Impact of mixed-parallelism on parallel implementations of the Strassen and Winograd matrix multiplication algorithms

摘要

In this paper we study the impact of the simultaneous exploitation of data- and task-parallelism, so called mixed-parallelism, on the Strassen and Winograd matrix multiplication algorithms. This work takes place in the context of Grid computing and, in particular, in the Client-Agent(s)-Server(s) model, where data can already be distributed on the platform. For each of those algorithms, we propose two mixed-parallel implementations. The former follows the phases of the original algorithms while the latter has been designed as the result of a list scheduling algorithm. We give a theoretical comparison, in terms of memory usage and execution time, between our algorithms and classical data-parallel implementations. This analysis is corroborated by experiments. Finally, we give some hints about heterogeneous and recursive versions of our algorithms.