An optimal scheduling scheme for tiling in distributed systems

There exist several scheduling schemes for parallelizing loops without dependences for shared and distributed memory systems. However, efficiently parallelizing loops with dependences is a more complicated task. This becomes even more difficult when the loops are executed on a distributed memory cluster where communication and synchronization can be a bottleneck. The problem lies in the processor idle time which occurs during the beginning and final stages of the execution. In this paper we propose a new scheduling scheme that minimizes the processor idle time and thus it enhances load balancing and performance. The new scheme is applied to two-dimensional iteration spaces with dependences. The proposed scheduling scheme follows a tiled wavefront pattern in which the tile size gradually decreases in all dimensions. We have tested the proposed scheme on a dedicated and homogeneous cluster of workstations and we verified that it significantly improves execution times over scheduling using traditional tiling.