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Combinatorial Optimization: Theory and Algorithms (Algorithms and Combinatorics, nr. 21)

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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 sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial optimization.
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Specificații

ISBN-13: 9783662560389
ISBN-10: 3662560380
Pagini: 688
Dimensiuni: 155 x 235 x 47 mm
Greutate: 1.24 kg
Ediția: 6th ed. 2018
Editura: Springer
Colecția Springer
Seria Algorithms and Combinatorics

Locul publicării: Berlin, Heidelberg, Germany

Cuprins

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.

Notă biografică

Bernhard Korte is professor of operations research and director of the Research Institute for Discrete Mathematics at the University of Bonn. He founded the Arithmeum in Bonn and received numerous awards, including a honorary doctoral degree and the "Staatspreis NRW". His research interests include combinatorial optimization and chip design.
Jens Vygen is professor of discrete mathematics at the University of Bonn and principal investigator of the Hausdorff Center for Mathematics. He also co-authored the textbook “Algorithmic Mathematics” and has served as editor of several books and journals. His research interests include combinatorial optimization and algorithms for chip design.


Textul de pe ultima copertă

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 sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent 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 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. The book also provides insights into and pointers to adjacent areas that could not be covered in full length for the interested reader. “Combinatorial Optimization” can easily serve as an (almost) complete reference for current research and is state-of-the-art. […]”
Zentralblatt MATH 1237.90001
 

Caracteristici

Well-written, popular textbook on combinatorial optimization
One of very few textbooks on this topic
Subject area has manifold applications
Offers complete but concise proofs, making it an invaluable practical tool for students
Updated sixth edition

Recenzii

From the reviews of the 2nd Edition:
"Provides a useful collection of the major techniques, results and references in combinatorial optimization for researchers and teachers in the field."—
MATHEMATICAL REVIEWS
"This book on combinatorial optimization is a beautiful example of the ideal textbook."
Operations Resarch 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
From the reviews of the third edition:
"In the last years Korte and J. Vygen’s ‘Combinational Optimization. Theory and Algorithms’ has become a standard textbook in the field. 5 years after the first edition … the 3rd revised edition is available. … several proofs have been streamlined, the references have been updated and new exercises have been added. That makes this volume to one of the most comprehensive and up-to-date textbooks in the field of combinatorial optimization."
Rainer E. Burkard, Zentralblatt MATH, Vol. 1099 (1), 2007
"This volume is an encyclopedic reference and textbook on theory and algorithms in combinatorial optimization. … As befits a reference book, the references are very complete and up to date. … The book has separate topic and author indexes and a very useful glossary of notation. … The book … will appeal primarily to readers who want an advanced textbook that can also serve as a concise reference. … The current volume by Korte and Vygen is a worthy successor."
Brian Borchers, MathDL, May, 2006