On scheduling in map-reduce and flow-shops

Abstract

The map-reduce paradigm is now standard in industry and academia for processing large-scale data. In this work, we formalize job scheduling in map-reduce as a novel generalization of the two-stage classical <i>flexible</i> flow shop (FFS) problem: instead of a single task at each stage, a job now consists of a set of tasks per stage. For this generalization, we consider the problem of minimizing the total <i>flowtime</i> and give an efficient 12-approximation in the offline setting and an online (1+&#181;)-speed <i>O</i>(1/&#181;<sup>2</sup>)-competitive algorithm. Motivated by map-reduce, we revisit the two-stage flow shop problem, where we give a dynamic program for minimizing the total <i>flowtime</i> when all jobs arrive at the same time. If there are fixed number of job-types the dynamic program yields a PTAS; it is also a QPTAS when the processing times of jobs are polynomially bounded. This gives the first improvement in approximation of flowtime for the two-stage flow shop problem since the trivial 2-approximation algorithm of Gonzalez and Sahni [29] in 1978, and the first known approximation for the FFS problem. We then consider the generalization of the two-stage FFS problem to the unrelated machines case, where we give an offline 6-approximation and an online (1+&#181;)-speed <i>O</i>(1/&#181;<sup>4</sup>)-competitive algorithm.

DOI: 10.1145/1989493.1989540

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@inproceedings{Moseley2011OnSI, title={On scheduling in map-reduce and flow-shops}, author={Benjamin Moseley and Anirban Dasgupta and Ravi Kumar and Tam{\'a}s Sarl{\'o}s}, booktitle={SPAA}, year={2011} }