Makespan Minimization for Parallel Jobs with Energy Constraint

Abstract

We are given a set of parallel jobs that have to be executed on a set of speed-scalable processors varying their speeds dynamically. Running a job at a slower speed is more energy efficient, however it takes longer time and affects the performance. Every job is characterized by the processing volume and the number of the required processors. Our objective is to minimize the maximum completion time so that the energy consumption is not greater than a given energy budget. For various particular cases we propose polynomial-time approximation algorithms, consisting of two stages. At the first stage, we give an auxiliary convex program. By solving this problem in polynomial time, we find processing times of jobs and a lower bound on the makespan. Then, at the second stage, we transform our problem to the classical problem without speed scaling and construct a feasible schedule.