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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 both the case $m>2$ had not been satisfactorily solved yet. Here, we provide and efficient algorithm to compute the optimal threshold and the probability of success for every $m$. Moreover, we give a method to determine their asymtoptic values based on the solution of a system of $m$ ODEs.
In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experie
In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of maximum value
We consider the online problem in which an intermediary trades identical items with a sequence of n buyers and n sellers, each of unit demand. We assume that the values of the traders are selected by an adversary and the sequence is randomly permuted
In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of revealed el
We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of stochasti