPENDIX A DATA STRUCTURES, 765
A.1 Introduction, 765
A.2 Elementary Data Structures, 766
A.3 d-Heaps, 773
A.4 Fibonacci Heaps, 779
Reference Notes, 787
APPENDIX B N9-COMPLETENESS, 788
B.1 Introduction, 788
B.2 Problem Reductions and Transformations, 790
B.3 Problem Classes 9,N9, N9-Complete, and N9-Hard, 792
B.4 Proving N9-Completeness Results, 796
B.5 Concluding Remarks, 800
Reference Notes, 801
APPENDIX C LINEAR PROGRAMMING, 802
C.1 Introduction, 802
C.2 Graphical Solution Procedure, 804
C.3 Basic Feasible Solutions, 805
C.4 Simplex Method, 810
C.5 Bounded Variable Simplex Method, 814
C.6 Linear Programming Duality, 816
Reference Notes, 820
REFERENCES, 821
INDEX, 84O
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