Combinatorial Optimization: Theory and Algorithms

Authors: Korte, Bernhard, Vygen, Jens
Well-written textbook on combinatorial optimization
One of very few textbooks on this topic
Subject area has manifold applications

About this Textbook

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
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

Topics
Combinatorics
Calculus of Variations and Optimal Control; Optimization
Mathematics of Computing

More info and Hardcover at Springer

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