**Proceedings of Symposia in Applied Mathematics**

Volume: 26;
1982;
142 pp;
Softcover

MSC: Primary 90;

Print ISBN: 978-0-8218-0031-7

Product Code: PSAPM/26

List Price: $31.00

Individual Member Price: $24.80

**Electronic ISBN: 978-0-8218-9241-1
Product Code: PSAPM/26.E**

List Price: $31.00

Individual Member Price: $24.80

# The Mathematics of Networks

Share this page *Edited by *
*Stefan A. Burr*

The theory of networks is a very lively one, both in terms of
developments in the theory itself and of the variety of its applications.
This book, based on the 1981 AMS Short Course on the Mathematics of
Networks, introduces most of the basic ideas of network theory and
develops some of these ideas considerably. A number of more
specialized topics are introduced, including areas of active research
and a wide variety of applications.

Frank Boesch gives the basic definitions in the
mathematics of networks and in the closely-related topic of graph
theory. He discusses two of the most fundamental network problems —
the shortest path problem and the minimum spanning tree
problem as well as some of their variants. Boesch also gives an
interesting presentation in the area of network reliability. Frances
Yao considers maximum flows in networks, the problem most often thought
of in connection with the mathematics of networks. Richard Karp gives
an account of the computational complexity of network problems. Using
the case study method, Shen Lin demonstrates the effective use of
heuristic algorithms in network design. Four applications of the
mathematics of networks are presented by Daniel Kleitman. These
include: the design of irrigation systems, the theory of electrical
networks, the scheduling of delivery trucks, and the physics of ice.
Finally, Nicholas Pippenger presents a chapter on telephone switching
networks, an area of network theory that leads to difficult mathematics
drawn from such apparently unrelated fields as harmonic analysis.

#### Readership

# Table of Contents

## The Mathematics of Networks

- Contents vii8 free
- Preface ix10 free
- Introduction to basic network problems 112 free
- Maximum flows in networks 3142
- The computational complexity of network problems 4556
- Effective use of heuristic algorithms in network design 6374
- Some practical network problems 8596
- Telephone switching networks 101112
- Concluding remarks 135146