Related papers: It's Not Easy Being Three: The Approximability of …
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 Balanced Stable Marriage problem is a central optimization version of the classic Stable Marriage problem. Here, the output cannot be an arbitrary stable matching, but one that balances between the dissatisfaction of the two parties,…
Stable Marriage is a fundamental problem to both computer science and economics. Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage…
We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and…
Motivated by group-project distribution, we introduce and study stable matching under the constraint of applicants needing to share a location to be matched with the same institute, which we call the Location-Restricted Stable Matching…
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…
The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…
The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the…
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…
An instance $I$ of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in $I$ is the exchange of two consecutive vertices in a preference list. A swap can be viewed as…
We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer…
Motivated by the application of Hall's Marriage Theorem in various LP-rounding problems, we introduce a generalization of the classical marriage problem (CMP) that we call the Fractional Marriage Problem. We show that the Fractional…
In the Stable Roommates Problem (SR), a set of $2n$ agents rank one another in a linear order. The goal is to find a matching that is stable: one that has no pair of agents who mutually prefer each other over their assigned partners. We…
In the stable marriage problem (SM), a mechanism that always outputs a stable matching is called a stable mechanism. One of the well-known stable mechanisms is the man-oriented Gale-Shapley algorithm (MGS). MGS has a good property that it…
We study the three-dimensional stable matching problem with cyclic preferences. This model involves three types of agents, with an equal number of agents of each type. The types form a cyclic order such that each agent has a complete…
We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
Given $n$ men, $n$ women, and $n$ dogs, we assume that each man has a complete preference list of women, while each woman does a complete preference list of dogs, and each dog does a complete preference list of men. We study the so-called…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
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…