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Among the numerous DAG scheduling heuristics suitable for heterogeneous systems, the Heterogeneous Earliest Finish Time (HEFT) heuristic is known to give good results in short time. In this paper, we propose an improvement of HEFT, where the locally optimal decisions made by the heuristic do not rely on estimates of a single task only, but also look ahead in the schedule and take into account information about the impact of this decision to the children of the task being allocated. Preliminary simulation results indicate that the lookahead variation of HEFT can effectively reduce the makespan of the schedule in most cases without making the algorithm's execution time prohibitively high.
Bittencourt et al. (Mon,) studied this question.