Fast pipelined prefix computations on MIMD hypercubes

This paper presents a one-pass parallel algorithm to perform k prefix computations, each of which concerning with n/2 operands, on an MIMD hypercube with 2n nodes. Our one-pass algorithm takes k + 2 log n + O(1) time steps for performing these k prefix computations on the hypercube. With the same time bound, the number of operands in each prefix computation can be extended to n - 1. Furthermore, when the number of processors used, say, 2p, is much less than 29, our one-pass algorithm can be slightly modified to perform these k prefix computations in k n/p + 2 log p + O(1) time steps.