Related papers: On Submodular Prophet Inequalities and Correlation…
We consider a combinatorial auction setting where buyers have fractionally subadditive (XOS) valuations over the items and the seller's objective is to maximize the social welfare. A prophet inequality in this setting bounds the competitive…
We study the submodular secretary problem with a cardinality constraint. In this problem, $n$ candidates for secretaries appear sequentially in random order. At the arrival of each candidate, a decision maker must irrevocably decide whether…
We consider the problem of selling perishable items to a stream of buyers in order to maximize social welfare. A seller starts with a set of identical items, and each arriving buyer wants any one item, and has a valuation drawn i.i.d. from…
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings…
Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et…
A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables $X_1,\dots,X_n$ drawn independently from a distribution $F$,…
In online sales, sellers usually offer each potential buyer a posted price in a take-it-or-leave fashion. Buyers can sometimes see posted prices faced by other buyers, and changing the price frequently could be considered unfair. The…
We show that the matroid secretary problem is equivalent to correlated contention resolution in the online random-order model. Specifically, the matroid secretary conjecture is true if and only if every matroid admits an online random-order…
In this work we initiate the study of buy-and-sell prophet inequalities. We start by considering what is arguably the most fundamental setting. In this setting the online algorithm observes a sequence of prices one after the other. At each…
This paper studies the fundamental limits of availability and throughput for independent and heterogeneous demands of a limited resource. Availability is the probability that the demands are below the capacity of the resource. Throughput is…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the…
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of $1-\frac{1}{e}$ on the approximation factor of their algorithm. They conjectured that the best…
We consider the online stochastic matching problem for bipartite graphs where edges adjacent to an online node must be probed to determine if they exist, based on known edge probabilities. Our algorithms respect commitment, in that if a…
We study the classic single-choice prophet secretary problem through a resource augmentation lens. Our goal is to bound the $(1-\epsilon)$-competition complexity for different classes of online algorithms. This metric asks for the smallest…
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…
It is well known that there is a strong connection between entropy inequalities and submodularity, since the entropy of a collection of random variables is a submodular function. Unifying frameworks for information inequalities arising from…