BibTeX
@MISC{Grigoriev05schedulingparallel,
author = {Alexander Grigoriev and Marc Uetz},
title = {Scheduling Parallel Jobs with Monotone Speedup },
year = {2005}
}
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Abstract
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 discrete 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 objective is to find a resource allocation and a schedule that minimizes the makespan. In contrast to previous approaches, we explicitly allow for succinctly encodable time-resource tradeoff functions. This assumption calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, with performance bound (3 + ε) for any ε> 0. Our approach relies on a fully polynomial time approximation scheme to solve the mathematical programming relaxation. This result is interesting in itself, because we also show that the underlying mathematical program is NP-hard to solve. We also derive lower bounds for the approximation.
Keyphrases
monotone speedup1 parallel job processing time scheduling problem encodable time-resource tradeoff function approach relies performance bound parallel machine mathematical programming polynomial time approximation scheme integer mathematical program mathematical programming technique previous approach discrete renewable resource first polynomial time approximation algorithm approximation algorithm key word underlying mathematical program resource allocation computa-tional complexity history mathematical programming relaxation
