A Graph Grammar to Transform a Dataflow Graph into a Multithread Graph and its Application in Task Scheduling

The scheduling of tasks in a parallel program is an NP-complete problem, where scheduling tasks over multiple processing units requires an effective strategy to maximize the exploitation of the parallel hardware. Several studies focus on the scheduling of parallel programs described into DAGs (Directed Acyclic Graphs). However, this representation does not describe a multithreaded program suitably. This paper shows the structure and semantics of a DCG, an abstraction which describes a multithreaded program, and proposes standards to map structures found in DAGs into segments of a DCG. A graph grammar has been developed to perform the proposed transformation and case studies using DAGs found in the literature validate the transformation process. Besides the automatic translation and precise definition of the mapping, the use of a formal language also allowed the verification of the existence and uniqueness of the out coming model.