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DOI: 10.4230/LIPIcs.ESA.2025.27

Online Makespan Scheduling Under Scenarios

Authors: Ekin Ergen

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds for our problem, which in turn leads to lower bounds for several variants of online hypergraph coloring.

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Ekin Ergen. Online Makespan Scheduling Under Scenarios. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ergen:LIPIcs.ESA.2025.27,
  author =	{Ergen, Ekin},
  title =	{{Online Makespan Scheduling Under Scenarios}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.27},
  URN =		{urn:nbn:de:0030-drops-244950},
  doi =		{10.4230/LIPIcs.ESA.2025.27},
  annote =	{Keywords: online scheduling, scenario-based model, online algorithms}
}

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Online Makespan Scheduling Under Scenarios

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