Algorithms and Complexity for Variants of Covariates Fine Balance

TL;DR

This paper explores various covariates fine balance problem variants, providing complexity classifications, polynomial algorithms using network flows, and fixed-parameter tractability results for specific parameters.

Contribution

It offers a comprehensive complexity analysis and introduces polynomial algorithms and fixed-parameter tractability results for covariates fine balance variants.

Findings

Polynomial time algorithms for some variants

NP-hardness proofs for others

Fixed-parameter tractability results

Abstract

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.