The multi-returning secretary problem

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has m identical copies. The case m = 2 has already been completely solved by several authors using different methods, but the case m > 2 had not been satisfactorily solved yet. Here, under the conjecture of certain (very likely true) uniform convergence results, we provide an efficient algorithm to compute the optimal threshold and the probability of success for every m. Moreover, we give a method to determine their asymptotic values based on the solution of a system of m ODEs. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper discusses the Multi-returning secretary problem, where each candidate has m identical copies. The paper provides an efficient algorithm to compute the optimal threshold and the probability of success for every m, based on certain conjectures. Additionally, a method for determining their asymptotic values is given by solving a system of m ODEs.