Adaptive Cyclic Scheduling of Nested Loops

The parallelization of computational intensive programs can lead to dramatic performance improvements. Usually these programs contain repetitive iterations, the majority in the form of nested DO(FOR) loops. The iterations within a loop nest fall into two types: independent iterations and precedence constrained iterations. Furthermore, the precedence constraints can be uniform (constant) or nonuniform throughout the execution of the program. The index space of a uniform dependence loop, due to the existence of dependence vectors, This work was partially supported by the PROTAGORAS project of NTUA. is partitioned into subspaces of points that can be executed at a certain time instance. The geometric representations of these sets form polygonal shapes called wavefronts or hyperplanes, with special attributes and characteristics. In this paper we tackle the uniform precedence constraints case, and we present a novel scheduling technique for perfectly nested loops. Our technique is suitable for the two most common network architectures: homogeneous and heterogeneous systems, regardless of their underlying interconnection network. The presented method exploits the geometric properties of the index space in order to arrive at an efficient geometric decomposition. This approach significantly reduces the communication cost, which in most cases is the main drawback of the parallel performance.