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Related papers: Prophet Secretary: Surpassing the $1-1/e$ Barrier

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A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who…

Information Theory · Computer Science 2018-06-25 Siddharth Barman , Omar Fawzi

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

This paper answers a long-standing open question concerning the $1/e$-strategy for the problem of best choice. $N$ candidates for a job arrive at times independently uniformly distributed in $[0,1]$. The interviewer knows how each candidate…

Probability · Mathematics 2020-12-25 F. Thomas Bruss , L. C. G. Rogers

The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the…

Data Structures and Algorithms · Computer Science 2017-08-28 Martin Hoefer , Bojana Kodric

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the…

Computer Science and Game Theory · Computer Science 2019-05-10 Piotr Krysta , David Manlove , Baharak Rastegari , Jinshan Zhang

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching…

Data Structures and Algorithms · Computer Science 2026-04-21 Brian Brubach , Nathaniel Grammel , Will Ma , Calum MacRury , Aravind Srinivasan

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

We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio…

Data Structures and Algorithms · Computer Science 2009-05-27 Jon Feldman , Aranyak Mehta , Vahab Mirrokni , S. Muthukrishnan

Prophet inequalities are a useful tool for designing online allocation procedures and comparing their performance to the optimal offline allocation. In the basic setting of $k$-unit prophet inequalities, the well-known procedure of Alaei…

Computer Science and Game Theory · Computer Science 2023-10-10 Jiashuo Jiang , Will Ma , Jiawei Zhang

We study the online fair division problem, where indivisible goods arrive sequentially and must be allocated immediately and irrevocably. Prior work establishes strong impossibility results for approximating classic notions such as…

Computer Science and Game Theory · Computer Science 2026-05-29 Davin Choo , Winston Fu , Derek Khu , Tzeh Yuan Neoh , Tze-Yang Poon , Nicholas Teh

For $2\le k\in\mathbb{N}$, consider the following adaptation of the classical secretary problem. There are $k$ items at each of $n$ linearly ordered ranks. The $kn$ items are revealed, one item at a time, in a uniformly random order, to an…

Probability · Mathematics 2022-08-24 Ross G. Pinsky

In the matroid secretary problem, the elements of a matroid $\mathcal{M}$ arrive in random order. Once we observe an item we need to irrevocably decide whether or not to accept it. The set of selected elements should form an independent set…

Data Structures and Algorithms · Computer Science 2020-01-06 Mohammad Shadravan

The random-order or secretary model is one of the most popular beyond-worst case model for online algorithms. While it avoids the pessimism of the traditional adversarial model, in practice we cannot expect the input to be presented in…

Data Structures and Algorithms · Computer Science 2020-06-23 Thomas Kesselheim , Marco Molinaro

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

In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…

Probability · Mathematics 2021-03-09 Alexander Gnedin

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

Computer Science and Game Theory · Computer Science 2018-06-12 Georgios Amanatidis , Evangelos Markakis , Afshin Nikzad , Amin Saberi

Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the…

Data Structures and Algorithms · Computer Science 2025-04-29 Flavio Chierichetti , Mirko Giacchini , Alessandro Panconesi , Andrea Vattani

We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a…

Optimization and Control · Mathematics 2019-12-24 Bart P. G. Van Parys , Peyman Mohajerin Esfahani , Daniel Kuhn

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

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