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A. Gerasoulis, T. Yang, "On the Granularity and Clustering of Directed Acyclic Task Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 6, pp. 686701, June, 1993.  
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@article{ 10.1109/71.242154, author = {A. Gerasoulis and T. Yang}, title = {On the Granularity and Clustering of Directed Acyclic Task Graphs}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {4}, number = {6}, issn = {10459219}, year = {1993}, pages = {686701}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.242154}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  On the Granularity and Clustering of Directed Acyclic Task Graphs IS  6 SN  10459219 SP686 EP701 EPD  686701 A1  A. Gerasoulis, A1  T. Yang, PY  1993 KW  Index Termsscheduling; task graphs; clusterings; directed acyclic task graph; DAG; granularity; graphtheory; parallel algorithms; scheduling VL  4 JA  IEEE Transactions on Parallel and Distributed Systems ER   
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.
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