Combinatorial Optimization 2012: Theory and Algorithms

Combinatorial Optimization 2012: Theory and Algorithms

Hardback Algorithms and Combinatorics

By (author) Bernhard Korte, By (author) Jens Vygen

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  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Format: Hardback | 680 pages
  • Dimensions: 162mm x 244mm x 42mm | 1,139g
  • Publication date: 13 January 2012
  • Publication City/Country: Berlin
  • ISBN 10: 3642244874
  • ISBN 13: 9783642244872
  • Edition: 5, Revised
  • Edition statement: 5th Revised edition
  • Illustrations note: biography
  • Sales rank: 712,738

Product description

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.

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Review quote

From the reviews of the fifth edition: "The book would be most suitable as a graduate text for a mathematics or computer science course. It offers a good number of exercises ... . This book excels at providing very up-to-date results that give an idea of the state of the art, but also makes it clear that this is still a very active area of research. Overall, it is a comprehensive and interesting text that manages to present both the most classical and the most recent ideas in the field." (Angele M. Hamel, ACM Computing Reviews, August, 2012) "This is the 5th edition of one of the standard books in combinatorial optimization. It is an excellent book covering everything from the basics up to the most advanced topics (graduate level and current research). It provides theoretical results, underlying ideas, algorithms and the needed basics in graph theory in a very nice, comprehensive way. ... 'Combinatorial Optimization' can easily serve as ... complete reference for current research and is state-of-the-art. In this new edition references have been updated and new exercises were added." (Sebastian Pokutta, Zentralblatt MATH, Vol. 1237, 2012)

Back cover copy

This comprehensive textbook on combinatorial optimization places specialemphasis on theoretical results and algorithms with provably goodperformance, 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 numerousexercises and references.This fifth edition has again been updated, revised, and significantlyextended, with more than 60 new exercises and new material on varioustopics, including Cayley's formula, blocking flows, faster"b-"matching separation, multidimensional knapsack, multicommoditymax-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"

Table of contents

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.- 22 Facility Location.- Indices.