A robust compile time method for scheduling task parallelism on distributed memory machines

A desirable property of a compile time scheduling algorithm is robustness against the variations in the computation and communication costs so that the run time performance is close to the compile time estimates; this aspect of scheduling has been left open in the literature. This paper introduces a compile time scheduling algorithm for variable number of available processors and then examines the impact of change of computation and communication costs on the generated schedule. The cost variations for all the nodes and all the edges are assumed to be uniform (in other words, all the node costs change by the same ratio and the edge costs change by the same ratio). This type of cost variation could result from either (i) an inaccuracy in the estimation of the instruction execution cost or the unit message passing delay, or (ii) upgrade in the CPU or routing schemes. The percentage change in the schedule time due to differences in compile time estimated performance and the run time performance with coat variations is a measure of the robustness of the algorithm. We discuss the essential conditions for robustness of the proposed algorithm and demonstrate it through an experimental study.