
How hard is it to satisfy (almost) all roommates?
The classical Stable Roommates problem (which is a nonbipartite general...
read it

On (Coalitional) ExchangeStable Matching
We study (coalitional) exchange stability, which Alcalde [Economic Desig...
read it

Stable Noncrossing Matchings
Given a set of n men represented by n points lying on a line, and n wome...
read it

Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters
We continue and extend previous work on the parameterized complexity ana...
read it

On popularitybased random matching markets
Stable matching in a community consisting of N men and N women is a clas...
read it

Characterization of Superstable Matchings
An instance of the superstable matching problem with incomplete lists a...
read it

How good are Popular Matchings?
In this paper, we consider the Hospital Residents problem (HR) and the H...
read it
On the (Parameterized) Complexity of Almost Stable Marriage
In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most reallife situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the "no blocking pair" condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, we find a matching whose size exceeds that of stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k+t+d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is "closest", in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm.
READ FULL TEXT
Comments
There are no comments yet.