Related papers: Improved Paths to Stability for the Stable Marriag…
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality…
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…
The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity…
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 study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…
In a stable matching setting, we consider a query model that allows for an interactive learning algorithm to make precisely one type of query: proposing a matching, the response to which is either that the proposed matching is stable, or a…
We introduce and study a new model that we call the {\em matching model}. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be {\em matched}. There is a finite…
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 say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
For a many-to-one matching model, we study the matchings obtained through the restabilization of stable matchings that had been disrupted by a change in the population. We include a simple representation of the stable matching obtained in…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
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…
To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition…
Let $G$ be a graph and suppose we are given, for each $v \in V(G)$, a strict ordering of the neighbors of $v$. A set of matchings ${\cal M}$ of $G$ is called internally stable if there are no matchings $M,M' \in {\cal M}$ such that an edge…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
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 topic of stable matchings (marriages) in a bipartite graph has become widely popular, starting with the appearance of the classical work by Gale and Shapley. We give a detailed survey on selected known results in this field that…
Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in…
In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…