License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2021.79
URN: urn:nbn:de:0030-drops-146603
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14660/
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Sagnol, Guillaume ; Schmidt genannt Waldschmidt, Daniel

Restricted Adaptivity in Stochastic Scheduling

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LIPIcs-ESA-2021-79.pdf (0.9 MB)

Abstract

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((log m)/(log log m)). 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 ?(log log m)-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.

BibTeX - Entry

@InProceedings{sagnol_et_al:LIPIcs.ESA.2021.79,
  author =	{Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel},
  title =	{{Restricted Adaptivity in Stochastic Scheduling}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14660},
  URN =		{urn:nbn:de:0030-drops-146603},
  doi =		{10.4230/LIPIcs.ESA.2021.79},
  annote =	{Keywords: stochastic scheduling, makespan minimzation, approximation algorithm, fixed assignment policy, non-anticipatory policy}
}

Keywords: stochastic scheduling, makespan minimzation, approximation algorithm, fixed assignment policy, non-anticipatory policy
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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