Preemptive Scheduling of Parallel Tasks

Consider a system of independent parallel tasks which are to be scheduled on a parallel computer. Preemptive execution of the tasks is allowed as long as there is no task magration between the processors, and all subtasks associated with a task are active at the same time. For each task the number of processors, the execution time and a weight are known. The problem is to find a schedule that minimizes the mean weighted flow time. Recently, a polynomial algorithm has been presented for this NP-hard problem which does not allow preemption and produces solutions within a fixed multiplicative constant (10.45) of the optimal non-preemptive schedule. It has also been shown that when all the tasks require only a single processor preemption does not reduce the cost of the optimal schedule. In this paper we show that when tasks run across multiple processors preemption can produce better solutions. We describe a new algorithm with a bound of approximately 2.42 and show that this bound is tight for the algorithm. An interesting feature of our method is that it requires that at most two tasks be resident at any time on a give processor.