Abstract
In this paper, we introduce a new online scheduling framework for minimizing total weighted completion time in a general setting. The framework is inspired by the work of Hall et al. [10] and Garg et al. [8], who show how to convert an offline approximation to an online scheme. Our framework uses two offline approximation algorithms—one for the simpler problem of scheduling without release times, and another for the minimum unscheduled weight problem—to create an online algorithm with provably good competitive ratios.
We illustrate multiple applications of this method that yield improved competitive ratios. Our framework gives algorithms with the best or only-known competitive ratios for the concurrent open shop, coflow, and concurrent cluster models. We also introduce a randomized variant of our framework based on the ideas of Chakrabarti et al. [3] and use it to achieve improved competitive ratios for these same problems.
All authors performed this work at the University of Maryland, College Park, under the support of NSF REU Grant CNS 156019. We would also like to thank An Zhu and Google for their support, and the LILAC program at Bryn Mawr College.
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Notes
- 1.
We make the critical assumption that the offline \(\gamma \)-approximation algorithm does not increase the makespan of the given subset of jobs, so as to ensure that the schedule fits inside of \(\alpha I_k\). For the scheduling models studied in this paper, this assumption will indeed hold. In fact, if it can be shown that the \(\gamma \)-approximation algorithm also approximates the makespan criteria within some factor \(\mu \), then it is straightforward to incorporate this into the model, at the expense of an additional \(\mu \) factor in the approximation guarantee. For example, Chakrabarti et al. [3] provide bicriteria approximation algorithms for the total weighted completion time and makespan objective functions.
- 2.
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Khuller, S., Li, J., Sturmfels, P., Sun, K., Venkat, P. (2018). Select and Permute: An Improved Online Framework for Scheduling to Minimize Weighted Completion Time. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_49
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