Related papers: The Secretary Problem with Independent Sampling
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial…
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…
A version of the secretary problem called the duration problem, in which the objective is to maximize the time of possession of relatively best objects or the second best, is treated. It is shown that in this duration problem there are…
Peer reviews, evaluations, and selections are a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals from those submitted for funding. The problem of peer selection,…
We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or…
Traditionally, the problem of apportioning the seats of a legislative body has been viewed as a one-shot process with no dynamic considerations. While this approach is reasonable for some settings, dynamic aspects play an important role in…
Assume $k$ candidates need to be selected. The candidates appear over time. Each time one appears, it must be immediately selected or rejected -- a decision that is made by a group of individuals through voting. Assume the voters use…
We consider an online multi-weighted generalization of several classic online optimization problems, called the online combinatorial assignment problem. We are given an independence system over a ground set of elements and agents that…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
In the prophet inequality problem, a gambler faces a sequence of items arriving online with values drawn independently from known distributions. On seeing an item, the gambler must choose whether to accept its value as her reward and quit…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two…
We study a variant of the secretary problem where candidates come from independent, not necessarily identical distributions known to us, and show that we can do at least as well as in the IID setting. This resolves a conjecture of…
Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…
We study a "pen testing" problem, in which we are given $n$ pens with unknown amounts of ink $X_1, X_2, \ldots, X_n$, and we want to choose a pen with the maximum amount of remaining ink in it. The challenge is that we cannot access each…
We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related…
We study online combinatorial allocation problems in the secretary setting, under interdependent values. In the interdependent model, introduced by Milgrom and Weber (1982), each agent possesses a private signal that captures her…
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…
An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…