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The Map-Reduce computing framework rose to prominence with datasets of suchsize that dozens of machines on a single cluster were needed for individualjobs. As datasets approach the exabyte scale, a single job may need distributedprocessing not only on multiple machines, but on multiple clusters. We considera scheduling problem to minimize weighted average completion time of N jobs onM distributed clusters of parallel machines. In keeping with the scale of theproblems motivating this work, we assume that (1) each job is divided into M"subjobs" and (2) distinct subjobs of a given job may be processedconcurrently.  When each cluster is a single machine, this is the NP-Hard concurrent openshop problem. A clear limitation of such a model is that a serial processingassumption sidesteps the issue of how different tasks of a given subjob mightbe processed in parallel. Our algorithms explicitly model clusters as pools ofresources and effectively overcome this issue.  Under a variety of parameter settings, we develop two constant factorapproximation algorithms for this problem. The first algorithm uses an LPrelaxation tailored to this problem from prior work. This LP-based algorithmprovides strong performance guarantees. Our second algorithm exploits asurprisingly simple mapping to the special case of one machine per cluster.This mapping-based algorithm is combinatorial and extremely fast. These are thefirst constant factor approximations for this problem.

Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms [Full Version]