Approximation algorithms for energy, reliability and makespan optimization problems

TL;DR

This paper develops approximation algorithms for scheduling tasks on unreliable, energy-efficient processors, balancing energy, reliability, and makespan constraints, with optimal solutions for chains and approximate solutions for independent tasks.

Contribution

It introduces a fully polynomial approximation scheme for linear task chains and an approximation algorithm with relaxed makespan for independent tasks, addressing complex tri-criteria scheduling.

Findings

Polynomial-time approximation scheme for linear chains.

No constant-factor approximation for independent tasks unless P=NP.

Approximation algorithm with relaxed makespan for independent tasks.

Abstract

In this paper, 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 to re-execute or replicate tasks (i.e., execute twice a 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 these particular classes of task graphs. 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 are able in this case to propose an approximation algorithm with a relaxation on the makespan constraint.