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| Preface Chapter 1 INTRODUCTION 1. What is Combinatorial Optimization ? 2. Some Representative Optimization Problems 3. When is a Problem Solved? 4. The Criterion of Polynomial Boundedness 5. Some Apparently Nonpolynomial-Bounded Problem: 6. Methods of Solution Comments and References Chapter 2 MATHEMATICAL PRELIMINARIES 1. Mathematical Prerequisites 2. Sets and Relations 3. Graphs and Digraphs 4. Subgraphs, Cliques, Multigraphs 5. Connectivity in Graphs 6. Connectivity in Digraphs 7. Cocyeles and Directed Coeycles 8. Planarity and Duality 9. Eulerian and Hami'ltonian Graphs 10. Linear Programming Problems II. The Simplex Method 12. Geometric Interpretation 13. Duality Theory Comments and References Chapter 3 SHORTEST PATHS 1. Introduction 2. Some Problem Formulations 3. Bellman's Equations 4. Acyclic Networks 5. Networks with Positive Arcs: Dijkstra's Method 6. Solution by Successive Approximations." Bellman-Ford Method Method 7. Improvements in Efficiency: Yen's Modifications 8. Linear Programming Interpretation and Relaxation Procedures 9. Shortest Paths between all Pairs of Nodes: Matrix Multiplication 10. Floyd-Warshall Method 11. Detection of Negative Cycles 12. Networks with Transit Times 13. The Minimal Cost-to-time Ratio Cycle Problem 14. M Shortest Paths: Dreyfus Method 15. M Shortest Paths without Repeated Nodes Comments and References Chapter 4 NETWORK FLOWS 1. Introduction 2. Maximal Flows 3. Maximal Flow Algorithm 4. Efficiency of the Maximal Flow Algorithm 5. Combinatorial Implications of Max-Flow Min-Cut Theorem 6. Linear Programming Interpretation of Max-Flow Min-Cut Theorem 7. Minimum Cost Flows 8. Networks with Losses and Gains 9. Lower Bounds and Circulations 10. The Out-of-Kilter Method 11. Theoretical Improvement in Efficiency of Out-oJ:Kilter Method 12. Integrality of Flows and the Unimodular Property 13. Application to Project Scheduling 14. Transhipment and Transportation Problems Chapter 5 BIPARTTE MATCHING Chapter 6 NONBIPARTITE MATCHING Chapter 7 MATROIDS AND THE GREEDY ALGORITHM Chapter 8 MATROID INTERSCETIONGS Chapter 9 THE MATROID PARITY PROBLEM Auther Index Subject Index |
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