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  • © 2000

Combinatorial Optimization

Theory and Algorithms

  • Well-written textbook on combinatorial optimization
  • One of very few textbooks on this topic
  • Subject area has manifold applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Algorithms and Combinatorics (AC, volume 21)

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Table of contents (21 chapters)

  1. Front Matter

    Pages I-XI
  2. Introduction

    • Bernhard Korte, Jens Vygen
    Pages 1-12
  3. Graphs

    • Bernhard Korte, Jens Vygen
    Pages 13-47
  4. Linear Programming

    • Bernhard Korte, Jens Vygen
    Pages 49-64
  5. Linear Programming Algorithms

    • Bernhard Korte, Jens Vygen
    Pages 65-90
  6. Integer Programming

    • Bernhard Korte, Jens Vygen
    Pages 91-116
  7. Spanning Trees and Arborescences

    • Bernhard Korte, Jens Vygen
    Pages 117-137
  8. Shortest Paths

    • Bernhard Korte, Jens Vygen
    Pages 139-152
  9. Network Flows

    • Bernhard Korte, Jens Vygen
    Pages 153-184
  10. Minimum Cost Flows

    • Bernhard Korte, Jens Vygen
    Pages 185-204
  11. Maximum Matchings

    • Bernhard Korte, Jens Vygen
    Pages 205-233
  12. Weighted Matching

    • Bernhard Korte, Jens Vygen
    Pages 235-260
  13. b-Matchings and T-Joins

    • Bernhard Korte, Jens Vygen
    Pages 261-278
  14. Matroids

    • Bernhard Korte, Jens Vygen
    Pages 279-309
  15. Generalizations of Matroids

    • Bernhard Korte, Jens Vygen
    Pages 311-326
  16. NP-Completeness

    • Bernhard Korte, Jens Vygen
    Pages 327-359
  17. Approximation Algorithms

    • Bernhard Korte, Jens Vygen
    Pages 361-396
  18. The Knapsack Problem

    • Bernhard Korte, Jens Vygen
    Pages 397-406
  19. Bin-Packing

    • Bernhard Korte, Jens Vygen
    Pages 407-422
  20. Multicommodity Flows and Edge-Disjoint Paths

    • Bernhard Korte, Jens Vygen
    Pages 423-444

About this book

Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. It became a subject in its own right about 50 years ago. This book describes the most important ideas, theoretical results, and algo­ rithms in combinatorial optimization. We have conceived it as an advanced gradu­ ate text which 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. Applications and heuristics are mentioned only occasionally. Combinatorial optimization has its roots in combinatorics, operations research, and theoretical computer science. A main motivation is that thousands of real-life problems can be formulated as abstract combinatorial optimization problems. We focus on the detailed study of classical problems which occur in many different contexts, together with the underlying theory. Most combinatorial optimization problems can be formulated naturally in terms of graphs and as (integer) linear programs. Therefore this book starts, after an introduction, by reviewing basic graph theory and proving those results in linear and integer programming which are most relevant for combinatorial optimization.

Reviews

“This book describes the most important ideas, theoretical results, algorithms in combinatorial optimization and covers an advanced graduate text which can also be used as an up-to-date reference work for current research. … At the end of each chapter there are a number of exercises containing additional results and applications of the material in that chapter. Each chapter ends with a list of references, incuding texts recommended for further study.” (J.Fiamčik, zbMATH 0953.90052, 2022)

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

Authors and Affiliations

  • Research Institute for Discrete Mathematics, University of Bonn, Bonn, Germany

    Bernhard Korte, Jens Vygen

Bibliographic Information

Buy it now

Buying options

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access