Prearranged Communication in Link-Bound Machines *,+

Hypercube algorithms are developed for a variety of communication-intensive tasks such as transposing a matrix, histogramming, sending a (long) message from one node to another, broadcasting a message from one node to all others, broadcasting a message from each node to all others, and exchanging messages between nodes via a fixed permutation. The algorithm for exchanging via a fixed permutation can be viewed as a deterministic analog of Valiant’s randomized routing. The algorithms are for link-bound hypercubes in which local processing time is ignored, communication time predominates, message headers are not needed because all nodes know the task being performed, and all nodes can use all communication links simultaneously. Through systematic use of techniques such as pipelining, batching, variable packet sizing, symmetrizing, and completing, for all these problems algorithms which achieve a time with an optimal highest-order term are obtained. o 1990 Academic PISS, IW.