Complexity Issues in VLSI Optimal Layouts for the Shuffle-Exchange Graph and Other Networks

About Complexity Issues in VLSI Optimal Layouts for the Shuffle-Exchange Graph and…

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…

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