English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The Secretary problem is a classical sequential decision-making question thatcan be succinctly described as follows: a set of rank-ordered applicants areinterviewed sequentially for a single position. Once an applicant isinterviewed, an immediate and irrevocable decision is made if the person is tobe offered the job or not and only applicants observed so far can be used inthe decision process. The problem of interest is to identify the stopping rulethat maximizes the probability of hiring the highest-ranked applicant. Amultiple-choice version of the Secretary problem, known as the Dowry problem,assumes that one is given a fixed integer budget for the total number ofselections allowed to choose the best applicant. It has been solved using toolsfrom dynamic programming and optimal stopping theory. We provide the firstcombinatorial proof for a related new \emph{query-based model} for which we areallowed to solicit the response of an expert to determine if an applicant isoptimal. Since the selection criteria differ from those of the Dowry problem weobtain nonidentical expected stopping times.  Our result indicates that an optimal strategy is the $(a_s, a_{s-1}, \ldots,a_1)$-strategy, i.e., for the $i^{th}$ selection, where $1 \le i \le s$ and $1\le j = s+1-i \le s$, we reject the first $a_j$ applicants, wait until thedecision of the $(i-1)^{th}$ selection (if $i \ge 2$), and then accept the nextapplicant whose qualification is better than all previously appearedapplicants. Furthermore, our optimal strategy is right-hand based, i.e., theoptimal strategies for two models with $s_1$ and $s_2$ selections in total($s_1 < s_2$) share the same sequence $a_1, a_2, \ldots, a_{s_1}$ when it isviewed from the right. When the total number of applicants tends to infinity,our result agrees with the thresholds obtained by Gilbert and Mosteller.

A combinatorial proof for the secretary problem with multiple choices