Analysis of Data Flow for SIMD (Single Instruction Multiple Data) Systems.

摘要

Starting with an exact definition of classes of SIMD (single instruction, multiple data) systems, a general approach to obtaining lower time bounds by data flow analysis is presented. Several interconnection schemes, such as the square net, the perfect shuffle, the infinite binary tree, etc. are analyzed with respect to their data transfer possibilities. For some types of computational problems the data dependencies are analyzed in a quantitative way. From both types of analysis, lower time bounds result for many combinations of SIMD systems and computational problems, for example, omega(log N) for on-line quadtree-net systems and the computation of Voronoi diagrams for N planar points, omega(N) for off-line diagonal-net systems and the two-dimensional discrete Fourier transform, and omega(square root of N) for off- or on-line Illiac-net systems and sorting of N items. (Author)