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We consider a variant of the secretary problem in which the candidates state their expected salary at the interview, which we assume is in accordance with their qualifications. The goal is for the employer to hire the best or the worst…

Probability · Mathematics 2016-03-22 L. Bayon , J. Grau , A. M. Oller-Marcen , M. Ruiz , P. M. Suarez

In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The…

Computer Science and Game Theory · Computer Science 2020-05-27 Niklas Hahn , Martin Hoefer , Rann Smorodinsky

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…

Data Structures and Algorithms · Computer Science 2023-08-21 Kaito Fujii , Yuichi Yoshida

The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous $K$ choices immediately prior to the current choice. We consider a case of this…

Probability · Mathematics 2015-09-01 Shan-Yuan Ho , Abijith Krishnan

In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made as candidates randomly arrive for a job interview. Standard SSP variants, such as the well-known secretary problem, begin with an empty selection…

Discrete Mathematics · Computer Science 2019-11-11 Mathilde Fekom , Nicolas Vayatis , Argyris Kalogeratos

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…

Logic in Computer Science · Computer Science 2022-04-01 Michael Pinsker

The well-known secretary problem in sequential analysis and optimal stopping theory asks one to maximize the probability of finding the optimal candidate in a sequentially examined list under the constraint that accept/reject decisions are…

Combinatorics · Mathematics 2021-07-13 Xujun Liu , Olgica Milenkovic

This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…

Applications · Statistics 2025-11-14 Eugene Seong

The objective of this paper is to show that the so-called unified approach to stopping problems with unknown cardinality introduced in Bruss (1984) proves to be efficient for solving other types of best-choice problems. We show that what we…

Probability · Mathematics 2016-10-03 Rémi Dendievel

The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/\mathrm{e} \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with…

Data Structures and Algorithms · Computer Science 2024-10-01 Alexander Braun , Sherry Sarkar

There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In…

Data Structures and Algorithms · Computer Science 2026-03-03 Tian Bai , Zhiyi Huang , Chui Shan Lee , Dongchen Li

In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…

Probability · Mathematics 2023-07-21 Ross G. Pinsky , Tomer Zilca

Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…

Computer Science and Game Theory · Computer Science 2015-10-16 Hossein Esfandiari , MohammadTaghi Hajiaghayi , Vahid Liaghat , Morteza Monemizadeh

We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…

Combinatorics · Mathematics 2012-06-29 Bryn Garrod , Robert Morris

Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing…

Data Structures and Algorithms · Computer Science 2020-12-02 Susanne Albers , Leon Ladewig

Given integers $1\leq k<n$, the Gusein-Zade version of a generalized secretary problem is to choose one of the $k$ best of $n$ candidates for a secretary, which are interviewing in random order. The stopping rule in the selection is based…

Combinatorics · Mathematics 2016-10-19 Adam Woryna

We consider a variant of the classical Secretary Problem. In this setting, the candidates are ranked according to some exchangeable random variable and the quest is to maximize the expected quality of the chosen aspirant. We find an upper…

Probability · Mathematics 2017-09-15 Pablo Blanc , Juan Pablo Borthagaray , Daniel Kohen , Martín Mereb

This note considers a variation of the full-information secretary problem where the random variables to be observed are independent and identically distributed. Consider $X_1,\dots,X_n$ to be an independent sequence of random variables, let…

Probability · Mathematics 2017-09-11 José A. Islas

We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting…

Probability · Mathematics 2017-11-22 Tomomi Matsui , Katsunori Ano

Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This…

Applications · Statistics 2019-12-13 Simon Demers