Related papers: New algorithms for matching problems
We define and study greedy matchings in vertex-ordered bipartite graphs. It is shown that each vertex-ordered bipartite graph has a unique greedy matching. The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a…
In the classical version of online bipartite matching, there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online. When each item arrives, its incident edges -- the agents who like the…
We study mechanism design problems in the {\em ordinal setting} wherein the preferences of agents are described by orderings over outcomes, as opposed to specific numerical values associated with them. This setting is relevant when agents…
Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik,…
In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the…
In the field of algorithmic fairness, many fairness criteria have been proposed. Oftentimes, their proposal is only accompanied by a loose link to ideas from moral philosophy -- which makes it difficult to understand when the proposed…
Machine learning algorithms are now frequently used in sensitive contexts that substantially affect the course of human lives, such as credit lending or criminal justice. This is driven by the idea that `objective' machines base their…
Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…
One-sided matching mechanisms are fundamental for assigning a set of indivisible objects to a set of self-interested agents when monetary transfers are not allowed. Two widely-studied randomized mechanisms in multiagent settings are the…
Designing two-sided matching mechanisms is challenging when practical demands for matching outcomes are difficult to formalize and the designed mechanism must satisfy theoretical conditions. To address this, prior work has proposed a…
We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture…
We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every…
The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance. At a high level, the problem is to assign a set of items that are either…
The law forbids discrimination. But the ambiguity of human decision-making often makes it extraordinarily hard for the legal system to know whether anyone has actually discriminated. To understand how algorithms affect discrimination, we…
An increasing number of decisions regarding the daily lives of human beings are being controlled by artificial intelligence (AI) algorithms in spheres ranging from healthcare, transportation, and education to college admissions,…
The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when…
Algorithms in public services such as child welfare, criminal justice, and education are increasingly being used to make high-stakes decisions about human lives. Drawing upon findings from a two-year ethnography conducted at a child welfare…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
This paper studies algorithmic decision-making under human's strategic behavior, where a decision maker uses an algorithm to make decisions about human agents, and the latter with information about the algorithm may exert effort…
We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the…