General Multiprocessor Task Scheduling: Approximate Solutions in Linear Time
We study the problem of scheduling a set of n independent tasks on a fixed number of parallel processors, where the execution time of a task is a function of the subset of processors assigned to the task. We propose a fully polynomial approximation scheme that for any fixed ∈ > 0 finds a preemptive schedule of length at most (1 + ∈) times the optimum in O(n) time.We also discuss the non-preemptive variant of the problem, and present a polynomial approximation scheme that computes an approximate solution of any fixed accuracy in linear time. In terms of the running time, this linear complexity bound gives a substantial improvement of the best previously known polynomial bound .
KeywordsTotal Execution Time Total Processing Time Polynomial Time Approximation Scheme Preemptive Schedule Small Task
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