## 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.

Original language | English (US) |
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Pages (from-to) | 2777-2798 |

Number of pages | 22 |

Journal | Algorithmica |

Volume | 80 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2018 |

## Keywords

- Approximation algorithms
- Distributed computing
- LP relaxations
- Machine scheduling
- Primal-dual algorithms

## ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics