Efficient granularity and clustering of the directed acyclic graphs

The granularity of the DAG which determines the trade-off between communication and execution costs is the most important factor in DAG scheduling. So we firstly give a DAG model and its clustering problem; Secondly, we address the drawbacks of the existing granularity definitions; Thirdly, we propose a new granularity definition of the DAG which is very useful for the large communication delay DAGs. Based on this new definition, we prove that nonlinearly clustering is better for linearly clustering for the fine grain DAGs; Finally, we give the bounds for linearly clustering for the DAGs.