Scheduling DAGs with random parallel tasks on binarily partitionable systems

Abstract

We investigate the problem of scheduling dags with parallel tasks on binarily partitionable systems by analyzing a n ðLLÞ; 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 a 1 ðLLÞ ¼ 1: 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 a n ðLLÞ ¼ 1 þ Oðlog n=nÞ; 1 þ Oððlog nÞ 2 =nÞ; 1 þ Oððlog nÞ 2 =nÞ and 1 þ Oððlog nÞ 2 = ffiffi ffi n p Þ; respectively.