An Asymptotically Optimal Layout for the Shuffle-exchange Graph

Abstract

The shuffle-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, perform permutations and sort lists. The algorithms needed for these operations are quite simple and many require no more than logarithmic time and constant space per processor. In this paper, we describe an O(n^2/log^2N)-area layout for the shuffle-exchange graph on a two-dimentional grid. The layout is the first which is known to achieve Thompson's asymptotic lower bound.