Submodular Functions and Optimization 2nd Edition by Satoru Fujishige ISBN 0444520864 9780444520869
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Product details:
ISBN 10: 0444520864
ISBN 13: 9780444520869
Author: Satoru Fujishige
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.
Submodular Functions and Optimization 2nd Table of contents:
Part I
Introduction to Part I
Chapter I: Introduction
1 Introduction
Chapter II: Submodular Systems and Base Polyhedra
2 From Matroids to Submodular Systems
3 Submodular Systems
3.3 Structures of Base Polyhedra
3.5 Related Polyhedra
3.6 Submodular Systems of Network Type [Tomi+Fuji81]
Chapter III: Neoflows
4 The Intersection Problem
5 Neoflows
5.6 Matroid Optimization
Chapter IV: Submodular Analysis
6 Submodular Functions and Convexity
7 Submodular Programs
7.2 Submodular Programs –– Constrained Optimization
Chapter V: Nonlinear Optimization with Submodular Constraints
8 Separable Convex Optimization
9 The Lexicographically Optimal Base Problem
10 The Weighted Max-Min and Min-Max Problems
11 The Fair Resource Allocation Problem
12 A Neoflow Problem with a Separable Convex Cost Function
Part II
Introduction to Part II
Chapter VI: Submodular Function Minimization
13 Symmetric Submodular Function Minimization: Queyranne’s Algorithm
14 Submodular Function Minimization
Chapter VII: Discrete Convex Analysis
15 Locally Polyhedral Convex Functions and Conjugacy
17 M- and L-convex Functions
18 Conjugacy between M-convex Functions and L-convex Functions
19 The Discrete Fenchel-Duality Theorem
20 Algorithmic and Structural Properties of Discrete Convex Functions
21 Other Related Topics
22 Historical Notes
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