parallel architectures, multitasked parallel architectures, pipelined computations
The availability of large scale multitasked parallel architectures introduces the following processor assignment problem: we are given a long sequence of data sets, each of which is to undergo processing by a collection of tasks whose inter-task data dependencies form a series-parallel partial order. Each individual task is potentially parallelizable, with a known experimentally determined execution signature. Recognizing that data sets can be pipelined through the task structure, the problem is to find a "good" assignment of processors to tasks. Two objectives interest us: minimal response time per data set given a throughput requirement, and maximal throughput given a response time requirement. Our approach is to decompose a series-parallel task system into its essential "serial" and "parallel" components; our problem admits the independent solution and re-composition of each such component. We provide algorithms for the series analysis, and use an algorithm due to Krishnamurti and Ma for the parallel analysis. For a p processor system and a series-parallel precedence graph with n constituent tasks, we give a O(np2) algorithm that finds the optimal assignment (over a broad class of assignments) for the response time optimization problem; we find the assignment optimizing the constrained throughput in O(np2log p) time. Our techniques are applied to a task system in computer vision.
Choudhary, Alok N.; Narahari, Bhagirath; Nicol, David; and Simha, Rahul, "Optimal Processor Assignment for a Class of Pipelined Computations" (1994). Electrical Engineering and Computer Science. 33.