In a distributed system, which consists of an unknown number of processors, it is important to derive an appropriate number of processors by which the good schedule length is obtained by a task scheduling. Many task clustering heuristics have been proposed to determine the number of processors and to minimize the schedule length for scheduling a directed acyclic graph (DAG) application. However, those heuristics are not aware of the actual number of existing processors. As a result, the number of processors determined by an existing task clustering may exceed that of actually existing processors. Therefore, conventional approaches adopt merging of each cluster for reducing the number of clusters at the expense of decreasing degree of task parallelism. In this paper, we present a static cluster size determination method, which derives the lower bound of the cluster size with considering the DAG structure and the task size to data size ratio to suppress the schedule length with the small number of processors. Our experimental evaluations by simulations show that the lower bound of each cluster size determined by the proposed method has a good impact on both the schedule length and the processor utilization.
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