More on 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. In a previous paper, we have reported how to derive optimal schedules made up of successive communication-steps. In this paper we assume that successive steps may overlap. We show how to obtain 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. We use graph-theoretic algorithms, and modular algebra techniques to derive these optimal schedulings