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Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem

Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem

Year:    2024

Author:    Giangvuthanh Nguyen, Xiang Xu, Yanxiang Zhao

Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 476–485

Abstract

In this paper, we study some basic analytic properties of a sequence of functions $\{S^{\mu,σ}_n\}$ that is directly derived in an adaptive algorithm originating from the classical score-based secretary problem. More specifically, we show that: 1. the uniqueness of maximum points of the function sequence $\{S^{\mu,σ}_n\};$ 2. the maximum point sequence of $\{S^{\mu,σ}_n\}$ monotone increases to infinity as $n$ tends to infinity. All of the proofs are elementary but nontrivial.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v57n4.24.05

Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 476–485

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Secretary problem adaptive algorithm expected score uniqueness of maximum points.

Author Details

Giangvuthanh Nguyen

Xiang Xu

Yanxiang Zhao