2006 | OriginalPaper | Buchkapitel
Scheduling Parallel Jobs with Linear Speedup
verfasst von : Alexander Grigoriev, Marc Uetz
Erschienen in: Approximation and Online Algorithms
Verlag: Springer Berlin Heidelberg
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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.