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

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. From the reviews of the 2nd edition: "This book on combinatorial optimization is a beautiful example of the ideal textbook. [....] 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." J. Köhler, Halle an der Saale ELSEVIER Operations Research Letters, 2005, Issue 33. It was more than a surprise to us that the first edition of this book already went out of print about a year after its first appearance. We were flattered by the many positive and even enthusiastic comments and letters from colleagues and the gen­ eral readership. Several of our colleagues helped us in finding typographical and other errors. In particular, we thank Ulrich Brenner, Andras Frank, Bernd Gartner and Rolf Mohring. Of course, all errors detected so far have been corrected in this second edition, and references have been updated. Moreover, the first preface had a flaw. We listed all individuals who helped us in preparing this book. But we forgot to mention the institutional support, for which we make amends here. It is evident that a book project which took seven years benefited from many different grants. We would like to mention explicitly the bilateral Hungarian­ German Research Project, sponsored by the Hungarian Academy of Sciences and the Deutsche Forschungsgemeinschaft, two Sonderforschungsbereiche (special re­ search units) of the Deutsche Forschungsgemeinschaft, the Ministere Franc;ais de la Recherche et de la Technologie and the Alexander von Humboldt Foundation for support via the Prix Alexandre de Humboldt, and the Commission of the Eu­ ropean Communities for participation in two projects DONET. Our most sincere thanks go to the Union of the German Academies of Sciences and Humanities and to the Northrhine-Westphalian Academy of Sciences. 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. "This 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. For the second edition several corrections and many updates have been made in the text."--Jacket "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."--BOOK JACKET.