  The classical stable marriage problem asks for a matching between a set of
men and a set of women with no blocking pairs, which are pairs formed by a man
and a woman who would both prefer switching from their current status to be
paired up together. When both men and women have strict preferences over the
opposite group, all stable matchings have the same cardinality, and the famous
Gale-Shapley algorithm can be used to find one. Differently, if we allow ties
in the preference lists, finding a stable matching of maximum cardinality is an
NP-hard problem, already when the ties are one-sided, that is, they appear only
in the preferences of one group. For this reason, many researchers have focused
on developing approximation algorithm for this problem.
  In this paper, we give a refined analysis of an approximation algorithm given
by Huang and Telikepalli (IPCO14) for the stable marriage problem with
one-sided ties, which shows an improved 13/9 -approximation factor for the
problem. Interestingly, our analysis is tight.

Data Structures and Algorithms