Abstract
We consider in this work a classical online scheduling problem with release times on a single machine. The quality of service of a job is measured by its stretch, which is defined as the ratio of its response time over its processing time. Our objective is to schedule the jobs non-preemptively in order to optimize the maximum stretch. We present both positive and negative theoretical results. First, we provide an online algorithm based on a waiting strategy which is \((1+\frac{\sqrt{5}-1}{2}\varDelta )\)-competitive where \(\varDelta \) is the upper bound on the ratio of processing times of any two jobs. Then, we show that no online algorithm has a competitive ratio better than \(\frac{\sqrt{5}-1}{2}\varDelta \). The proposed algorithm is asymptotically the best algorithm for optimizing the maximum stretch on a single machine.
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Notes
- 1.
Here we assume that the optimal schedule is non-lazy, that is all jobs are scheduled at the earliest time and there is no unnecessary idle time.
- 2.
Note that job \(l\) starts processing after time \(r_z\) in both schedule \(OPT\) and \(WDA\).
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Acknowledgments
This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program Investissement d’avenir. Erik Saule is a 2015 Data Fellow of the National Consortium for Data Science (NCDS) and acknowledges the NCDS for funding parts of the presented research.
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Dutot, PF., Saule, E., Srivastav, A., Trystram, D. (2016). Online Non-preemptive Scheduling to Optimize Max Stretch on a Single Machine. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_39
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DOI: https://doi.org/10.1007/978-3-319-42634-1_39
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