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书名 | 网络流(理论算法与应用英文版香农信息科学经典) |
分类 | 科学技术-自然科学-数学 |
作者 | (美)拉文德拉·阿胡亚//托马斯·马尼安提//詹姆斯·奥林 |
出版社 | 世界图书出版公司 |
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简介 | 内容推荐 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。 目录 PREFACE 1 INTRODUCTION 1.1 Introduction 1.2 Network Flow Problems 1.3 Applications 1.4 Summary Reference Notes Exercises 2 PATHS, TREES, AND CYCLES 2.1 Introduction 2.2 Notation and Definitions 2.3 Network Representations 2.4 Network Transformations 2.5 Summary Reference Notes Exercises 3 ALGORITHM DESIGN AND ANALYSIS 3.1 Introduction 3.2 Complexity Analysis 3.3 Developing Polynomial-Time Algorithms 3.4 Search Algorithms 3.5 Flow Decomposition Algorithms 3.6 Summary Reference Notes Exercises 4 SHORTEST PATHS: LABEL-SETTING ALGORITHMS 4.1 Introduction 4.2 Applications 4.3 Tree of Shortest Paths 4.4 Shortest Path Problems in Acyclic Networks 4.5 Dijkstra's Algorithm 4.6 Dial's Implementation 4.7 Heap Implementations 4.8 Radix Heap Implementation 4.9 Summary Reference Notes Exercises 5 SHORTEST PATHS: LABEL-CORRECTING ALGORITHMS 5.1 Introduction 5.2 Optimality Conditions 5.3 Generic Label-Correcting Algorithms 5.4 Special Implementations of the Modified Label-Correcting Algorithm, 5.5 Detecting Negative Cycles 5.6 All-Pairs Shortest Path Problem 5.7 Minimum Cost-to-Time Ratio Cycle Problem 5.8 Summary Reference Notes Exercises 6 MAXIMUM FLOWS: BASIC DEAS 6.1 Introduction 6.2 Applications 6.3 Flows and Cuts 6.4 Generic Augmenting Path Algorithm 6.5 Labeling Algorithm and the Max-Flow Min-Cut Theorem 6.6 Combinatorial Implications of the Max-Flow Min-Cut Theorem 6.7 Flows with Lower Bounds 6.8 Summary Reference Notes Exercises 7 MAXIMUM FLOWS: POLYNOMIAL ALGORITHMS 7.1 Introduction 7.2 Distance Labels 7.3 Capacity Scaling Algorithm 7.4 Shortest Augmenting Path Algorithm 7.5 Distance Labels and Layered Networks 7.6 Generic Preflow-Push Algorithm 7.7 FIFO Preflow-Push Algorithm 7.8 Highest-Label Preflow-Push Algorithm 7.9 Excess Scaling Algorithm 7.10 Summary Reference Notes Exercises 8 MAXIMUM FLOWS: ADDITIONAL TOPICS 8.1 Introduction 8.2 Flows in Unit Capacity Networks 8.3 Flows in Bipartite Networks 8.4 Flows in Planar Undirected Networks 8.5 Dynamic Tree 8.6 Implementations 8.7 Network Connectivity 8.8 All-Pairs Minimum Value Cut Problem 8.9 Summary Reference Notes Exercises 9 MINIMUM COST FLOWS: BABIC ALGORITHMS 9.1 Introduction 9.2 Applications 9.3 Optimality Conditions 9.4 Minimum Cost Flow Duality 9.5 Relating Optimal Flows to Optimal Node Potentials 9.6 Cycle-Canceling Algorithm and the Integrality Property 9.7 Successive Shortest Path Algorithm 9.8 Primal-Dual Algorithm 9.9 Out-of-Kilter Algorithm 9.10 Relaxation Algorithm 9.11 Sensitivity Analysis 9.12 Summary Reference Notes Exercises 10 MINIMUM COST FLOWB: POLYNOMIAL ALGORITHMS 10.1 Introduction 10.2 Capacity Scaling Algorithm 10.3 Cost Scaling Algorithm 10.4 Double Scaling Algorithm 10.5 Minimum Mean Cycle-Canceling Algorithm 10.6 Repeated Capacity Scaling Algorithm 10.7 Enhanced Capacity Scaling Algorithm 10.8 Summary Reference Notes Exercises 11 MINIMUM COST FLOWS: NETWORK SIMPLEX ALGORITHMS 11.1 Introduction 11.2 Cycle Free and Spanning Tree Solutions 11.3 Maintaining a Spanning Tree Structure 11.4 Computing Node Potentials and Flows 11.5 Network Simplex Algorithm 11.6 Strongly Feasible Spanning Trees 11.7 Network Simplex Algorithm for the Shortest Path Problem 11.8 Network Simplex Algorithm for the Maximum Flow Problem 11.9 Related Network Simplex Algorithms 11.10 Sensitivity Analysis 11.11 Relationship to Simplex Method 11.12 Unimodularity Property 11.13 Summary Reference Notes Exercises 12 ASSIGNMENTS AND MATCHINGS 12.1 Introduction 12.2 Applications 12.3 Bipartite Cardinality Matching Problem 12.4 |
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