A First Course in Combinatorial Optimization

This self-contained beginning graduate text covers linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows.

Jon Lee (Author)

9780521010122, Cambridge University Press

Paperback, published 9 February 2004

228 pages
22.9 x 15.2 x 1.7 cm, 0.312 kg

'The author, with his light but rigorous mathematical writing style, takes delight in revealing the stars of combinatorial optimization. This is an excellent teaching book; I recommend it highly.' International Statistical Institute

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.

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-&-bound
8. Optimizing submodular functions
Appendix.

Subject Areas: Combinatorics & graph theory [PBV], Optimization [PBU], Operational research [KJT]