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50 Years of Integer Programming 1958-2008

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

  • Book
  • © 2010

Overview

Editors:
  1. Michael Jünger

    1. Inst. Informatik, Universität Köln, Köln, Germany

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  2. Thomas M. Liebling

    1. Fac. Sciences de Base (FSB), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  3. Denis Naddef

    1. Ensimag, Institut Polytechnique de Grenoble, Grenoble CX 1, France

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  4. George L. Nemhauser

    1. School of Industrial &, Georgia Institute of Technology, Atlanta, USA

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  5. William R. Pulleyblank

    1. IBM Corporation, Somers, USA

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  6. Gerhard Reinelt

    1. Inst. Informatik, Universität Heidelberg, Heidelberg, Germany

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  7. Giovanni Rinaldi

    1. ed Informatica, CNR - Ist. Analisi dei Sistemi, Roma, Italy

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  8. Laurence A. Wolsey

    1. Center for Operations Reserach &, Université Catholique de Louvain, Leuven, Belgium

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  • Lectures of the pioneers of integer programming
  • Includes supplementary material: sn.pub/extras

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About this book

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.

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xvi
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  2. The Early Years

    1. Front Matter

      Pages 1-6
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    2. Solution of a Large-Scale Traveling-Salesman Problem

      • Vašek Chvátal, William Cook, George B. Dantzig, Delbert R. Fulkerson, Selmer M. Johnson
      Pages 7-28

    3. The Hungarian Method for the Assignment Problem

      • Harold W. Kuhn
      Pages 29-47

    4. Integral Boundary Points of Convex Polyhedra

      • Alan J. Hoffman, Joseph B. Kruskal
      Pages 49-76

    5. Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem

      • Ralph E. Gomory
      Pages 77-103

    6. An Automatic Method for Solving Discrete Programming Problems

      • Ailsa H. Land, Alison G. Doig
      Pages 105-132

    7. Integer Programming: Methods, Uses, Computation

      • Michel Balinski
      Pages 133-197

    8. Matroid Partition

      • Jack Edmonds
      Pages 199-217

    9. Reducibility Among Combinatorial Problems

      • Richard M. Karp
      Pages 219-241

    10. Lagrangian Relaxation for Integer Programming

      • Arthur M. Geoffrion
      Pages 243-281

    11. Disjunctive Programming

      • Egon Balas
      Pages 283-340

  3. From the Beginnings to the State-of-the-Art

    1. Front Matter

      Pages 341-342
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    2. Polyhedral Approaches to Mixed Integer Linear Programming

      • Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
      Pages 343-385

    3. Fifty-Plus Years of Combinatorial Integer Programming

      • William Cook
      Pages 387-430

    4. Reformulation and Decomposition of Integer Programs

      • François Vanderbeck, Laurence A. Wolsey
      Pages 431-502

  4. Current Topics

    1. Front Matter

      Pages 503-504
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    2. Integer Programming and Algorithmic Geometry of Numbers

      • Friedrich Eisenbrand
      Pages 505-559

    3. Nonlinear Integer Programming

      • Raymond Hemmecke, Matthias Köppe, Jon Lee, Robert Weismantel
      Pages 561-618

    4. Mixed Integer Programming Computation

      • Andrea Lodi
      Pages 619-645
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Reviews

“It is a concise, yet voluminous, book giving the theoretical, algorithmic and computational aspects of integer programming. … The book provides and serves as an excellent introduction to integer programming. In addition it gives an in depth and great historical perspective of the huge amount of research and development that has taken place in the field of integer programming over a period of 50 years.” (Hans W. Ittmann, IFORS News, Vol. 12 (2), June, 2018)


From the reviews:

“This volume originates from the 12th Combinatorial Optimization Workshop in Aussois, 2008, where 50 years of integer programming were celebrated. It describes the history and the present state of integer programming. Thevolume consists of four parts … . This volume is a precious account of the history and the current state of integer programming.” (Rainer Burkard, Mathematical Reviews, Issue 2011 f)

Editors and Affiliations

  • Inst. Informatik, Universität Köln, Köln, Germany

    Michael Jünger

  • Fac. Sciences de Base (FSB), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Thomas M. Liebling

  • Ensimag, Institut Polytechnique de Grenoble, Grenoble CX 1, France

    Denis Naddef

  • School of Industrial &, Georgia Institute of Technology, Atlanta, USA

    George L. Nemhauser

  • IBM Corporation, Somers, USA

    William R. Pulleyblank

  • Inst. Informatik, Universität Heidelberg, Heidelberg, Germany

    Gerhard Reinelt

  • ed Informatica, CNR - Ist. Analisi dei Sistemi, Roma, Italy

    Giovanni Rinaldi

  • Center for Operations Reserach &, Université Catholique de Louvain, Leuven, Belgium

    Laurence A. Wolsey

Bibliographic Information

  • Book Title: 50 Years of Integer Programming 1958-2008

  • Book Subtitle: From the Early Years to the State-of-the-Art

  • Editors: Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, … Laurence A. Wolsey

  • DOI: https://doi.org/10.1007/978-3-540-68279-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Hardcover ISBN: 978-3-540-68274-5Published: 10 December 2009

  • Softcover ISBN: 978-3-662-50181-8Published: 30 April 2017

  • eBook ISBN: 978-3-540-68279-0Published: 06 November 2009

  • Edition Number: 1

  • Number of Pages: XX, 804

  • Topics: Combinatorics, Optimization, Discrete Mathematics in Computer Science, Operations Research/Decision Theory

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