Related papers: The Stable Marriage Problem: an Interdisciplinary …
We present a generalization of the marriage problem underlying Hall's famous Marriage Theorem to what we call the Symmetric Marriage Problem, a problem that can be thought of as a special case of Maximal Weighted Bipartite Matching. We show…
In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability…
The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each…
Given $n$ men, $n$ women, and $n$ dogs, each man has an incomplete preference list of women, each woman does an incomplete preference list of dogs, and each dog does an incomplete preference list of men. We understand a family as a triple…
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…
We study a dynamic model of the relationship between two people where the states depend on the "power" in the relationship. We perform a comprehensive analysis of stability of the system, and determine a set of conditions under which stable…
We consider equilibrium one-on-one conversations between neighbors on a circular table, with the goal of assessing the likelihood of a (perhaps) familiar situation: sitting at a table where both of your neighbors are talking to someone…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in 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…
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…
In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the…
Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
Many countries around the world, including Korea, use the school choice lottery system. However, this method has a problem in that many students are assigned to less-preferred schools based on the lottery results. In addition, the task of…
One of the most challenging issues of evolutionary biology concerns speciation, the emergence of new species from an initial one. The huge amount of species found in nature demands a simple and robust mechanism. Yet, no consensus has been…
Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of…
In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in $O(n^2)$ communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each…
The Stable Matching Problem with Couples (SMP-C) is a ubiquitous real-world extension of the stable matching problem (SMP) involving complementarities. Although SMP can be solved in polynomial time, SMP-C is NP-Complete. Hence, it is not…
We give a solution of the following combinatorial problem: "Let one from $n$ married couples in the m\'enage problem (see Problem 1) be a couple of a known mathematician $M$ and his wife. After the ladies are seated at every other chair,…