Scheduling Moldable Tasks with Precedence Constraints and Arbitrary Speedup Functions on Multiprocessors

Abstract

Due to the increasing number of cores of current parallel machines, the question arises to which cores parallel tasks should be mapped. Thus, parallel task scheduling is now more relevant than ever, especially under the moldable task model, in which tasks are allocated a fixed number of processors before execution. Scheduling algorithms commonly assume that the speedup function of moldable tasks is either non-decreasing, sub-linear or concave. In practice, however, the resulting speedup of parallel programs on current hardware with deep memory hierarchies is most often neither non-decreasing nor concave.

We present a new algorithm for the problem of scheduling moldable tasks with precedence constraints for the makespan objective and for arbitrary speedup functions. We show through simulation that the algorithm not only creates competitive schedules for moldable tasks with arbitrary speedup functions, but also outperforms other published heuristics and approximation algorithms for non-decreasing speedup functions.