Related papers: The stable marriage problem with ties and restrict…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
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 consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an…
In this paper, we consider the communication complexity of protocols that compute stable matchings. We work within the context of Gale and Shapley's original stable marriage problem\cite{GS62}: $n$ men and $n$ women each privately hold a…
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 (SM) 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. In the classical formulation, n…
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 study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
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…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
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…
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…
Some aspects of the problem of stable marriage are discussed. There are two distinguished marriage plans: the fully transferable case, where money can be transferred between the participants, and the fully non transferable case where each…
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain…
We consider Stable Marriage with Covering Constraints (SMC): in this variant of Stable Marriage, we distinguish a subset of women as well as a subset of men, and we seek a matching with fewest number of blocking pairs that matches all of…
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…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no…
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…