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 has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. It contains complete but concise proofs, also for many deep results, some of which did not appear in a textbook before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This fourth edition is again significantly extended, most notably with new material on linear programming, the network simplex algorithm, and the max-cut problem. Many further additions and updates are included as well. 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), p.216-217 "The second edition (with corrections and many updates) of 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), p.42 " ... has become a standard textbook in the field." Zentralblatt MATH 1099.90054 Front Matter....Pages I-XVII Introduction....Pages 1-12 Graphs....Pages 13-47 Linear Programming....Pages 49-69 Linear Programming Algorithms....Pages 71-97 Integer Programming....Pages 99-126 Spanning Trees and Arborescences....Pages 127-149 Shortest Paths....Pages 151-164 Network Flows....Pages 165-197 Minimum Cost Flows....Pages 199-226 Maximum Matchings....Pages 227-256 Weighted Matching....Pages 257-283 b -Matchings and T -Joins....Pages 285-303 Matroids....Pages 305-336 Generalizations of Matroids....Pages 337-357 NP -Completeness....Pages 359-392 Approximation Algorithms....Pages 393-437 The Knapsack Problem....Pages 439-448 Bin-Packing....Pages 449-465 Multicommodity Flows and Edge-Disjoint Paths....Pages 467-489 Network Design Problems....Pages 491-525 The Traveling Salesman Problem....Pages 527-562 Facility Location....Pages 563-598 Back Matter....Pages 599-627 Graphs -- Linear Programming -- Linear Programming Algorithms -- Integer Programming -- Spanning Trees And Arborescences -- Shortest Paths -- Network Flows -- Minimum Cost Flows -- Maximum Matchings -- Weighted Matching -- B-matchings And T-joins -- Matroids -- Generalizations Of Matroids -- Np-completeness -- Approximation Algorithms -- The Knapsack Problem -- Bin-packing -- Multicommodity Flows And Edge-disjoint Paths -- Network Design Problems -- The Traveling Salesman Problem -- Facility Location. Bernhard Korte, Jens Vygen. Includes Bibliographical References And Indexes.