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DOI: 10.4230/LIPIcs.ICALP.2019.86
URN: urn:nbn:de:0030-drops-106621
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10662/
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Moseley, Benjamin

Scheduling to Approximate Minimization Objectives on Identical Machines

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LIPIcs-ICALP-2019-86.pdf (0.5 MB)


Abstract

This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are n jobs and each job j is associated with a monotonically increasing function g_j. The goal is to design a schedule that minimizes sum_{j in [n]} g_{j}(C_j) where C_j is the completion time of job j in the schedule. An O(1)-approximation is known for the single machine case. On multiple machines, this paper shows that if the scheduler is required to be either non-migratory or non-preemptive then any algorithm has an unbounded approximation ratio. Using preemption and migration, this paper gives a O(log log nP)-approximation on multiple machines, the first result on multiple machines. These results imply the first non-trivial positive results for several special cases of the problem considered, such as throughput minimization and tardiness. Natural linear programs known for the problem have a poor integrality gap. The results are obtained by strengthening a natural linear program for the problem with a set of covering inequalities we call job cover inequalities. This linear program is rounded to an integral solution by building on quasi-uniform sampling and rounding techniques.

BibTeX - Entry

@InProceedings{moseley:LIPIcs:2019:10662,
  author =	{Benjamin Moseley},
  title =	{{Scheduling to Approximate Minimization Objectives on Identical Machines}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{86:1--86:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10662},
  URN =		{urn:nbn:de:0030-drops-106621},
  doi =		{10.4230/LIPIcs.ICALP.2019.86},
  annote =	{Keywords: Scheduling, LP rounding, Approximation Algorithms}
}

Keywords: Scheduling, LP rounding, Approximation Algorithms
Seminar: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 08.07.2019


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