Abstract
We study the problem of assigning n tasks to m identical parallel machines in the real-time scheduling setting, where each task recurrently releases jobs that must be completed by their deadlines. The goal is to find a partition of the task set over the machines such that each job that is released by a task can meet its deadline. Since this problem is co-NP-hard, the focus is on finding α-approximation algorithms in the resource augmentation setting, i.e., finding a feasible partition on machines running at speed α ≥ 1, if some feasible partition exists on unit-speed machines.
Recently, Chen and Chakraborty gave a polynomial-time approximation scheme if the ratio of the largest to the smallest relative deadline of the tasks, λ, is bounded by a constant. However, their algorithm has a super-exponential dependence on λ and hence does not extend to larger values of λ. Our main contribution is to design an approximation scheme with a substantially improved running-time dependence on λ. In particular, our algorithm depends exponentially on logλ and hence has quasi-polynomial running time even if λ is polynomially bounded. This improvement is based on exploiting various structural properties of approximate demand bound functions in different ways, which might be of independent interest.
Supported by the NWO VIDI grant 639.022.211.
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Bansal, N., Rutten, C., van der Ster, S., Vredeveld, T., van der Zwaan, R. (2014). Approximating Real-Time Scheduling on Identical Machines. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_48
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DOI: https://doi.org/10.1007/978-3-642-54423-1_48
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