|Title:|| MINIMIZING THE FLOW TIME
FOR PARALLELIZABLE TASK SYSTEMS (PRELIMINARY VERSION).
|Authors:|| J. Glasgow and H. Shachnai
Consider the problem of scheduling tasks on a multiprocessor where each task can be parallelized to run simultaneously on several processors. The number of processors assigned to the execution of a task is chosen at runtime. In general, increasing the number of processors assigned to a task will decrease its execution time. Our objective is to schedule the tasks so as to minimize the mean flow time (MFT), also known as the average response time of the system. We show that this problem is NP-hard in the strong sense. For scenarios in which the runtime per task decreases linearly with the number of processors allotted to it, we present the Sorted Earliest Completion Time (SECT) heuristic. SECT is shown to achieve a worst case bound of 3 to the MFT of the optimal schedule in time O(n \log n+nm), where m is the number of processors, and n is the number of tasks.
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