A first course in combinatorial optimization
著者
書誌事項
A first course in combinatorial optimization
（Cambridge texts in applied mathematics）
Cambridge University Press, 2004
- : hbk
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.
目次
- Introduction
- Polytopes and linear programming
- 1. Matroids and the greedy algorithm
- 2. Minimum-weight dipaths
- 3. Matroid intersection
- 4. Matching
- 5. Flows and cuts
- 6. Cutting planes
- 7. Branch- 8. Optimizing submodular functions
- Appendix.
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