We consider a variant of socially stable marriage problem where preference lists may be incomplete, may contain ties and may have bounded length. In the real-world application like NRMP and Scottish medical matching scheme such restrictions arise very frequently where a set of agents (man/woman) is very large and providing a complete and strict order preference list is practically infeasible. In presence of ties in preference lists, the most common solution is weakly socially stable matching. It is a fact that in an instance, weakly stable matching can have different sizes. This motivates the problem of finding a maximum cardinality weakly socially stable matching. In this paper, we find maximum size weakly socially stable matching for an instance of Stable Marriage problem with Ties and Incomplete bounded length preference list with Social Stability. The motivation to consider this instance is the known fact, any larger instance of this problem is NP-hard.
Discrete Applied Mathematics 16 (1987) 217-222 North-Holland 217 A FURTHER NOTE ON THE STABLE MATCHING PROBLEM Gabrielle DEMANGE Laboratoire d'Economtrie de l'Ecole Polytechnique, Paris, France David GALE Dept. Of Mathematics, University of California, Berkeley, CA 94720, USA Marilda SOTOMAYOR. Pontifica Universidade Catolica do Rio de Janeiro, Brasil. Existence of a Stable Outcome under Observable Substitutability across Doctors in Many-to-Many Matching with Contracts Keisuke Bandoy Toshiyuki Hiraiz July 1, 2018 Abstract We consider a many-to-many matching problem with contracts between hospitals and doctors. We examine the existence of a stable outcome under observable.