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Restricted Adaptivity in Stochastic Scheduling

  • We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee Ω(logm/loglogm). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of δ-delay and τ-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an O(loglogm)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any δ-delay and τ-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy.

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Author:Guillaume Sagnol, Daniel Schmidt genannt Waldschmidt
Document Type:Article
Parent Title (English):29th Annual European Symposium on Algorithms (ESA 2021)
First Page:79:1
Last Page:79:14
Series:Leibniz International Proceedings in Informatics (LIPIcs)
Year of first publication:2021
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