Optimal mapping of sequences of data parallel tasks

Many applications in a variety of domains including digital signal processing, image processing and computer vision are composed of a sequence of tasks that act on a stream of input data sets in a pipelined manner. Recent research has established that these applications are best mapped to a massively parallel machine by dividing the tasks into modules and assigning a subset of the available processors to each module. This paper addresses the problem of optimally mapping such applications onto a massively parallel machine. We formulate the problem of optimizing throughput in task pipelines and present two new solution algorithms. The formulation uses a general and realistic model for inter-task communication, takes memory constraints into account, and addresses the entire problem of mapping which includes clustering tasks into modules, assignment of processors to modules, and possible replication of modules. The first algorithm is based on dynamic programming and finds the optimal mapping of k tasks onto P processors in O(P⁴k²) time. We also present a heuristic algorithm that is linear in the number of processors and establish with theoretical and practical results that the solutions obtained are optimal in practical situations. The entire framework is implemented as an automatic mapping tool for the Fx parallelizing compiler for High Performance Fortran. We present experimental results that demonstrate the importance of choosing a good mapping and show that the methods presented yield efficient mappings and predict optimal performance accurately.