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 augmentation.