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<p>The authors consider the impact of the granularity on scheduling task graphs. Schedulingconsists of two parts, the processors assignment of tasks, also called clustering, and theordering of tasks for execution in each processor. The authors introduce two types of clusterings: nonlinear and linear clusterings. A clustering is nonlinear if two parallel tasksare mapped in the same cluster otherwise it is linear. Linear clustering fully exploits thenatural parallelism of a given directed acyclic task graph (DAG) while nonlinear clustering sequentializes independent tasks to reduce parallelism. The authors also introduce a new quantification of the granularity of a DAG and define a coarse grain DAG as the one whose granularity is greater than one. It is proved that every nonlinear clustering of a coarse grain DAG can be transformed into a linear clustering that has less or equal parallel time than the nonlinear one. This result is used to prove the optimality of some important linear clusterings used in parallel numerical computing.</p>
Index Termsscheduling; task graphs; clusterings; directed acyclic task graph; DAG; granularity; graphtheory; parallel algorithms; scheduling

A. Gerasoulis and T. Yang, "On the Granularity and Clustering of Directed Acyclic Task Graphs," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 686-701, 1993.
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