Layouts for the Suffle-Exchange Graph Based on the Complex Plane Diagram

Abstract

The shuffule-exchange graph is one of the best structures known for parallel computation. Among other things, a shuffle-exchange computer can be used to compute discrete. Fourier transforms, multiply matrices, evaluate polynomials, performa permutations and sort lists. The algorithms needed for these operations are extremely simple and many require no more than logarithmic time and constant space per processor. In this paper, we analyze the algebraic structure of the shuffle-exchange graph in order to find area-efficient embeddings of the graph in a two-dimensinoal grid. The results are applicable to the design of Very Large Scale Integration (VLSI) circuit layouts for a shuffle-exchange computer.