Optimal Parallel Prefix on the Postal Model

This paper explores the prefix operation on a message-passing fully connected multicomputer with multiport postal communication. We present an exact communication lower bound for the prefix operation on the model. Two efficient parallel prefix algorithms are also presented; they are optimal in terms of the number of communication steps. For an input of size n, one of the algorithms using n processors is also time-optimal; the other algorithm using p < n processors can be cost-optimal and can achieve linear speedup.