Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/222076
Authors: 
Cseh, Ágnes
Heeger, Klaus
Year of Publication: 
2020
Series/Report no.: 
CERS-IE Working Papers No. CERS-IE WP - 2020/7
Abstract: 
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability. Besides this, acceptable pairs in the instance can be restricted in their ability of blocking a matching or being part of it, which again generates three categories of restrictions on acceptable pairs. Forced pairs must be in a stable matching, forbidden pairs must not appear in it, and lastly, free pairs cannot block any matching.Our computational complexity study targetsthe existence of a stable solution for each of the three stability definitions, in the presence of each of the three types of restricted pairs. We solve all cases that were still open. As a byproduct, we also derive that the maximum size weakly stable matching problem is hard even in very dense graphs, which may be of independent interest
Subjects: 
stable matchings
restricted edges
complexity
JEL: 
C63
C78
Document Type: 
Working Paper

Files in This Item:
File
Size
448.08 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.