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 matching resident doctors to hospitals, to matching students to schools or
more generally to any two-sided market. In the classical stable marriage
problem, both men and women express a strict preference order over the members
of the other sex, in a qualitative way.
The stable marriage problem has a wide variety of practical applications,
ranging from matching resident doctors to hospitals, to matching students to
schools, or more generally to any two-sided market. We consider a useful
variation of the stable marriage problem, where the men and women express their
preferences using a preference list with ties over a subset of the members of
the other sex. Matchings are permitted only with people who appear in these
preference lists. In this setting, we study the problem of finding a stable
matching that marries as many people as possible.