It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.
Key features:
- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.
- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.
1. Introduction to Part I 2. Chapter I: Introduction 3. Chapter II: Submodular Systems and Base Polyhedra 4. 2 From Matroids to Submodular Systems 5. 3 Submodular Systems 6. 3.3 Structures of Base Polyhedra 7. 3.5 Related Polyhedra 8. 3.6 Submodular Systems of Network Type [Tomi+Fuji81] 9. Chapter III: Neoflows 10. Chapter IV: Submodular Analysis 11. Chapter V: Nonlinear Optimization with Submodular Constraints 12. Part II 13. Introduction to Part II 14. Chapter VI: Submodular Function Minimization 15. Chapter VII: Discrete Convex Analysis 16. References 17. Index
It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.
Key features:
- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.
- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.
1. Introduction to Part I 2. Chapter I: Introduction 3. Chapter II: Submodular Systems and Base Polyhedra 4. 2 From Matroids to Submodular Systems 5. 3 Submodular Systems 6. 3.3 Structures of Base Polyhedra 7. 3.5 Related Polyhedra 8. 3.6 Submodular Systems of Network Type [Tomi+Fuji81] 9. Chapter III: Neoflows 10. Chapter IV: Submodular Analysis 11. Chapter V: Nonlinear Optimization with Submodular Constraints 12. Part II 13. Introduction to Part II 14. Chapter VI: Submodular Function Minimization 15. Chapter VII: Discrete Convex Analysis 16. References 17. Index
