Related papers: The Competition Complexity of Prophet Inequalities…
We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and…
We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or job has an arrival time, a deadline, a length and a weight. The objective is to maximize the total weight of completed intervals or jobs.…
We study a fundamental problem in optimization under uncertainty. There are $n$ boxes; each box $i$ contains a hidden reward $x_i$. Rewards are drawn i.i.d. from an unknown distribution $\mathcal{D}$. For each box $i$, we see $y_i$, an…
We consider the problem of a revenue-maximizing seller with m items for sale to n additive bidders with hard budget constraints, assuming that the seller has some prior distribution over bidder values and budgets. The prior may be…
We consider an online resource allocation problem where multiple resources, each with an individual initial capacity, are available to serve random requests arriving sequentially over multiple discrete time periods. At each time period, one…
This chapter introduces resource augmentation, in which the performance of an algorithm is compared to the best-possible solution that is handicapped by less resources. We consider three case studies: online paging, with cache size as the…
In this paper, we survey literature on prophet inequalities for subadditive combinatorial auctions. We give an overview of the previous best $O(\log \log m)$ prophet inequality as well as the preceding $O(\log m)$ prophet inequality. Then,…
The Prophet Inequality and Pandora's Box problems are fundamental stochastic problem with applications in Mechanism Design, Online Algorithms, Stochastic Optimization, Optimal Stopping, and Operations Research. A usual assumption in these…
We consider non-clairvoyant scheduling with online precedence constraints, where an algorithm is oblivious to any job dependencies and learns about a job only if all of its predecessors have been completed. Given strong impossibility…
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…
A fundamental assumption in classical mechanism design is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or a lack of information, and may not be able to perfectly…
We consider the problem of finding an incremental solution to a cardinality-constrained maximization problem that not only captures the solution for a fixed cardinality, but also describes how to gradually grow the solution as the…
We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and…
We analyze a two-period principal-agent model in which the principal faces a budget constraint, and the agent's private costs of performing tasks across the two periods may be correlated. We examine the optimal design of the reward scheme…
The problem of online matching with stochastic rewards is a generalization of the online bipartite matching problem where each edge has a probability of success. When a match is made it succeeds with the probability of the corresponding…
Motivated by the dynamic assortment offerings and item pricings occurring in e-commerce, we study a general problem of allocating finite inventories to heterogeneous customers arriving sequentially. We analyze this problem under the…
Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of…
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 consider the revenue maximization problem with sharp multi-demand, in which $m$ indivisible items have to be sold to $n$ potential buyers. Each buyer $i$ is interested in getting exactly $d_i$ items, and each item $j$ gives a benefit…
We study a general model on reusable resource allocation under model uncertainty. A heterogeneous population of customers arrive at the decision maker's (DM's) platform sequentially. Upon observing a customer's type, the DM selects an…