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Frank Thomson Leighton

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

Titles by This Author

Optimal Layouts for the Shuffle-Exchange Graph and Other Networks

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.

Titles by This Editor

Proceedings of the Fifth MIT Conference

The field of VLSI (Very Large Scale Integration) is concerned with the design, production, and use of highly complex integrated circuits. The research collected here comes from many disciplines, including computer architecture, computer-aided design, parallel algorithms, semiconductor technology, and testing. It extends to novel uses of the technology and concepts originally developed for integrated circuits, including integrated sensor arrays, digital photography, highly parallel computers, microactuators, neural networks, and a variety of special-purpose architectures and networks of special-purpose devices.