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.

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

Review

...a well-designed book containing a wealth of very interesting results. The book can be used as a reference book and as a source for a reading class. -- Zentralblatt f�r Mathematik

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