TY - JOUR
T1 - The stable marriage problem with ties and restricted edges
AU - Cseh, Ágnes
AU - Heeger, Klaus
N1 - Funding Information:
The authors were supported by the Cooperation of Excellences, Hungary Grant (KEP-6/2019), the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2019), its János Bolyai Research Fellowship, Hungary, OTKA grant K128611, the DFG, Germany Research Training Group 2434 “Facets of Complexity”, and COST Action CA16228 European Network for Game Theory.
Publisher Copyright:
© 2020 The Author(s)
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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 targets the 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.
AB - 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 targets the 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.
KW - Complexity
KW - Restricted edges
KW - Stable matchings
UR - http://www.scopus.com/inward/record.url?scp=85080148283&partnerID=8YFLogxK
U2 - 10.1016/j.disopt.2020.100571
DO - 10.1016/j.disopt.2020.100571
M3 - Article
AN - SCOPUS:85080148283
SN - 1572-5286
VL - 36
JO - Discrete Optimization
JF - Discrete Optimization
M1 - 100571
ER -