  We study here several variants of the covariates fine balance problem where
we generalize some of these problems and introduce a number of others. We
present here a comprehensive complexity study of the covariates problems
providing polynomial time algorithms, or a proof of NP-hardness. The polynomial
time algorithms described are mostly combinatorial and rely on network flow
techniques. In addition we present several fixed-parameter tractable results
for problems where the number of covariates and the number of levels of each
covariate are seen as a parameter.
