  This paper develops an integer programming approach on two-sided many-to-one
matching by investigating stable integral matchings of a fictitious continuum
market induced from the original matching market. Each stable integral matching
of the continuum market corresponds to a stable matching of the original
matching market. We show that a stable matching exists in the original matching
market when firms' preference profile satisfies a unimodularity condition. Our
result indicates that a stable matching is guaranteed to exist with various
forms of complementary preferences.
