Broadcasting algorithms in faulty SIMD hypercubes

Abstract

The authors consider an important global operation, namely, broadcasting in a faulty hypercube. In particular, they study the problem of broadcasting in an n-dimensional single-instruction multiple data (SIMD) hypercube, Q/sub n/, with up to n-1 node faults. Given a set of at most n-1 faults, they develop an ordering d/sub 1/, d/sub 2/, . ., d/sub n/ of n dimensions, depending on where the faults are located. An important and useful property of this dimension ordering is the following: if the n-cube is partitioned into k-subcubes using the first k dimensions of this ordering, namely d/sub 1/, d/sub 2/,. . .d/sub k/ for any 1>