Related papers: Representing All Stable Matchings by Walking a Max…
In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for…
The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum stable matching becomes…
The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…
We generalize several schedule matching theorems of Baiou-Balinski (Math. Oper. Res., 27 (2002), 485) and Alkan-Gale (J. Econ. Th. 112 (2003), 289) by applying a fixed point method of Fleiner (Math. Oper. Res., 28 (2003), 103). Thanks to a…
We initiate the study of distortion in stable matching. Concretely, we aim to design algorithms that have limited access to the agents' cardinal preferences and compute stable matchings of high quality with respect to some aggregate…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
We present an algorithm that enumerates all the perfect matchings in a given bipartite graph G = (V,E). Our algorithm requires a constant amortized time to visit one perfect matching of G, in contrast to the current fastest algorithm,…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
This paper focuses on two-sided matching where one side (a hospital or firm) is matched to the other side (a doctor or worker) so as to maximize a cardinal objective under general feasibility constraints. In a standard model, even though…
Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of…
I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…
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…
We consider a stochastic matching model with a general compatibility graph, as introduced in \cite{MaiMoy16}. We show that the natural necessary condition of stability of the system is also sufficient for the natural matching policy 'First…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the…
This paper aims to provide insight into stability of collaboration choices in P2P networks. We study networks where exchanges between nodes are driven by the desire to receive the best service available. This is the case for most existing…
Stable marriage of a two-sided market with unit demand is a classic problem that arises in many real-world scenarios. In addition, a unique stable marriage in this market simplifies a host of downstream desiderata. In this paper, we explore…