Related papers: On the Complexity of Robust Stable Marriage
The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…
This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
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…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…
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 study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…
We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
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…
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…
We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among…
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…
We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…
We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it…
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…
In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…
Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for…