We consider a scheduling problem where a set of jobs is a-priori distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g. personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3 + ε)-approximation algorithm for that problem, for any ε > 0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve. We also derive lower bounds, and discuss further generalizations of the results. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Grigoriev, A., & Uetz, M. (2006). Scheduling parallel jobs with linear speedup. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3879 LNCS, pp. 203–215). https://doi.org/10.1007/11671411_16
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