Abstract
This paper considers scheduling jobs online on m identical machines such that the jobs can be parallelized across the machines. Two models of parallelizability are considered, one is the speed-up curves model, and the other is the directed-acyclic-graph (DAG) model. For both models, the objectives considered are the average, maximum, and ℓk-norms of flow time for k≥1.We establish an Ω(m) lower bound on the competitive ratio of any algorithm for optimizing average flow time in both models without resource augmentation. With resource augmentation, we give a (1+ϵ)-speed O(1ϵ2k+1)-competitive algorithm in the DAG model for the ℓk-norms of flow time. This essentially matches the best-known result in the speed-up curve model for the ℓk-norms of flow time. Finally, we show an O(1)-competitive algorithm for minimizing the maximum flow time in the speed-up curves model.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
