Prefix Computation on a Faulty Hypercube

The fundamental question addressed in this paper is that of computing the parallel prefix operation. In particular, we study the problem of performing such an operation in an n-dimensional SIMD hypercube, Q_n, with up to n-1 node faults. In an SIMD hypercube, during a communication step, nodes can exchange information with their neighbors only across a specific dimension. We exhibit an n+5 logn algorithm for this problem. The development of the algorithm is based on the existence of two so-called free dimensions in such a faulty hypercube [6].