Algorithms and Complexities of Matching Variants in Covariate Balancing

Here, we study several variants of matching problems that arise in covariate balancing. Covariate balancing problems can be viewed as variants of matching, or b-matching, with global side constraints. We present here a comprehensive complexity study of the covariate balancing 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.

Funding: This work was supported by National Science Foundation [Grants CMMI-1760102 and NSF 2112533]; Israel Science Foundation (308/18).

Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2286.