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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

In the paper the generalisation of the well known "secretary problem" is considered. The aim of the paper is to give a generalised model in such a way that the chosen set of the possible best $k$ elements have to be independent of all…

Discrete Mathematics · Computer Science 2021-12-09 Wojciech Kordecki

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

First, for the for the submodular $k$-secretary problem with shortlists [1], we provide a near optimal $1-1/e-\epsilon$ approximation using shortlist of size $O(k poly(1/\epsilon))$. In particular, we improve the size of shortlist used in…

Data Structures and Algorithms · Computer Science 2021-02-22 Mohammad Shadravan

In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…

Data Structures and Algorithms · Computer Science 2026-05-22 Franziska Eberle , Alexander Lindermayr

We define a new selection problem, \emph{Selecting with History}, which extends the secretary problem to a setting with historical information. We propose a strategy for this problem and calculate its success probability in the limit of a…

Data Structures and Algorithms · Computer Science 2018-09-27 Tom Hess , Sivan Sabato

Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…

Data Structures and Algorithms · Computer Science 2024-05-08 George V. Moustakides , Xujun Liu , Olgica Milenkovic

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

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…

Probability · Mathematics 2020-10-16 L. Bayon , P. Fortuny , J. M. Grau , A. Oller Marcen , M. M. Ruiz

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 various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…

Data Structures and Algorithms · Computer Science 2016-08-01 Thomas Kesselheim , Andreas Tönnis

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 a Mallows distribution with parameter $q\in(0,1)$, so that higher ranked…

Probability · Mathematics 2021-12-02 Ross G. Pinsky

We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$…

Probability · Mathematics 2023-07-10 Josef Rukavicka

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

In the matroid secretary problem, elements $N := [n]$ of a matroid $\mathcal{M} \subseteq 2^N$ arrive in random order. When an element arrives, its weight is revealed and a choice must be made to accept or reject the element, subject to the…

Data Structures and Algorithms · Computer Science 2025-12-09 Rishi Gujjar , Kevin Hua , Robert Kleinberg , Frederick V. Qiu

This article considers a problem arising from a two-player game based on the classical secretary problem. First, Player 1 selects one object from a sequence as in the secretary problem. All of the other objects are then presented to Player…

Computer Science and Game Theory · Computer Science 2024-09-09 David Ramsey

We study memory-bounded algorithms for the $k$-secretary problem. The algorithm of Kleinberg (SODA 2005) achieves an optimal competitive ratio of $1 - O(1/\sqrt{k})$, yet a straightforward implementation requires $\Omega(k)$ memory. Our…

Data Structures and Algorithms · Computer Science 2026-05-11 Mingda Qiao , Wei Zhang

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…

Computer Science and Game Theory · Computer Science 2017-08-30 Daniel G. Goldstein , R. Preston McAfee , Siddharth Suri , James R. Wright

The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a…

Data Structures and Algorithms · Computer Science 2024-11-05 Ziyun Chen , Zhiyi Huang , Dongchen Li , Zhihao Gavin Tang