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Both grid and cloud applications may require specific software for their execution. Introducing such requirements into the DAG describing the dependencies among the tasks of an application leads to a combinatorial problem with numerous possibilities of modified DAGs. This paper introduces an algorithm to obtain a single DAG with the minimum possible makespan by reducing the need for data transfer over the network. Grid networks (Grids) have been designed to provide computational resources on a large scale for advanced science and engineering. In grids, computational resources spread around the world are connected by network links composing virtual organizations for the execution of highly demanding applications.
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