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.2018.26
URN: urn:nbn:de:0030-drops-94890
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Englert, Matthias ; Mezlaf, David ; Westermann, Matthias

Online Makespan Scheduling with Job Migration on Uniform Machines

LIPIcs-ESA-2018-26.pdf (0.4 MB)


In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to reassign up to k jobs to different machines in the final assignment.
For m identical machines, Albers and Hellwig (Algorithmica, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and ~~ 1.4659. They show that k = O(m) is sufficient to achieve this bound and no k = o(n) can result in a better bound.
We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a delta = Theta(1) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than 1.4659 + delta with k = o(n).
We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and ~~ 1.7992 with k = O(m). We also show that k = Omega(m) is necessary to achieve a competitive ratio below 2.
Our algorithm is based on a subtle imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

BibTeX - Entry

  author =	{Matthias Englert and David Mezlaf and Matthias Westermann},
  title =	{{Online Makespan Scheduling with Job Migration on Uniform Machines}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-94890},
  doi =		{10.4230/LIPIcs.ESA.2018.26},
  annote =	{Keywords: online algorithms, competitive analysis, minimum makespan scheduling, job migration}

Keywords: online algorithms, competitive analysis, minimum makespan scheduling, job migration
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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