Consider a system of independent tasks to be scheduled without preemption on a parallel computer. For each task the number of processors required, the execution time, and a weight are known. The problem is to find a schedule with minimum weighted average response time. We present an algorithm called SMART (which stands for scheduling to minimize average response time) for this problem that produces solutions that are within a factor of 8.53 of optimal. To our knowledge this is the first polynomial-time algorithm for the minimum weighted average response time problem that achieves a constant bound. In addition, for the unweighted case (that is, where all the weights are unity) we describe a variant of SMART that produces solutions that are within a factor of 8 of optimal, improving upon the best known bound of 32 for this special case.

A parallelizable (or malleable) task is one which can be run on an arbitrary number of processors, with a task execution time that depends on the number of processors allotted to it. Consider a system of M independent parallelizable tasks which are to be scheduled without preemption on a parallel computer consisting of P identical processors. For each task, the execution time is a known function of the number of processors allotted to it. The goal is to find (1) for each task i, an allotment of processors β, and (2) overall, a non-preemptive schedule assigning the tasks to the processors which minimizes the average response time of the tasks. Equivalently, we can minimize the flow time which is the sum of the completion times of each of the tasks.