Effect of variation in compile time costs on scheduling tasks on distributed memory systems

One of the major limitations of compile time scheduling schemes is the inability to precisely determine the computation and communication costs prior to generating the schedule. The authors address the issue of sensitivity of a given scheduling algorithm to the variations in imprecisely known compile time costs. The variations in the compile time costs can affect in one of the two ways: (i) original schedule found by the algorithm using estimated compile time costs does not change (schedule is invariant), or (ii) original schedule found by the algorithm changes when the costs change. For the first scenario, they have derived the conditions under which the schedule found by our algorithm would be invariant. For those cases where the schedule length changes, they have also introduced a measure of sensitivity of the schedule or the scheduling algorithm, defined as the ratio of percentage change in schedule length to that of maximum allowable percentage change in a node computation cost or an edge communication cost. Through an experimental study they show that the proposed algorithm is extremely insensitive and can be used in practical scheduling situations, where the compile time costs are known imprecisely.