An E cient Algorithm for Gray { to { BinaryPermutation

Both Gray code and binary code are frequently used in mapping arrays into hy-percube architectures. While the former is preferred when communication between adjacent array elements is needed, the latter is preferred for FFT-type communication. When diierent phases of computations have diierent types of communication patterns, the need arises to remap the data. We give a nearly optimal algorithm for permuting data from a Gray code mapping to a binary code mapping on a hy-percube with communication restricted to one input and one output channel per node at a time. Our algorithm improves over the best previously known algorithm 6] by nearly a factor of two and is optimal to within a factor of n=(n ? 1) with respect to data transfer time on an n-cube. The expected speedup is connrmed by measurements on an Intel iPSC/2 hypercube.