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Competitive Kill-and-Restart and Preemptive Strategies for Non-clairvoyant Scheduling

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Integer Programming and Combinatorial Optimization (IPCO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13904))

Abstract

We study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of 3 for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any \(b > 1\) a tight analysis for the natural b-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of \((1+3\sqrt{3})\approx 6.197\) for the deterministic and of \(\approx 3.032\) for the randomized strategy by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is 2-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Furthermore, we prove performance guarantees smaller than 10 for adaptions of the b-scaling strategy to online release dates and unweighted jobs on identical parallel machines.

Full version preprint: http://arxiv.org/abs/2211.02044.

The research of the second, third and fourth authors was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy — The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).

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Acknowledgements

We thank Sungjin Im for helpful comments on an earlier version of this manuscript.

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Authors and Affiliations

  1. RPTU Kaiserslautern-Landau, Paul-Ehrlich-Straße 14, 67663, Kaiserslautern, Germany

    Sven Jäger

  2. TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Guillaume Sagnol & Daniel Schmidt genannt Waldschmidt

  3. HU Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Philipp Warode

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Correspondence to Guillaume Sagnol .

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  1. University of Wisconsin-Madison, Madison, WI, USA

    Alberto Del Pia

  2. Otto-von-Guericke-Universität, Magdeburg, Sachsen-Anhalt, Germany

    Volker Kaibel

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Jäger, S., Sagnol, G., Schmidt genannt Waldschmidt, D., Warode, P. (2023). Competitive Kill-and-Restart and Preemptive Strategies for Non-clairvoyant Scheduling. In: Del Pia, A., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2023. Lecture Notes in Computer Science, vol 13904. Springer, Cham. https://doi.org/10.1007/978-3-031-32726-1_18

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