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The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we give the algorithm to improve its success probability? We propose a general model that unifies a broad range…

Data Structures and Algorithms · Computer Science 2020-11-16 Paul Dütting , Silvio Lattanzi , Renato Paes Leme , Sergei Vassilvitskii

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

The decision-maker (DM) sequentially evaluates up to N of different, rankable options. DM must select exactly the best one at the moment of its appearance. In the process of searching, DM finds out with each applicant whether she is the…

Optimization and Control · Mathematics 2022-05-23 Krzysztof J. Szajowski

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

We revisit three fundamental problems in algorithms under uncertainty: the Secretary Problem, Prophet Inequality, and Stochastic Probing, each subject to general downward-closed constraints. When elements have binary values, all three…

Data Structures and Algorithms · Computer Science 2026-04-02 Aviad Rubinstein , Sahil Singla

The game of best choice, also known as the secretary problem, is a model for sequential decision making with many variations in the literature. Notably, the classical setup assumes that the sequence of candidate rankings is uniformly…

Combinatorics · Mathematics 2019-03-13 Madeline Crews , Brant Jones , Kaitlyn Myers , Laura Taalman , Michael Urbanski , Breeann Wilson

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 consider a stochastic online problem where $n$ applicants arrive over time, one per time step. Upon arrival of each applicant their cost per time step is revealed, and we have to fix the duration of employment, starting immediately. This…

Data Structures and Algorithms · Computer Science 2017-05-31 Yann Disser , John Fearnley , Martin Gairing , Oliver Göbel , Max Klimm , Daniel Schmand , Alexander Skopalik , Andreas Tönnis

We consider two variations of the classical secretary problem. * A variation of the returning secretary problem where each interviewee may appear a second time with a fixed probability p. The decision-maker observes interviewees…

Data Structures and Algorithms · Computer Science 2026-04-13 Sarthak Agrawal , Sanjeev Saxena

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 investigate two variants of the secretary problem. In these variants, we are presented with a sequence of numbers $X_i$ that come from distributions $\mathcal{D}_i$, and that arrive in either random or adversarial order.…

Data Structures and Algorithms · Computer Science 2022-08-22 Pranav Nuti , Jan Vondrák

We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request…

Data Structures and Algorithms · Computer Science 2011-12-07 Siddharth Barman , Seeun Umboh , Shuchi Chawla , David Malec

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is a…

Probability · Mathematics 2010-09-06 Chris Dietz , Dinard van der Laan , Ad Ridder

The \emph{Temp Secretary Problem} was recently introduced by Fiat et al. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved…

Data Structures and Algorithms · Computer Science 2016-06-23 Thomas Kesselheim , Andreas Tönnis

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

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

In the online random-arrival model, an algorithm receives a sequence of n requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We…

Data Structures and Algorithms · Computer Science 2014-07-08 Shai Vardi

Consider a hiring process with candidates coming from different universities. It is easy to order candidates with the same background, yet it can be challenging to compare them otherwise. The latter case requires additional costly…

Computer Science and Game Theory · Computer Science 2024-11-19 Ziyad Benomar , Evgenii Chzhen , Nicolas Schreuder , Vianney Perchet

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 the Secretary Problem, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well…

Data Structures and Algorithms · Computer Science 2015-07-23 Moran Feldman , Rani Izsak