Softcover ISBN:  9780821800317 
Product Code:  PSAPM/26 
142 pp 
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AMS Member Price:  $26.40 
Electronic ISBN:  9780821892411 
Product Code:  PSAPM/26.E 
142 pp 
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Book DetailsProceedings of Symposia in Applied MathematicsVolume: 26; 1982MSC: Primary 90;
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 closelyrelated 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

Articles

Frank Boesch  Introduction to basic network problems

Frances Yao  Maximum flows in networks

R. M. Karp  The computational complexity of network problems

Shen Lin  Effective use of heuristic algorithms in network design

Daniel J. Kleitman  Some practical network problems

Nicholas Pippenger  Telephone switching networks

Stefan A. Burr  Concluding remarks


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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 closelyrelated 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.

Articles

Frank Boesch  Introduction to basic network problems

Frances Yao  Maximum flows in networks

R. M. Karp  The computational complexity of network problems

Shen Lin  Effective use of heuristic algorithms in network design

Daniel J. Kleitman  Some practical network problems

Nicholas Pippenger  Telephone switching networks

Stefan A. Burr  Concluding remarks