Secretary problem with hidden information; searching for a high merit candidate

Real numbers from the interval [0,1] are randomly selected with uniform distribution. There are n of them and they measure shortcomings of the candidates from the pool of n secretaries in a search process; a smaller number indicates a better candidate. The numbers come one by one. We know only their...

Full description

Saved in:
Bibliographic Details
Published in:Advances in applied mathematics 2023-03, Vol.144, p.102468, Article 102468
Main Authors: Kubicka, Ewa M., Kubicki, Grzegorz, Kuchta, Małgorzata, Morayne, Michał
Format: Article
Language:English
Subjects:
Combinatorial optimization
Optimal stopping
Secretary problem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Real numbers from the interval [0,1] are randomly selected with uniform distribution. There are n of them and they measure shortcomings of the candidates from the pool of n secretaries in a search process; a smaller number indicates a better candidate. The numbers come one by one. We know only their relative ranks but do not know their values. We want to stop on the current element maximizing the probability that its value is smaller than 1n. We provide a complete solution of this model by constructing an optimal stopping algorithm, establishing its asymptotic performance, and showing how to calculate all characteristics of the algorithm with desired accuracy.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2022.102468