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In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make…

Data Structures and Algorithms · Computer Science 2026-02-16 Mohammad Mahdian , Jieming Mao , Enze Sun , Kangning Wang , Yifan Wang

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…

Combinatorics · Mathematics 2019-11-06 Brant Jones

The J-choice K-best secretary problem, also known as the (J,K)-secretary problem, is a generalization of the classical secretary problem. An algorithm for the (J,K)-secretary problem is allowed to make J choices and the payoff to be…

Data Structures and Algorithms · Computer Science 2013-07-03 T-H. Hubert Chan , Fei Chen

We study a twist on the classic secretary problem, which we term the secretary ranking problem: elements from an ordered set arrive in random order and instead of picking the maximum element, the algorithm is asked to assign a rank, or…

Data Structures and Algorithms · Computer Science 2018-11-16 Sepehr Assadi , Eric Balkanski , Renato Paes Leme

In this paper we introduce the hiring under uncertainty problem to model the questions faced by hiring committees in large enterprises and universities alike. Given a set of $n$ eligible candidates, the decision maker needs to choose the…

Data Structures and Algorithms · Computer Science 2019-05-08 Manish Raghavan , Manish Purohit , Sreenivas Gollupadi

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

We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by the left-to-right-minimum exponentially tilted distribution with parameter…

Probability · Mathematics 2023-07-18 Ross G. Pinsky

The classical secretary problem investigates the question of how to hire the best secretary from $n$ candidates who come in a uniformly random order. In this work we investigate a parallel generalizations of this problem introduced by…

Data Structures and Algorithms · Computer Science 2014-09-18 Xiaoming Sun , Jia Zhang , Jialin Zhang

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

One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe $n$ independent indicator variables $I_1,I_2,\dotsc,I_n$ sequentially and we try to stop on the last…

Probability · Mathematics 2013-09-13 Rémi Dendievel

Motivated by hiring pipelines, we study three selection and ordering problems in which applicants for a finite set of positions must be interviewed or sent offers. There is a finite time budget for interviewing/sending offers, and every…

Data Structures and Algorithms · Computer Science 2023-10-30 Boris Epstein , Will Ma

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

In the secretary problem of Cayley (1875) and Moser (1956), $n$ non-negative, independent, random variables with common distribution are sequentially presented to a decision maker who decides when to stop and collect the most recent…

Probability · Mathematics 2019-10-22 Alessandro Arlotto , Itai Gurvich

We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe…

Combinatorics · Mathematics 2019-04-24 Aaron Fowlkes , Brant Jones

Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…

Data Structures and Algorithms · Computer Science 2019-10-10 Hossein Esfandiari , MohammadTaghi HajiAghayi , Brendan Lucier , Michael Mitzenmacher

We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the "random assignment" model where the weights are assigned randomly to…

Data Structures and Algorithms · Computer Science 2011-12-13 Shayan Oveis Gharan , Jan Vondrák

The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where…

Data Structures and Algorithms · Computer Science 2017-04-11 Moran Feldman , Ola Svensson , Rico Zenklusen

We investigate the hiring problem where a sequence of applicants is sequentially interviewed, and a decision on whether to hire an applicant is immediately made based on the applicant's score. For the maximal and average improvement…

Computer Science and Game Theory · Computer Science 2025-06-03 P. L. Krapivsky

For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…

Data Structures and Algorithms · Computer Science 2015-02-10 Thomas Kesselheim , Robert Kleinberg , Rad Niazadeh

We study a game between $N$ job applicants who incur a cost $c$ (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best. We define a full learning…

Theoretical Economics · Economics 2025-07-11 Longjian Li , Alexis Akira Toda