Approximation Algorithms for Energy, Reliability, and Makespan Optimization Problems

Guillaume Aupy 1, 2 Anne Benoit 1, 2
Abstract : 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.
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Parallel Processing Letters, World Scientific Publishing, 2016, Parallel Processing Letters, 26 (01), pp.23. 〈http://www.worldscientific.com〉
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Guillaume Aupy, Anne Benoit. Approximation Algorithms for Energy, Reliability, and Makespan Optimization Problems. Parallel Processing Letters, World Scientific Publishing, 2016, Parallel Processing Letters, 26 (01), pp.23. 〈http://www.worldscientific.com〉. 〈hal-01252333〉

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