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Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling
Zitatschlüssel JaegerSkutella2018
Autor Jäger, Sven and Skutella, Martin
Buchtitel 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Seiten 43:1–43:14
Jahr 2018
ISBN 978-3-95977-062-0
ISSN 1868-8969
DOI 10.4230/LIPIcs.STACS.2018.43
Ort Caen
Adresse Dagstuhl, Germany
Jahrgang 96
Herausgeber Niedermeier, Rolf and Vallée, Brigitte
Verlag Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik
Serie Leibniz International Proceedings in Informatics (LIPIcs)
Zusammenfassung Minimizing the sum of weighted completion times on m identical parallel machines is one of the most important and classical scheduling problems. For the stochastic variant where processing times of jobs are random variables, Möhring, Schulz, and Uetz (1999) presented the first and still best known approximation result, achieving, for arbitrarily many machines, performance ratio 1+1/2(1+Δ), where Δ is an upper bound on the squared coefficient of variation of the processing times. We prove performance ratio 1+1/2(√2-1)(1+Δ) for the same underlying algorithm–-the Weighted Shortest Expected Processing Time (WSEPT) rule. For the special case of deterministic scheduling (i.e., Δ=0), our bound matches the tight performance ratio 1/2(1+√2) of this algorithm (WSPT rule), derived by Kawaguchi and Kyan in a 1986 landmark paper. We present several further improvements for WSEPT's performance ratio, one of them relying on a carefully refined analysis of WSPT yielding, for every fixed number of machines m, WSPT's exact performance ratio of order 1/2(1+√2)-O(1/m²).
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