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Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks (Foundations of computing).

Leighton, Frank Thomson

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ISBN 10: 0262121042 / ISBN 13: 9780262121040
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Beschreibung

Cambridge, MA:. The MIT Press, 1983. Hardcover. 155 pp.- This book solves several mathematical problems in the areas of Very Large Scale Integration (VLSI) and parallel computation. In particular, it describes optimal layouts for the shuffle-exchange graph, one of the best known networks for parallel computation. Attempts to design a shuffle-exchange computer have been hampered in part by the fact that, until now, no good layouts for the shuffle-exchange graph were known. The mesh of trees network (which may eventually prove as useful as the shuffle-exchange graph) is introduced and the book shows how it can be used to perform a variety of computations, including sorting and matrix multiplication, in a logarithmic number of steps. Next, the book introduces the tree of meshes, the first planar graph that was discovered not to have a linear-area layout. Most recently, the structure of this graph has been used to develop a general framework for solving VLSI graph layout problems. English text. Condition : as new. Condition : as new copy. ISBN 9780262121040[KEYWORDS: computer studies, Buchnummer des Verkäufers 257056

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Titel: Complexity Issues in VLSI: Optimal Layouts ...

Einband: Hardcover

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Inhaltsangabe:

This book solves several mathematical problems in the areas of Very Large Scale Integration (VLSI) and parallel computation. In particular, it describes optimal layouts for the shuffle-exchange graph, one of the best known networks for parallel computation. Attempts to design a shuffle-exchange computer have been hampered in part by the fact that, until now, no good layouts for the shuffle-exchange graph were known.

The mesh of trees network (which may eventually prove as useful as the shuffle-exchange graph) is introduced and the book shows how it can be used to perform a variety of computations, including sorting and matrix multiplication, in a logarithmic number of steps.

Next, the book introduces the tree of meshes, the first planar graph that was discovered not to have a linear-area layout. Most recently, the structure of this graph has been used to develop a general framework for solving VLSI graph layout problems.

Finally, the book develops techniques for proving lower bounds on the bisection width, crossing number, and layout area of a graph. These techniques significantly extend the power and range of previous methods.

Researchers in the fields of VLSI, parallel computation, and graph theory will find this study of particular value; it is also accessible to anyone with an elementary knowledge of mathematics and computer science. The book is self-contained and presents in a unified and original manner many results scattered in the technical literature, while also covering new and fundamental results for the first time.

About the Author:

Tom Leighton is Assistant Professor of Mathematics in the Department of Applied Mathematics and Laboratory for Computer Science at MIT.

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