Scheduling Block-Cyclic Array Redistribution

This article is devoted to the run-time redistribution of arrays that are distributed in a blockcyclic fashion over a multidimensional processor grid. While previous studies have concentrated on e ciently 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. This work was supported in part by the National Science Foundation Grant No. ASC-9005933; by the Defense Advanced Research Projects Agency under contract DAAH04-95-1-0077, administered by the Army Research O ce; by the Department of Energy O ce of Computational and Technology Research, Mathematical, Information, and Computational Sciences Division under Contract DE-AC05-84OR21400; by the National Science Foundation Science and Technology Center Cooperative Agreement No. CCR-8809615; by the CNRS{ENS Lyon{INRIA project ReMaP; and by the Eureka Project EuroTOPS. Yves Robert is on leave from Ecole Normale Sup erieure de Lyon and is partly supported by DRET/DGA under contract ERE 96-1104/A000/DRET/DS/SR. The authors acknowledge the use of the Intel Paragon XP/S 5 computer, located in the Oak Ridge National Laboratory Center for Computational Sciences, funded by the Department of Energy's Mathematical, Information, and Computational Sciences Division subprogram of the O ce of Computational and Technology Research.