  While there exists a rich array of matrix column subset selection problem
(CSSP) algorithms for use with interpolative and CUR-type decompositions, their
use can often become prohibitive as the size of the input matrix increases. In
an effort to address these issues, the authors in
\cite{emelianenko2024adaptive} developed a general framework that pairs a
column-partitioning routine with a column-selection algorithm. Two of the four
algorithms presented in that work paired the Centroidal Voronoi Orthogonal
Decomposition (\textsf{CVOD}) and an adaptive variant (\textsf{adaptCVOD}) with
the Discrete Empirical Interpolation Method (\textsf{DEIM})
\cite{sorensen2016deim}. In this work, we extend this framework and pair the
\textsf{CVOD}-type algorithms with any CSSP algorithm that returns linearly
independent columns. Our results include detailed error bounds for the
solutions provided by these paired algorithms, as well as expressions that
explicitly characterize how the quality of the selected column partition
affects the resulting CSSP solution.
