Intensive Hypercube Communication. Prearranged Communication in Link-Bound Machines

Hypercube algorithms are developed for a variety of communication-intensive tasks such as transposing a matrix, histogramming, one node sending a (long) message to another, broadcasting a message from one node to all others, each node broadcasting a message to all others, and nodes exchanging messages via a fixed permutation. The algorithm for exchanging via a fixed permutation can be viewed as a deterministic analogue 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 sizes, symmetrizing, and completing, for all problems algorithms are obtained which achieve a time with an optimal highest-order term.