A Graph Grammar to Transform DAGs into Graphs Describing Multithreaded Programs

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 DAG found in the literature, validate the transformation process.