Related papers: Preference Swaps for the Stable Matching Problem
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley[GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
The pattern matching problem with swaps is to find all occurrences of a pattern in a text while allowing the pattern to swap adjacent symbols. The goal is to design fast matching algorithm that takes advantage of the bit parallelism of…
One of the most natural optimization problems is the k-Set Packing problem, where given a family of sets of size at most k one should select a maximum size subfamily of pairwise disjoint sets. A special case of 3-Set Packing is the well…
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given…
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…
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 matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…
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…
We consider a far generalization of the well-known stable roommates and non-bipartite stable allocation problems. In its setting, one is given a finite non-bipartite graph $G=(V,E)$ with nonnegative integer edge capacities $b(e)\in{\mathbb…
As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for computing $\ell$ disjoint stable matchings with minimum total…
We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of…
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 Problem (SMP) has been extremely discussed in the literature and it is useful to a number of real-world applications. We propose a generalized version of the SMP in which numbers of the matching groups are different as…
We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a…
Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…
Given a set of $n$ men represented by $n$ points lying on a line, and $n$ women represented by $n$ points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his/her acceptable…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
Genome rearrangements are events in which large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, based on finding the minimum number of rearrangements to…
In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e.,…
We study the many-to-many bipartite matching problem in the presence of preferences where ties, as well as lower quotas, may appear on both sides of the bipartition. The input is a bipartite graph $G=(A \cup B, E)$, where each vertex in $A…