Optimal Bounds for Finding Maximum on Array of Processors with k Global Buses

The problem of finding the maximum of a set of values stored one per processor on a two-dimensional array of processors with a time-shared global bus is considered. The algorithm given by Bokhari is shown to be optimal, within a multiplicative constant, for this network and for other d-dimensional arrays. We generalize this model and demonstrate optimal bounds for finding the maximum of a set of values stored in a d-dimensional array with k time-shared global buses.