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We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose--accept rounds executed by the Gale--Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at…

In scenarios that require teamwork, we usually have at hand a variety of specific tasks, for which we need to form a team in order to carry out each one. Here we target the problem of matching teams with tasks within the context of…

We define and study a new variant of the secretary problem. Whereas in the classic setting multiple secretaries compete for a single position, we study the case where the secretaries arrive one at a time and are assigned, in an on-line…

We examine the problem of assigning teachers to public schools over time when teachers have tenured positions and can work simultaneously in multiple schools. To do this, we investigate a dynamic many-to-many school choice problem where…

In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…

In this work, we consider a school choice scenario where a student does not exactly know which college is better for her. Although it is hard for a student to obtain an exact preference, she can usually compare specific features of…

In the assignment problem, a set of items must be allocated to unit-demand agents who express ordinal preferences (rankings) over the items. In the assignment problem with priorities, agents with higher priority are entitled to their…

Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley, who…

With the advent of location-based social networks, users can tag their daily activities in different locations through check-ins. These check-in locations signify user preferences for various socio-spatial activities and can be used to…

Recent studies on many-to-one matching markets have explored agents with flexible capacity and truthful preference reporting, focusing on mechanisms that jointly design capacities and select a matching. However, in real-world applications…

We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements,…

We examine a controlled school choice model where students are categorized into different types, and the distribution of these types within a school influences its priority structure. This study provides a general framework that integrates…

In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…

An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…

We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…

It is well known that every stable matching instance $I$ has a rotation poset $R(I)$ that can be computed efficiently and the downsets of $R(I)$ are in one-to-one correspondence with the stable matchings of $I$. Furthermore, for every poset…

The celebrated Efficiency-Adjusted Deferred Acceptance mechanism (EADA) improves the efficiency of the DA algorithm via consented priority violations. Notwithstanding its many merits, we show that EADA can improve only two students when an…

In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion…

Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…