Optimal latency - throughput tradeoffs for data parallel pipelines

Abstract

This paper addresses optimal mapping of parallel programs composed of a chain of data parallel tasks onto the processors of a parallel system. The input to this class of programs is a stream of data sets, each of which is processed in order by the chain of tasks. This computation structure, also referred to as a data parallel pipeline, is common in several application domains including digital signal processing, image processing, and computer vision. The parameters of the performance of stream processing are latency (the time to process an individual data set) and throughput (the aggregate rate at which the data sets are processed). These two criterion are distinct since multiple data sets can be pipelined or processed in parallel. We present a new algorithm to determine a processor mapping of a chain of tasks that optimizes the latency in the presence of throughput constraints, and discuss optimization of the throughput with latency constraints. The problem formulation uses a general and realistic model of inter-task communication, and addresses the entire problem of mapping, which includes clustering tasks into modules, assignment of processors to modules, and possible replication of modules. The main algorithms are based on dynamic programming and their execution time complexity is polynomial in the number of processors and tasks. The entire framework is implemented as an automatic mapping tool in the Fx parallelizing compiler for a dialect of High Performance Fortran.