Scheduling block-cyclic array redistribution

This article is devoted to the run-time redistribution of one-dimensional arrays that are distributed in a block-cyclic fashion over a processor grid. While previous studies have concentrated on efficiently generating the communication messages to be exchanged by the processors involved in the redistribution, we focus on the scheduling of those messages: how to organize the message exchanges into "structured" communication steps that minimize contention. We build upon results of Walker and Otto, who solved a particular instance of the problem, and we derive an optimal scheduling for the most general case, namely, moving from a CYCLIC(r) distribution on a P-processor grid to a CYCLIC(s) distribution on a Q-processor grid, for arbitrary values of the redistribution parameters P, Q, r, and s.