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On the Complexity of Restarting

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Computer Science – Theory and Applications (CSR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11532))

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Abstract

Restarting is a technique used by many randomized local search and systematic search algorithms. If the algorithm has not been successful for some time, the algorithm is reset and reinitialized with a new random seed. However, for some algorithms and some problem instances, restarts are not beneficial. Luby et al. [12] showed that if restarts are useful, then there is a restart time \(t^*\) such that the so-called fixed-cutoff strategy is the best possible strategy in expectation.

In this work, we show that deciding whether restarts are useful is NP-complete. Furthermore, we show that there is no feasible approximation algorithm for the optimal restart time \(t^*\). Lastly, we show that calculating the expected runtime for a known probability distribution and a given restart time is \(\#\)P-complete.

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, Ulm University, 89069, Ulm, Germany

    Jan-Hendrik Lorenz

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  1. Jan-Hendrik Lorenz
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Correspondence to Jan-Hendrik Lorenz .

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Editors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    René van Bevern

  2. Laboratoire d'Informatique Gaspard-Monge, Marne-la-Vallée, France

    Gregory Kucherov

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Lorenz, JH. (2019). On the Complexity of Restarting. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-19955-5_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19954-8

  • Online ISBN: 978-3-030-19955-5

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