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.2016.68
URN: urn:nbn:de:0030-drops-64104
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6410/
Murray, Riley ;
Chao, Megan ;
Khuller, Samir
Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms
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}
}
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Keywords: |
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approximation algorithms, distributed computing, machine scheduling, LP relaxations, primal-dual algorithms |
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Collection: |
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24th Annual European Symposium on Algorithms (ESA 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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18.08.2016 |
