A new look at the returning secretary problem

We consider a version of the secretary problem in which each candidate has an identical twin. As in the classical secretary problem, the aim is to choose a top candidate, i.e., one of the best twins, with the highest possible probability. We find an optimal stopping rule for such a choice, the proba...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 37; no. 4; pp. 1216 - 1236
Main Author Ribas, J. M. Grau
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2019
Springer Nature B.V
Subjects
Asymptotic properties
Combinatorics
Convex and Discrete Geometry
Differential equations
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Twins
Secretary problem
62L15
Combinatorial optimization
60G40
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Summary:We consider a version of the secretary problem in which each candidate has an identical twin. As in the classical secretary problem, the aim is to choose a top candidate, i.e., one of the best twins, with the highest possible probability. We find an optimal stopping rule for such a choice, the probability of success, and its asymptotic behavior. We use a novel technique that allows the problem to be solved exactly in linear time and obtain the asymptotic values by solving differential equations. Furthermore, the proposed technique may be used to study the variants of the same problem and in other optimal stopping problems.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-018-0349-8