Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. This book describes the most important ideas, theoretical results, and algorithms of this field. It is conceived as an advanced graduate text, and it can also be used as an up-to-date reference work for current research. The book includes the essential fundamentals of graph theory, linear and integer programming, and complexity theory. It covers classical topics in combinatorial optimization as well as very recent ones. The emphasis is on theoretical results and algorithms with provably good performance. Some applications and heuristics are mentioned, too.

Klappentext

This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.

Inhalt

1. Introduction.- 2. Graphs.- 3. Linear Programming.- 4. Linear Programming Algorithms.- 5. Integer Programming.- 6. Spanning Trees and Arborescences.- 7. Shortest Paths.- 8. Network Flows.- 9. Minimum Cost Flows.- 10. Maximum Matchings.- 11. Weighted Matching.- 12. b-Matchings and T-Joins.- 13. Matroids.- 14. Generalizations of Matroids.- 15. NP-Completeness.- 16. Approximation Algorithms.- 17. The Knapsack Problem.- 18. Bin-Packing.- 19. Multicommodity Flows and Edge-Disjoint Paths.- 20. Network Design Problems.- 21. The Traveling Salesman Problem.- Notation Index.- Author Index.