Total exchange in faulty SIMD hypercubes

We develop algorithms for performing total exchange (all-to-all broadcast) in an n-dimensional faulty SIMD hypercube, Q/sub n/, with up to n/spl minus/1 node faults. In an SIMD hypercube, during a communication step, nodes can exchange information with their neighbors only across a specific dimension. We describe a sequence of algorithms which take N log N, N log n, 3N/spl minus/7, 2.5N/spl minus/7 steps for this problem. By carefully analyzing these algorithms and a property of certain ordering of dimensions, we obtain an improved algorithm which takes 2N steps.<
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