Scheduling Precedence Constrained Parallel Tasks on Multiprocessors Using the Harmonic System Partitioning Scheme

Abstract

We present an algorithm for scheduling precedence constrained parallel tasks on multiprocessors with noncontiguous processor allocation. The algorithm is called LLH(subscript m) (Level-by-level and List scheduling using the Harmonic system partitioning scheme), where m≥1 is a positive integer, which is a parameter for the harmonic system partitioning scheme. Three basic techniques are employed in algorithm LLH(subscript m). First, a task graph is divided into levels, and tasks are scheduled level by level to follow the precedence constraints. Second, tasks in the same level are scheduled using algorithm H(subscript m) developed in [16] for scheduling independent parallel tasks. The list scheduling method is used to implement algorithm H(subscript m). Third, the harmonic system partitioning scheme is used for processor allocation. It is shown here that for wide task graphs and some common task size distributions, as the size of a computation and m increase, and as the task sizes become smaller, the average-case performance ratio of algorithm LLH(subscript m) approaches one.