Energy Efficient Scheduling of Parallelizable Jobs

This paper considers scheduling parallelizable jobs in the non-clairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of resource augmentation over the optimal solution. However, these lower bounds were given only for certain families of algorithms that do not recognize the parallelizability of alive jobs. In this work, we circumvent previous lower bounds shown and give a scalable algorithm under the natural assumption that the algorithm can know the current parallelizability of a job. When a general power function is considered, this is also the first algorithm that has a constant competitive ratio for the problem using any amount of resource A preliminary version of this paper appeared in the proceeding of the 24th ACM-SIAM Symposium on Discrete Algorithms, 2013 [27]. Email addresses: [email protected] (Kyle Fox ), [email protected] (Sungjin Im), [email protected] (Benjamin Moseley ) K. Fox was supported in part by the Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF), made possible in part by the American Recovery and Reinvestment Act of 2009, administered by ORISE-ORAU under contract no. DE-AC0506OR23100. S. Im was supported in part by NSF grants CCF-1016684, 1409130 and 1617653. B. Moseley was partially supported by NSF grants CCF-1617724, CCF-1733873 and CCF-1725661, a Google Research Award, and a Yahoo Research Award. Preprint submitted to Elsevier February 23, 2018