相关论文: Set systems related to a house allocation problem
We provide optimal solutions to an institution that has distributional objectives when choosing from a set of applications based on merit (or priority). For example, in college admissions, administrators may want to admit a diverse class in…
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…
We study fair mechanisms for the (asymmetric) one-sided allocation problem with m items and n multi-unit demand agents with additive, unit-sum valuations. The symmetric case (m=n), the one-sided matching problem, has been studied…
I develop a revealed preference framework to test whether an aggregate allocation of indivisible objects satisfies Pareto efficiency and individual rationality (PI) without observing individual preferences. Exploiting the type-based…
The Set Packing problem is, given a collection of sets $\mathcal{S}$ over a ground set $\mathcal{U}$, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems…
In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually accepted agents. If any…
A dominating set $S$ of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of $S$, and the minimum cardinality of such a set is called the…
In the application of machine learning to real-life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly…
We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
One of the major concerns of targeting interventions on individuals in social welfare programs is discrimination: individualized treatments may induce disparities across sensitive attributes such as age, gender, or race. This paper…
Fairness in clustering has been considered extensively in the past; however, the trade-off between the two objectives -- e.g., can we sacrifice just a little in the quality of the clustering to significantly increase fairness, or…
We improve the best known competitive ratio (from 1/4 to 1/2), for the online multi-unit allocation problem, where the objective is to maximize the single-price revenue. Moreover, the competitive ratio of our algorithm tends to 1, as the…
We study the problem of allocating $m$ indivisible items to $n$ agents with additive utilities. It is desirable for the allocation to be both fair and efficient, which we formalize through the notions of envy-freeness and Pareto-optimality.…
We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multi-item multi-bidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population.…
The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics…
In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a…
An assignment problem is the optimization problem of finding, in an m by n matrix of nonnegative real numbers, k entries, no two in the same row or column, such that their sum is minimal. Such an optimization problem is called a random…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…