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Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling
Citation key JaegerSkutella2018
Author Jäger, Sven and Skutella, Martin
Title of Book 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Pages 43:1–43:14
Year 2018
ISBN 978-3-95977-062-0
ISSN 1868-8969
DOI 10.4230/LIPIcs.STACS.2018.43
Location Caen
Address Dagstuhl, Germany
Volume 96
Editor Niedermeier, Rolf and Vallée, Brigitte
Publisher Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik
Series Leibniz International Proceedings in Informatics (LIPIcs)
Abstract 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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