Abstract
We investigate the problem of scheduling dags with parallel tasks on binarily partitionable systems by analyzing the average-case performance ratio of the level-by-level (LL) scheduling algorithm, where n is the number of tasks. It is shown that for arbitrary probability distributions of task parallelisms and task execution times, the asymptotic average-case performance ratio of algorithm LL in scheduling parallel computations with wide dags is In particular, for exponential distributions of task execution times, the average-case performance ratio of LL in scheduling iterative computations, complete trees, partitioning algorithms and diamond dags is and respectively.
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