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.2016.75
URN: urn:nbn:de:0030-drops-64162
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6416/
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Schwiegelshohn, Chris ; Schwiegelshohn, Uwe

The Power of Migration for Online Slack Scheduling

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LIPIcs-ESA-2016-75.pdf (0.5 MB)

Abstract

We investigate the power of migration in online scheduling for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. Once we decide to accept a job, we have to complete it before its deadline d that satisfies d >= (1+epsilon)p + r, where p is the processing time, r the submission time and the slack epsilon > 0 a system parameter. Typically, the hard case arises for small slack epsilon << 1, i.e. for near-tight deadlines. Without migration, a greedy acceptance policy is known to be an optimal deterministic online algorithm with a competitive factor of (1+epsilon)/epsilon (DasGupta and Palis, APPROX 2000). Our first contribution is to show that migrations do not improve the competitive ratio of the greedy acceptance policy, i.e. the competitive ratio remains (1+epsilon)/epsilon for any number of machines.

Our main contribution is a deterministic online algorithm with almost tight competitive ratio on any number of machines. For a single machine, the competitive factor matches the optimal bound of (1+epsilon)/epsilon of the greedy acceptance policy. The competitive ratio improves with an increasing number of machines. It approaches (1+epsilon) ln((1+epsilon)/epsilon) as the number of machines converges to infinity. This is an exponential improvement over the greedy acceptance policy for small epsilon. Moreover, we show a matching lower bound on the competitive ratio for deterministic algorithms on any number of machines.

BibTeX - Entry

@InProceedings{schwiegelshohn_et_al:LIPIcs:2016:6416,
  author =	{Chris Schwiegelshohn and Uwe Schwiegelshohn},
  title =	{{The Power of Migration for Online Slack Scheduling}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{75:1--75:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6416},
  URN =		{urn:nbn:de:0030-drops-64162},
  doi =		{10.4230/LIPIcs.ESA.2016.75},
  annote =	{Keywords: Online scheduling, deadlines, preemption with migration, competitive analysis}
}

Keywords: Online scheduling, deadlines, preemption with migration, competitive analysis
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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