Global semigroup operations in faulty SIMD hypercubes

The authors consider the problem of computing a global semigroup operation (such as addition and multiplication) on a faulty hypercube. In particular, they study the problem of performing such an operation in an n-dimensional SIMD hypercube Q/sub n/, with upto n-1 node and/or link faults. In an SIMD hypercube, during a communication step, nodes can exchange information with their neighbors only across a specific dimension. Given a set of 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 f this ordering, namely d/sub 1/,d/sub 2/. . .d/sub k/ for any 1>