Related papers: A short note about the learning-augmented secretar…
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} $x$…
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…
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…
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…
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…
Whereas there are simple algorithms that are proven to be optimal for the Classical and the Multiple Choice Secretary Problem, the Matroid Secretary Problem is less thoroughly understood. This paper proposes the generalization of some…
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…
Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…
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…
We study a generalization of the secretary problem, where decisions do not have to be made immediately upon candidates' arrivals. After arriving, each candidate stays in the system for some (random) amount of time and then leaves, whereupon…
This paper studies Makespan Minimization in the secretary model. Formally, jobs, specified by their processing times, are presented in a uniformly random order. An online algorithm has to assign each job permanently and irrevocably to one…
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…
In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the…
We revisit the problem of selecting an item from $n$ choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first…
The secretary problem has been a focus of extensive study with a variety of extensions that offer useful insights into the theory of optimal stopping. The original solution is to set one stopping threshold that gives rise to an immediately…
In the "secretary problem", well-known in the theory of optimal stopping, an employer is about to interview a maximum of N secretaries about which she has no prior information. Chow et al. proved that with an optimal strategy the expected…
In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…
We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following…
We study secretary problems in settings with multiple agents. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision…
As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%,…