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DOI: 10.4230/LIPIcs.ESA.2016.68
URN: urn:nbn:de:0030-drops-64104
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6410/
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Murray, Riley ; Chao, Megan ; Khuller, Samir

Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms

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Abstract

The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed processing not only on multiple machines, but on multiple clusters. We consider a scheduling problem to minimize weighted average completion time of n jobs on m distributed clusters of parallel machines. In keeping with the scale of the problems motivating this work, we assume that (1) each job is divided into m "subjobs" and (2) distinct subjobs of a given job may be processed concurrently. When each cluster is a single machine, this is the NP-Hard concurrent open shop problem. A clear limitation of such a model is that a serial processing assumption sidesteps the issue of how different tasks of a given subjob might be processed in parallel. Our algorithms explicitly model clusters as pools of resources and effectively overcome this issue. Under a variety of parameter settings, we develop two constant factor approximation algorithms for this problem. The first algorithm uses an LP relaxation tailored to this problem from prior work. This LP-based algorithm provides strong performance guarantees. Our second algorithm exploits a surprisingly simple mapping to the special case of one machine per cluster. This mapping-based algorithm is combinatorial and extremely fast. These are the first constant factor approximations for this problem.

BibTeX - Entry

@InProceedings{murray_et_al:LIPIcs:2016:6410,
  author =	{Riley Murray and Megan Chao and Samir Khuller},
  title =	{{Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{68:1--68:17},
  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/2016/6410},
  URN =		{urn:nbn:de:0030-drops-64104},
  doi =		{10.4230/LIPIcs.ESA.2016.68},
  annote =	{Keywords: approximation algorithms, distributed computing, machine scheduling, LP relaxations, primal-dual algorithms}
}

Keywords: approximation algorithms, distributed computing, machine scheduling, LP relaxations, primal-dual algorithms
Seminar: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016


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