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The Best-or-Worst and the Postdoc problems with random number of candidates

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Abstract

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution \({\mathcal {U}}[1,n]\) or a Poisson distribution \({\mathcal {P}} (\lambda )\). We show that in any case the optimal strategy is a threshold strategy, we provide the optimal cutoff values and the asymptotic probabilities of success. We also put our results in relation with closely related work.

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Acknowledgements

We wish to thank Prof. Dr. F. Thomas Bruss as well as Prof. Dr. Krzysztof Szajowski for their very useful comments that provided relevant references and increased the interest of the paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007, Oviedo, Spain

    L. Bayón, P. Fortuny, J. Grau & M. M. Ruiz

  2. Centro Universitario de la Defensa de Zaragoza - IUMA, Ctra. Huesca s/n, 50090, Saragossa, Spain

    A. M. Oller-Marcén

Authors
  1. L. Bayón
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  2. P. Fortuny
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  3. J. Grau
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  4. A. M. Oller-Marcén
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  5. M. M. Ruiz
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Correspondence to A. M. Oller-Marcén.

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Bayón, L., Fortuny, P., Grau, J. et al. The Best-or-Worst and the Postdoc problems with random number of candidates. J Comb Optim 38, 86–110 (2019). https://doi.org/10.1007/s10878-018-0367-6

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  • DOI: https://doi.org/10.1007/s10878-018-0367-6

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