Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times

A. Mäcker, M. Malatyali, F. Meyer auf der Heide, S. Riechers, in: Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA), Springer, 2017, pp. 207–222.

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Consider a problem in which $n$ jobs that are classified into $k$ types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time.The machine requires a setup taking $s$ time units whenever it switches from processing jobs of one type to jobs of a different type.We consider the problem as an online problem where each job is only known to the scheduler as soon as it arrives and where the processing time of a job only becomes known upon its completion (non-clairvoyance).We are interested in the potential of simple ``greedy-like'' algorithms.We analyze a modification of the FIFO strategy and show its competitiveness to be $\Theta(\sqrt{n})$, which is optimal for the considered class of algorithms.For $k=2$ types it achieves a constant competitiveness.Our main insight is obtained by an analysis of the smoothed competitiveness.If processing times $p_j$ are independently perturbed to $\hat p_j = (1+X_j)p_j$, we obtain a competitiveness of $O(\sigma^{-2} \log^2 n)$ when $X_j$ is drawn from a uniform or a (truncated) normal distribution with standard deviation $\sigma$.The result proves that bad instances are fragile and ``practically'' one might expect a much better performance than given by the $\Omega(\sqrt{n})$-bound.
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Proceedings Title
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA)
Volume
10787
Page
207-222
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Mäcker A, Malatyali M, Meyer auf der Heide F, Riechers S. Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times. In: Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA). Vol 10787. Lecture Notes in Computer Science. Springer; 2017:207-222. doi:10.1007/978-3-319-89441-6
Mäcker, A., Malatyali, M., Meyer auf der Heide, F., & Riechers, S. (2017). Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times. In Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA) (Vol. 10787, pp. 207–222). Springer. https://doi.org/10.1007/978-3-319-89441-6
@inproceedings{Mäcker_Malatyali_Meyer auf der Heide_Riechers_2017, series={Lecture Notes in Computer Science}, title={Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times}, volume={10787}, DOI={10.1007/978-3-319-89441-6}, booktitle={Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA)}, publisher={Springer}, author={Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören}, year={2017}, pages={207–222}, collection={Lecture Notes in Computer Science} }
Mäcker, Alexander, Manuel Malatyali, Friedhelm Meyer auf der Heide, and Sören Riechers. “Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times.” In Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA), 10787:207–22. Lecture Notes in Computer Science. Springer, 2017. https://doi.org/10.1007/978-3-319-89441-6.
A. Mäcker, M. Malatyali, F. Meyer auf der Heide, and S. Riechers, “Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times,” in Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA), 2017, vol. 10787, pp. 207–222.
Mäcker, Alexander, et al. “Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times.” Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA), vol. 10787, Springer, 2017, pp. 207–22, doi:10.1007/978-3-319-89441-6.
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