Submodular Functions and Optimization

Satoru Fujishige (Eds.)978-0-444-52086-9, 0444520864

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.

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Table of contents :
Content:
Preface
Pages v-vi
S.F.

Preface to the second edition
Pages vii-viii
S.F.

Chapter I. Introduction
Pages 3-20

Chapter II. Submodular systems and base polyhedra Original Research Article
Pages 21-125

Chapter III. Neoflows Original Research Article
Pages 127-197

Chapter IV. Submodular analysis Original Research Article
Pages 199-251

Chapter V. Nonlinear optimization with submodular constraints Original Research Article
Pages 253-283

Chapter VI. Submodular function minimization Original Research Article
Pages 287-314

Chapter VII. Discrete convex analysis Original Research Article
Pages 315-363

References
Pages 365-388

Index
Pages 389-395