A Threshold Scheduling Strategy for Sisal on Distributed-Memory Machines

Abstract

The problem of scheduling tasks on distributed memory machines is known to be NP-complete in the strong sense, ruling out the possibility of a pseudo-polynomial algorithm. This paper introduces a new heuristic algorithm for scheduling Sisal (Streams and Iterations In a Single Assignment Language) programs on a distributed memory machine, Intel Touchstone i860. Our compile time scheduling method works on IF-2, an intermediate form based on the dataflow parallelism in the program. We initially carry out a dependence analysis, to bind the implicit dependencies across IF-2 graph boundaries, followed by a cost assignment based on Intel Touchstone i860 timings. The scheduler works in two phases. The first phase of the scheduler finds the earliest and latest completion times of each task given by the shortest and longest paths from root task to the given task respectively. A threshold defined as the difference between the latest and the earliest start times of the task, is found. The scheduler varies the value of the allowable threshold, and determines the best value for minimal schedule length. In the second phase of the scheduler, we merge the processors to generate schedule to match the available number of processors. Schedule results for several benchmark programs have been included to demonstrate the effectiveness of our approach.