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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.
Combinatorial optimization. --- Optimisation combinatoire --- Combinatorial optimization --- Combinatorics. --- Calculus of variations. --- Computer science—Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics of Computing. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Combinatorics --- Algebra --- Mathematical analysis
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This comprehensive textbook on combinatorial optimization puts 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. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book 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 third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added. From the reviews of the 2nd edition: "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 .
519.212 --- 519.8 --- Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- Operational research --- Combinatorial optimization. --- Operations Research --- Algebra --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- 519.212 Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- 519.8 Operational research --- Optimization, Combinatorial
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Mathematical optimization --- Operations research --- Optimisation mathématique --- Recherche opérationnelle --- Congresses --- Congrès --- OPERATIONS RESEARCH --- congresses --- Congresses. --- Optimisation mathématique --- Recherche opérationnelle --- Congrès --- 519.8 --- 519.8 Operational research --- Operational research --- Numerical methods of optimisation --- Operational research. Game theory --- Mathematical optimization - Congresses --- Operations research - Congresses
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Bonn Workshop on Combinatorial Optimization
Combinatorial optimization --- Optimisation combinatoire --- Congresses --- Congrès --- ELSEVIER-B EPUB-LIV-FT --- Combinatorial analysis --- Combinatorial optimization - Congresses
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