9780691146676

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 inFlows in Networksare 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.Flows in Networksis rich with insights that remain relevant to current research in engineering, management, and other sciences. This landmark work belongs on the bookshelf of every researcher working with networks.

L. R. Ford, Jr., worked as a researcher for both CEIR Inc. and the Rand Corporation before his retirement. D. R. Fulkerson (1924-1976) was a mathematician at the Rand Corporation.

Foreword to the 2010 Edition	p. ix
Preface	p. xvii
Acknowledgements	p. xix
Static Maximal Flow
Introduction	p. 1
Networks	p. 2
Flows in networks	p. 4
Notation	p. 9
Cuts	p. 10
Maximal flow	p. 11
Disconnecting sets and cuts	p. 14
Multiple sources and sinks	p. 15
The labeling method for solving maximal flow problems	p. 17
Lower bounds on arc flows	p. 22
Flows in undirected and mixed networks	p. 23
Node capacities and other extensions	p. 23
Linear programming and duality principles	p. 26
Maximal flow value as a function of two arc capacities	p. 30
References	p. 35
Feasibility Theorems and Combinatorial Applications
Introduction	p. 36
A supply-demand theorem	p. 36
A symmetric supply-demand theorem	p. 42
Circulation theorem	p. 50
The König-Egerváry and Menger graph theorems	p. 53
Construction of a maximal independent set of admissible cells	p. 55
A bottleneck assignment problem	p. 57
Unicursal graphs	p. 59
Dilworth's chain decomposition theorem for partially ordered sets	p. 61
Minimal number of individuals to meet a fixed schedule of tasks	p. 64
Set representatives	p. 67
The subgraph problem for directed graphs	p. 75
Matrices composed of 0's and 1's	p. 79
References	p. 91
Minimal Cost Flow Problems
Introduction	p. 93
The Hitchcock problem	p. 95
The optimal assignment problem	p. 111
The general minimal cost flow problem	p. 113
Equivalence of Hitchcock and minimal cost flow problems	p. 127
A shortest chain algorithm	p. 130
The minimal cost supply-demand problem: non-negative directed cycle costs	p. 134
The warehousing problem	p. 137
The caterer problem	p. 140
Maximal dynamic flow	p. 142
Project cost curves	p. 151
Constructing minimal cost circulations	p. 162
References	p. 169
Multi-Terminal Maximal Flows
Introduction	p. 173
Forests, trees, and spanning subtrees	p. 173
Realization conditions	p. 176
Equivalent networks	p. 177
Network synthesis	p. 187
References	p. 191
Index	p. 193
Table of Contents provided by Ingram. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Amazon no longer offers textbook rentals. We do!

Flows in Networks

Flows in Networks

0691146675

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review