Combinatorial Optimization: Theory and Algorithms (Algorithms and Combinatorics Book 21)

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley's formula, blocking flows, faster __b__-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization. This comprehensive textbook on combinatorial optimization places special¡emphasis on theoretical results and algorithms with provably good¡performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, ¡it contains complete but concise proofs, and also provides numerous¡exercises and references. This fifth edition has again been updated, revised, and significantly¡extended, with more than 60 new exercises and new material on various¡topics, including Cayley's formula, blocking flows, faster¡b-matching separation, multidimensional knapsack, multicommodity¡max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization. From the reviews of the previous editions: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Research Letters 33 (2005) " ... this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003) " ... has become a standard textbook in the field." Zentralblatt MATH 1099.90054¡ " ... gives an excellent comprehensive view of the exciting field of combinatorial optimization."¡ Zentralblatt MATH 1149.90126 This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley's formula, blocking flows, faster b-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization. From the reviews of the previous editions: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Research Letters 33 (2005) "..... this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003) "... has become a standard textbook in the field." Zentralblatt MATH 1099.90054 "...gives an excellent comprehensive view of the exciting field of combinatorial optimization." Zentralblatt MATH 1149.90126 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-matching 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 -- 22. Facility Location. Bernhard Korte, Jens Vygen. Includes Bibliographical References And Indexes. This comprehensive textbook on combinatorial optimization emphasizes theoretical results and algorithms with provably good performance, in contrast to heuristics. The text contains complete but concise proofs, and also provides numerous exercises and references.