Related papers: The Competition Complexity of Prophet Inequalities
This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topic, versions with inventory constraints have proven difficult. We consider a formulation of inventory-constrained…
We consider an online version of the well-studied network utility maximization problem, where users arrive one by one and an operator makes irrevocable decisions for each user without knowing the details of future arrivals. We propose a…
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…
Prophet inequalities are fundamental optimal stopping problems, where a decision-maker observes sequentially items with values sampled independently from known distributions, and must decide at each new observation to either stop and gain…
Prophet inequalities and secretary problems have been extensively studied in recent years due to their elegance, connections to online algorithms, stochastic optimization, and mechanism design problems in game theoretic settings. Rubinstein…
We study a class of Bayesian online selection problems with matroid constraints. Consider a vendor who has several items to sell, with the set of sold items being subject to some structural constraints, e.g., the set of sold items should be…
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 novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an $O(1)$-competitive algorithm. For…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
We consider Bayesian online selection problem of a matching in bipartite graphs, i.e., online weighted matching problem with edge arrivals where online algorithm knows distributions of weights, that corresponds to the intersection of two…
Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either…
In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…
We investigate online scheduling with commitment for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. As soon as a job has been submitted, the commitment constraint forces us to decide…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
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…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…
We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the…
Motivated by the applications of rental services in e-commerce, we consider revenue maximization in online assortment of reusable resources for a stream of arriving consumers with different types. We design competitive online algorithms…
Free order prophet inequalities bound the ratio between the expected value obtained by two parties each selecting a value from a set of independent random variables: a "prophet" who knows the value of each variable and may select the…