Related papers: Pairwise-Independent Contention Resolution
We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the…
Contention resolution schemes have proven to be a useful and unifying abstraction for a variety of constrained optimization problems, in both offline and online arrival models. Much of prior work restricts attention to product distributions…
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…
The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an $O(1)$-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear…
In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of…
We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1,…
We use contention resolution schemes (CRS) to derive algorithms for the fair rationing of a single resource when agents have stochastic demands. We aim to provide ex-ante guarantees on the level of service provided to each agent, who may…
Online contention resolution schemes (OCRSs) are effective rounding techniques for online stochastic combinatorial optimization problems. These schemes randomly and sequentially round a fractional solution to a relaxed problem that can be…
We introduce a variant of the classic prophet inequality, called \emph{residual prophet inequality} (RPI). In the RPI problem, we consider a finite sequence of $n$ nonnegative independent random values with known distributions, and a known…
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…
Over the past two decades, significant strides have been made in stochastic problems such as revenue-optimal auction design and prophet inequalities, traditionally modeled with $n$ independent random variables to represent the values of $n$…
We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique,…
In this work, we study the single-choice prophet inequality problem, where a gambler faces a sequence of~$n$ online i.i.d. random variables drawn from an unknown distribution. When a variable reveals its value, the gambler needs to decide…
We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability…
We consider prophet inequalities in a setting where agents correspond to both elements in a matroid and vertices in a graph. A set of agents is feasible if they form both an independent set in the matroid and an independent set in the…
Choice correspondences are crucial in decision-making, especially when faced with indifferences or ties. While tie-breaking can transform a choice correspondence into a choice function, it often introduces inefficiencies. This paper…
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…
Prophet inequalities consist of many beautiful statements that establish tight performance ratios between online and offline allocation algorithms. Typically, tightness is established by constructing an algorithmic guarantee and a…
We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case…
In the \textit{Matroid Secretary Problem} (MSP), the elements of the ground set of a Matroid are revealed on-line one by one, each together with its value. An algorithm for the MSP is \textit{Matroid-Unknown} if, at every stage of its…