Michael Jünger

Giovanni Rinaldi

Laurence A. Wolsey

Gerhard Reinelt

George L. Nemhauser

William R. Pulleyblank

Thomas M. Liebling

Denis Naddef

In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.

From the Early Years to the State-of-the-Art

50 Years of Integer Programming 1958-2008

Alexander Schrijver

William J. Cook

William H. Cunningham

A complete, highly accessible introduction to one of today's mostexciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics,combinatorial optimization integrates techniques fromcombinatorics, linear programming, and the theory of algorithms.Because of its success in solving difficult problems in areas fromtelecommunications to VLSI, from product distribution to airlinecrew scheduling, the field has seen a ground swell of activity overthe past decade. Combinatorial Optimization is an ideal introduction to thismathematical discipline for advanced undergraduates and graduatestudents of discrete mathematics, computer science, and operationsresearch. Written by a team of recognized experts, the text offersa thorough, highly accessible treatment of both classical conceptsand recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations ofbasic and advanced concepts, many real-world examples, and helpful,skill-building exercises, Combinatorial Optimization is certain tobecome the standard text in the field for many years to come.

Combinatorial Optimization

William R. Pulleyblank

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