Related papers: Multidimensional Stable Roommates with Master List
We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…
In this paper, we study the Hospitals / Residents problem with Couples (HRC), where a solution is a stable matching or a report that none exists. We present a novel polynomial-time algorithm that can find a near-feasible stable matching…
For a two-sided ($n$ men/$n$ women) stable matching problem) Gale and Shapley studied a proposal algorithm (men propose/women select, or the other way around), that determines a matching, not blocked by any unmatched pair. Irving used this…
Stable matching, a classical model for two-sided markets, has long been studied with little consideration for how each side's preferences are learned. With the advent of massive online markets powered by data-driven matching platforms, it…
We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we…
The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications.…
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…
We introduce a new and broader formulation of the stable marriage problem (SMP), called the stable polygamy problem (SPP), where multiple individuals from a larger group $L$ of $|L|$ individuals can be matched with a single individual from…
A super-stable matching, which was introduced by Irving, is a solution concept in a variant of the stable matching problem in which the preferences may contain ties. Irving proposed a polynomial-time algorithm for the problem of finding a…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general…
We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over…
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…
Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a…
The dynamical stability of quadruple-star systems has traditionally been treated as a problem involving two `nested' triples which constitute a quadruple. In this novel study, we employed a machine learning algorithm, the multi-layer…
We study the Reaching Stable Marriage via Divorces (DivorceSM) problem of deciding, given a Stable Marriage instance and an initial matching $M$ , whether there exists a stable matching which is reachable from $M$ by divorce operations as…
While the existence of a stable matching for the stable roommates problem possibly with incomplete preference lists (SRI) can be decided in polynomial time, SRI problems with some fairness criteria are intractable. Egalitarian SRI that…