Semi on-line scheduling on three processors with known sum of the tasks

Authors:
Enrico Angelelli;Maria Grazia Speranza;Zsolt Tuza
Affiliations:
Department of Quantitative Methods, University of Brescia, Brescia, Italy;Department of Quantitative Methods, University of Brescia, Brescia, Italy;Comp. and Autom. Inst., Hungary Academy of Science, Budapest, Hungary and Department of Computer Science, University of Veszprem, Veszprem, Hungary
Venue:
Journal of Scheduling
Year:
2007

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Abstract

We consider a semi on-line version of the multiprocessor scheduling problem on three processors, where the total size of the tasks is known in advance. We prove a lower bound $1+\frac{\sqrt{129}-9}{6}1.3929$ on the competitive ratio of any algorithm and propose a simple algorithm with competitive ratio equal to 1.5. The performance is improved to $1+\frac{8}{19} by a preprocessing strategy. The latter algorithm is only 2% away from the lower bound.