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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
L R Ford; D R Fulkerson |

ISBN: | 9780691146676 0691146675 |

OCLC Number: | 466341415 |

Notes: | Originally published: 1962. |

Description: | xix, 194 pages : illustrations ; 24 cm. |

Contents: | Foreword to the 2010 Edition -- Preface -- Acknowledgements -- Chapter I. Static Maximal Flow -- Introduction -- 1. Networks -- 2. Flows in networks -- 3. Notation -- 4. Cuts -- 5. Maximal flow -- 6. Disconnecting sets and cuts -- 7. Multiple sources and sinks -- 8. The labeling method for solving maximal flow problems -- 9. Lower bounds on arc flows -- 10. Flows in undirected and mixed networks -- 11. Node capacities and other extensions -- 12. Linear programming and duality principles -- 13. Maximal flow value as a function of two arc capacities -- References -- Chapter II. Feasibility Theorems and Combinatorial Applications -- Introduction -- 1. A supply-demand theorem -- 2. A symmetric supply-demand theorem -- 3. Circulation theorem -- 4. The König-Egerváry and Menger graph theorems -- 5. Construction of a maximal independent set of admissible cells -- 6. A bottleneck assignment problem -- 7. Unicursal graphs -- 8. Dilworth's chain decomposition theorem for partially ordered sets -- 9. Minimal number of individuals to meet a fixed schedule of tasks -- 10. Set representatives -- 11. The subgraph problem for directed graphs -- 12. Matrices composed of 0's and 1's -- References -- Chapter III. Minimal Cost Flow Problems -- Introduction -- 1. The Hitchcock problem -- 2. The optimal assignment problem -- 3. The general minimal cost flow problem -- 4. Equivalence of Hitchcock and minimal cost flow problems -- 5. A shortest chain algorithm -- 6. The minimal cost supply-demand problem: non-negative directed cycle costs -- 7. The warehousing problem -- 8. The caterer problem -- 9. Maximal dynamic flow -- 10. Project cost curves -- 11. Constructing minimal cost circulations -- References -- Chapter IV. Multi-Terminal Maximal Flows -- Introduction -- 1. Forests, trees, and spanning subtrees -- 2. Realization conditions -- 3. Equivalent networks -- 4. Network synthesis -- References -- Index. |

Series Title: | Princeton landmarks in mathematics and physics. |

Responsibility: | L.R. Ford, Jr. & D.R. Fulkerson ; with a new foreword by Robert Bland and Jim Orlin. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"[Flows in Networks] should ... be of great value to the expert and a standard reference source for many years to come."--H. J. Ryser, Management Science "The book stands as the principal work on network flow theory. Its authors have performed almost as great a service in preparing this volume for publication as they did in originally developing much of its contents."--Ronald A. Howard, Proceedings of the IEEE "The book should be of value not only to those interested in linear programming but also those who are concerned with graph theory."--Arthur Ziffer, Physics Today "The book is a natural meeting ground for persons interested in communication engineering or combinatorial mathematics."--Journal of Data Management "The book is a very welcome addition to the literature and should be of extreme value to anyone interested in operations research, communication theory, or combinatorial mathematics."--A. Newhouse, Computing Review Read more...

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