Broadcasting algorithms in faulty SIMD hypercubes

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_n, with up to n -1 node faults. Given a set of at most n-1 faults, they develop an ordering d₁, d₂, . ., d_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 d₁, d₂,. . .d_k for any 1⩽k⩽n, then each k-subcube contains at most k-1 faults. This result is used to develop several new algorithms for broadcasting. These algorithms are n+3 log n, n+2 log n+2, n+ log n+0 (log log n), n + log n+5, and n+12 time steps, respectively, and thus improve upon the best known algorithms for this problem