The secretary problem with biased arrival order via a Mallows distribution

  title={The secretary problem with biased arrival order via a Mallows distribution},
  author={Ross G. Pinsky},
  journal={Adv. Appl. Math.},
  • R. Pinsky
  • Published 31 October 2021
  • Mathematics
  • Adv. Appl. Math.

Two measures of efficiency for the secretary problem with multiple items at each rank

. For 2 ≤ k ∈ N , consider the following adaptation of the classical secretary problem. There are k items at each of n linearly ordered ranks. The kn items are revealed, one item at a time, in a

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The full-information best choice problem asks one to find a strategy maximising the probability of stopping at the minimum (or maximum) of a sequence $$X_1,\cdots ,X_n$$ X 1 , ⋯ , X n

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. We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by the left-to-right-minimum



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  • R. Pinsky
  • Mathematics
    Latin American Journal of Probability and Mathematical Statistics
  • 2022
Given a probability distribution $p:=\{p_k\}_{k=1}^\infty$ on the positive integers, there are two natural ways to construct a random permutation of $\mathbb{N}$. One is called the $p$-biased

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  • D. Pfeifer
  • Mathematics
    Journal of Applied Probability
  • 1989
We consider a class of secretary problems in which the order of arrival of candidates is no longer uniformly distributed. By a suitable embedding in a time-transformed extremal process it is shown

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Abstract The classical dowry, secretary, or beauty contest problem is extended in several directions. In trying to find sequentially the maximum of a random sequence of fixed length, the chooser can

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The object of this article is to give a fresh view of the origins of the problem, touching upon Cayley and Kepler, and review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment.

Secretary Problems with Non-Uniform Arrival Order

This work initiates an investigation into relaxations of the random-ordering hypothesis in online algorithms, by focusing on the secretary problem and asking what performance guarantees one can prove under relaxed assumptions, and proves that Θ(log log n) is the minimum entropy of any permutation distribution that permits constant probability of correct selection in the secretaries problem with $n$ elements.

Comparing the inversion statistic for distribution-biased and distributionshifted permutations with the geometric and the GEM distributions, to appear in ALEA-Lat

  • Am. J. Probab. Math. Stat. Department of Mathematics, Technion—Israel Institute of Technology, Haifa,
  • 2000