Section: New Results

Approximation algorithms for energy, reliability and makespan optimization problems

Participants : Guillaume Aupy, Anne Benoit.

We consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of identical processors, whose speed can be dynamically modified. It is also subject to failures: if a processor is slowed down to decrease the energy consumption, it has a higher chance to fail. Therefore, the scheduling problem requires us to re-execute or replicate tasks (i.e., execute twice the same task, either on the same processor, or on two distinct processors), in order to increase the reliability. It is a tri-criteria problem: the goal is to minimize the energy consumption, while enforcing a bound on the total execution time (the makespan), and a constraint on the reliability of each task.

Our main contribution is to propose approximation algorithms for linear chains of tasks and independent tasks. For linear chains, we design a fully polynomial-time approximation scheme. However, we show that there exists no constant factor approximation algorithm for independent tasks, unless P=NP, and we propose in this case an approximation algorithm with a relaxation on the makespan constraint.

This work has been published in the Parallel Processing Letters [4] .