  We consider a variant of socially stable marriage problem where preference
lists may be incomplete, may contain ties and may have bounded length. In real
world application like NRMP and Scottish medical matching scheme such
restrictions arise very frequently where set of agents (man/woman) is very
large and providing a complete and strict order preference list is practically
in-feasible. 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.
