The secretary problem with biased arrival order via a Mallows distribution

@article{Pinsky2021TheSP,
  title={The secretary problem with biased arrival order via a Mallows distribution},
  author={Ross G. Pinsky},
  journal={Adv. Appl. Math.},
  year={2021},
  volume={140},
  pages={102386}
}
  • 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

Running minimum in the best-choice problem

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

The secretary problem with non-uniform arrivals via a left-to-right-minimum exponentially tilted distribution

. 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

References

SHOWING 1-10 OF 10 REFERENCES

Trapping the Ultimate Success

: We introduce a betting game where the gambler aims to guess the last success epoch in a series of inhomogeneous Bernoulli trials paced randomly in time. At a given stage, the gambler may bet on

Comparing the inversion statistic for distribution-biased and distribution-shifted permutations with the geometric and the GEM distributions

  • 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

Extremal processes, secretary problems and the 1/e law

  • 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

Recognizing the Maximum of a Sequence

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

Sum the odds to one and stop

The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication

The Secretary Problem and its Extensions: A Review

Summary The development of what has come to be known as the secretary problem is traced from its origins in the early 1960's. All published work to date on the problem and its extensions is reviewed.

Who Solved the Secretary Problem

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