  We consider Stable Marriage with Covering Constraints (SMC): in this variant
of Stable Marriage, we distinguish a subset of women as well as a subset of
men, and we seek a matching with fewest number of blocking pairs that matches
all of the distinguished people. We investigate how a set of natural
parameters, namely the maximum length of preference lists for men and women,
the number of distinguished men and women, and the number of blocking pairs
allowed determine the computational tractability of this problem. Our main
result is a complete complexity trichotomy that, for each choice of the studied
parameters, classifies SMC as polynomial-time solvable, NP-hard and
fixed-parameter tractable, or NP-hard and W[1]-hard. We also classify all cases
of one-sided constraints where only women may be distinguished.
