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We study here several variants of the covariates fine balance problem wherewe generalize some of these problems and introduce a number of others. Wepresent here a comprehensive complexity study of the covariates problemsproviding polynomial time algorithms, or a proof of NP-hardness. The polynomialtime algorithms described are mostly combinatorial and rely on network flowtechniques. In addition we present several fixed-parameter tractable resultsfor problems where the number of covariates and the number of levels of eachcovariate are seen as a parameter.

Algorithms and Complexity for Variants of Covariates Fine Balance