Flows in Networks

Lester Randolph Ford; D. R. Fulkerson

Book

Flows in Networks

Lester Randolph Ford and D. R. Fulkerson
Preface by: Robert G. Bland and James B. Orlin

Language: English

Published/Copyright: 2011

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This book is in the series

Princeton Landmarks in Mathematics and Physics

About this book

A landmark work that belongs on the bookshelf of every researcher working with networks

In this classic book, first published in 1962, L. R. Ford, Jr., and D. R. Fulkerson set the foundation for the study of network flow problems. The models and algorithms introduced in Flows in Networks are used widely today in the fields of transportation systems, manufacturing, inventory planning, image processing, and Internet traffic. The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction. With an incisive foreword by Robert Bland and James Orlin, Flows in Networks is rich with insights that remain relevant to current research in engineering, management, and other sciences.

Author / Editor information

L. R. Ford, Jr., (1927–2017) was a researcher at CEIR Inc. and the Rand Corporation. D. R. Fulkerson (1924–1976) was a mathematician at the Rand Corporation.

Reviews

“[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

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Mathematics Applied Mathematics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	vii
Foreword to the 2010 edition Publicly Available Download PDF	ix
PREFACE Publicly Available Download PDF	xvii
ACKNOWLEDGMENTS Publicly Available Download PDF	xix
CHAPTER I STATIC MAXIMAL FLOW
Introduction Requires Authentication Unlicensed Licensed	1
1. Networks Requires Authentication Unlicensed Licensed	2
2. Flows in networks Requires Authentication Unlicensed Licensed	4
3. Notation Requires Authentication Unlicensed Licensed	9
4. Cuts Requires Authentication Unlicensed Licensed	10
5. Maximal flow Requires Authentication Unlicensed Licensed	11
6. Disconnecting sets and cuts Requires Authentication Unlicensed Licensed	14
7. Multiple sources and sinks Requires Authentication Unlicensed Licensed	15
8. The labeling method for solving maximal flow problems Requires Authentication Unlicensed Licensed	17
9. Lower bounds on arc flows Requires Authentication Unlicensed Licensed	22
10. Flows in undirected and mixed networks Requires Authentication Unlicensed Licensed	23
11. Node capacities and other extensions Requires Authentication Unlicensed Licensed	23
12. Linear programming and duality principles Requires Authentication Unlicensed Licensed	26
13. Maximal flow value as a function of two arc capacities Requires Authentication Unlicensed Licensed	30
References Requires Authentication Unlicensed Licensed	35
CHAPTER II FEASIBILITY THEOREMS AND COMBINATORIAL APPLICATIONS
Introduction Requires Authentication Unlicensed Licensed	36
1. A supply-demand theorem Requires Authentication Unlicensed Licensed	36
2. A symmetric supply-demand theorem Requires Authentication Unlicensed Licensed	42
3. Circulation theorem Requires Authentication Unlicensed Licensed	50
4. The König-Egerváry and Menger graph theorems Requires Authentication Unlicensed Licensed	53
5. Construction of a maximal independent set of admissible cells Requires Authentication Unlicensed Licensed	55
6. A bottleneck assignment problem Requires Authentication Unlicensed Licensed	57
7. Unicursal graphs Requires Authentication Unlicensed Licensed	59
8. Dilworth's chain decomposition theorem for partially ordered sets Requires Authentication Unlicensed Licensed	61
9. Minimal number of individuals to meet a fixed schedule of tasks Requires Authentication Unlicensed Licensed	64
10. Set representatives Requires Authentication Unlicensed Licensed	67
11. The subgraph problem for directed graphs Requires Authentication Unlicensed Licensed	75
12. Matrices composed of O's and l's Requires Authentication Unlicensed Licensed	79
References Requires Authentication Unlicensed Licensed	91
CHAPTER III MINIMAL COST FLOW PROBLEMS
Introduction Requires Authentication Unlicensed Licensed	93
1. The Hitchcock problem Requires Authentication Unlicensed Licensed	95
2. The optimal assignment problem [56, 57, 60, 61, 68, 69] Requires Authentication Unlicensed Licensed	111
3. The general minimal cost flow problem Requires Authentication Unlicensed Licensed	113
4. Equivalence of Hitchcock and minimal cost flow problems Requires Authentication Unlicensed Licensed	127
5. A shortest chain algorithm Requires Authentication Unlicensed Licensed	130
6. The minimal cost supply-demand problem: non-negative directed cycle costs Requires Authentication Unlicensed Licensed	134
7. The warehousing problem Requires Authentication Unlicensed Licensed	137
8. The caterer problem Requires Authentication Unlicensed Licensed	140
9. Maximal dynamic flow Requires Authentication Unlicensed Licensed	142
10. Project cost curves Requires Authentication Unlicensed Licensed	151
11. Constructing minimal cost circulations [28] Requires Authentication Unlicensed Licensed	162
References Requires Authentication Unlicensed Licensed	169
CHAPTER IV MULTI-TERMINAL MAXIMAL FLOWS
Introduction Requires Authentication Unlicensed Licensed	173
1. Forests, trees, and spanning subtrees Requires Authentication Unlicensed Licensed	173
2. Realization conditions Requires Authentication Unlicensed Licensed	176
3. Equivalent networks Requires Authentication Unlicensed Licensed	177
4. Network synthesis Requires Authentication Unlicensed Licensed	187
References Requires Authentication Unlicensed Licensed	191
INDEX Requires Authentication Unlicensed Licensed	193

Publishing information

Pages and Images/Illustrations in book

eBook published on:

December 3, 2024

eBook ISBN:

9780691273457

Pages and Images/Illustrations in book

Main content:

216

https://doi.org/10.1515/9780691273457

eBook ISBN: 9780691273457

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College/higher education;Professional and scholarly;General/trade;

Flows in Networks

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