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We consider the problem of fairly allocating items to a set of individuals, when the items are arriving online. A central solution concept in fair allocation is competitive equilibrium: every individual is endowed with a budget of faux…
We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes…
Prophet inequalities compare the expected performance of an online algorithm for a stochastic optimization problem to the expected optimal solution in hindsight. They are a major alternative to classic worst-case competitive analysis, of…
There is a rising interest for studying the online benchmark as an alternative of the classical offline benchmark in online stochastic settings. Ezra, Feldman, Gravin, and Tang (SODA 2023) introduced the notion of order-competitive ratio,…
We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources "fairly", so that no group of customers is marginalized in terms of their overall service…
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…
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 consider the edge-weighted online stochastic matching problem, in which an edge-weighted bipartite graph G=(I\cup J, E) with offline vertices J and online vertex types I is given. The online vertices have types sampled from I with…
Our work introduces the effect of supply/demand imbalances into the literature on online matching with stochastic rewards in bipartite graphs. We provide a parameterized definition that characterizes instances as over- or undersupplied (or…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
Online matching and its variants are some of the most fundamental problems in the online algorithms literature. In this paper, we study the online weighted bipartite matching problem. Karp et al. (STOC 1990) gave an elegant algorithm in the…
In online combinatorial allocation, agents arrive sequentially and items are allocated in an online manner. The algorithm designer only knows the distribution of each agent's valuation, while the actual realization of the valuation is…
Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…
We study the power of multiple choices in online stochastic matching. Despite a long line of research, existing algorithms still only consider two choices of offline neighbors for each online vertex because of the technical challenge in…
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…
The online matching problem was introduced by Karp, Vazirani and Vazirani (STOC 1990) on bipartite graphs with vertex arrivals. It is well-known that the optimal competitive ratio is $1-1/e$ for both integral and fractional versions of the…
In modern sample-driven Prophet Inequality, an adversary chooses a sequence of $n$ items with values $v_1, v_2, \ldots, v_n$ to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase),…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one-sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
For numerous online bipartite matching problems, such as edge-weighted matching and matching under two-sided vertex arrivals, the state-of-the-art fractional algorithms outperform their randomized integral counterparts. This gap is…
We study the online load balancing problem on unrelated machines, with the objective of minimizing the square of the $\ell_2$ norm of the loads on the machines. The greedy algorithm of Awerbuch et al. (STOC'95) is optimal for deterministic…