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

Authors Riley Murray, Megan Chao, Samir Khuller

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Riley Murray
Megan Chao
Samir Khuller

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Riley Murray, Megan Chao, and Samir Khuller. Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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.
  • approximation algorithms
  • distributed computing
  • machine scheduling
  • LP relaxations
  • primal-dual algorithms


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