Modelling message-passing programs for static mapping

An efficient mapping of a parallel program in the processors is vital for achieving a high performance on a parallel computer. When the structure of the parallel program in terms of its task execution times, task dependencies, and amount communication data, is known a priori, mapping can be accomplished statically at compile time. Mapping algorithms start from a parallel application model and map automatically tasks to processors in order to minimise the execution time of the program. In this paper we discuss the current models used in mapping parallel programs: Task Precedence Graph (TPG), Task Interaction Graph (TIG) and we define a new model called Temporal Task Interaction Graph (TTIG). The contribution of the TTIG is that it enhances these two previous models with the ability to explicitly capture the potential degree of parallel execution between adjacent tasks allowing the development of efficient mapping algorithms. Experimentation had been performed in order to show the effectiveness of TTIG model for a set of graphs. The results are compared with the optimal assignment and the obtained using TIG model and they confirm that using the TTIG model, better assignments can be obtained.