A unified partitioning and scheduling scheme for mapping multi-stage regular iterative algorithms onto processor arrays

This paper addresses the partitioning and scheduling problems in mapping multi-stage regular iterative algorithms onto fixed size distributed memory processor arrays. We first propose a versatile partitioning model which provides a unified framework to integrate various partitioning schemes such as locally sequential globally parallel, locally parallel globally sequential and multi-projection. To alleviate the run time data migration overhead—a crucial problem to the mapping of multi-stage algorithms, we further relax the widely adopted atomic partitioning constraint in our model such that a more flexible partitioning scheme can be achieved. Based on this unified partitioning model, a novel hierarchical scheduling scheme which applies separate schedules at different processor hierarchies is then developed. The scheduling problem is then formulated into a set of ILP problem and solved by the existing software package for optimal solutions. Examples indicate that our partitioning model is a superset of the existing schemes and the proposed hierarchical scheduling scheme can outperform the conventional one-level linear schedule.