On symbolic scheduling and parallel complexity of loops

We first consider the symbolic scheduling and performance prediction of a partitioned single loop on message passing architectures with non zero communication and a sufficient number of processors. The loop body contains a set of coarse grain tasks whose computational weights change during the course of the iterations. Using the macro dataflow task: model and software pipelining techniques, we develop an algorithm for computing a heuristic schedule, and provide analytic and experimental results on the correctness and asymptotic performance of this schedule. Using this result, we can show the impact of partitioning on the performance of parallelization. While this result is effective for a class of loops, there are many other methods proposed for loop parallelization. An interesting fundamental question is whether every instance of a nested loop can be efficiently executed, We present some positive and negative results on this issue