License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.41
URN: urn:nbn:de:0030-drops-129076
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Eberle, Franziska ; Megow, Nicole ; Schewior, Kevin

Optimally Handling Commitment Issues in Online Throughput Maximization

LIPIcs-ESA-2020-41.pdf (0.6 MB)


We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on m machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis, it is commonly required that jobs contain some slack ε > 0, which means that the feasible time window for scheduling a job is at least 1+ε times its processing time. In this paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs. This is very relevant, e.g., in providing cloud-computing services and disallows last-minute rejections of critical tasks. We present the first online algorithm for handling commitment on parallel machines for arbitrary slack ε. When the scheduler must commit upon starting a job, the algorithm is Θ(1/ε)-competitive. Somewhat surprisingly, this is the same optimal performance bound (up to constants) as for scheduling without commitment on a single machine. If commitment decisions must be made before a job’s slack becomes less than a δ-fraction of its size, we prove a competitive ratio of 𝒪(1/(ε - δ)) for 0 < δ < ε. This result nicely interpolates between commitment upon starting a job and commitment upon arrival. For the latter commitment model, it is known that no (randomized) online algorithms admits any bounded competitive ratio.

BibTeX - Entry

  author =	{Franziska Eberle and Nicole Megow and Kevin Schewior},
  title =	{{Optimally Handling Commitment Issues in Online Throughput Maximization}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-129076},
  doi =		{10.4230/LIPIcs.ESA.2020.41},
  annote =	{Keywords: Deadline scheduling, throughput, online algorithms, competitive analysis}

Keywords: Deadline scheduling, throughput, online algorithms, competitive analysis
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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